refactor: symbolic flow support

Massive boost.
Hard to quantify everything.

We're almost batch/inverse design!
- All units are now correct at realization (they weren't before), and
  several operations were simply wrong.
- Near-optimal "flow narrowing", which globally minimizes `DataChanged`
  even in the face of complex internal property dependencies.
- Sockets now cache `FlowKind` output themselves, with invalidation
  provided for and flow narrowing happening before it even enters the
  node flow.
- New FlowKind (`PreviewsFlow`) w/plotting, 3D, efficient caching, with
  all previewed nodes already adapted.
- Drastically prettified plot output, due to seaborn theme integration,
  dict-like data transport w/better labelling, etc. .
- Deep, reliable unit/unit dimension deduction and arithmetic for
  `PhysicalType` deduction using dimensional analysis on arbitrary
  expression operations.
- Fourier transform w/Nyquist limits as boundary conditions (preserving original shift).
- Vastly improved math node operation checks.
- Symbol constant node, integrating domain presumptions.
- Flow integration for ExprSocket, including for flow-dynamic capabilities and color.
- Viewer node got a big update, incl. live-display of sympy types (even
  matrix) and a few Tidy3D types, as well as seperating deeper options
  into a "Debug" mode
- Deeply streamlined symbolic flow, including
- **Differentiable Box structure**, w/generic lazy parameter support - only the start!

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/__init__.py

@@ -46,10 +46,11 @@ from .flow_kinds import (
 	ArrayFlow,
 	CapabilitiesFlow,
 	FlowKind,
-	InfoFlow,
-	RangeFlow,
 	FuncFlow,
+	InfoFlow,
 	ParamsFlow,
+	PreviewsFlow,
+	RangeFlow,
 	ScalingMode,
 	ValueFlow,
 )
@@ -118,6 +119,7 @@ __all__ = [
 	'CapabilitiesFlow',
 	'FlowKind',
 	'InfoFlow',
+	'PreviewsFlow',
 	'RangeFlow',
 	'FuncFlow',
 	'ParamsFlow',

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/bl_socket_types.py

@@ -230,7 +230,6 @@ class BLSocketType(enum.StrEnum):
 		return {
 			# Blender
 			# Basic
-			BLST.Bool: MT.Bool,
 			# Float
 			BLST.Float: MT.Real,
 			BLST.FloatAngle: MT.Real,

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_events.py

@@ -35,10 +35,6 @@ class FlowEvent(enum.StrEnum):
 			This event can lock a subset of the node tree graph.
 		DisableLock: Indicates that the node/socket should disable locking.
 			This event can unlock part of a locked subgraph.
-		ShowPreview: Indicates that the node/socket should enable its primary preview.
-			This should be used if a more specific preview-esque event doesn't apply.
-		ShowPlot: Indicates that the node/socket should enable its plotted preview.
-			This should generally be used if the node is rendering to an image, for viewing through the Blender image editor.
 		LinkChanged: Indicates that a link to a node/socket was added/removed.
 			Is translated to `DataChanged` on sockets before propagation.
 		DataChanged: Indicates that data flowing through a node/socket was altered.
@@ -50,15 +46,12 @@ class FlowEvent(enum.StrEnum):
 	EnableLock = enum.auto()
 	DisableLock = enum.auto()
 
-	# Preview Events
-	ShowPreview = enum.auto()
-	ShowPlot = enum.auto()
-
 	# Data Events
 	LinkChanged = enum.auto()
 	DataChanged = enum.auto()
 
 	# Non-Triggered Events
+	ShowPlot = enum.auto()
 	OutputRequested = enum.auto()
 
 	# Properties
@@ -79,9 +72,6 @@ class FlowEvent(enum.StrEnum):
 			# Lock Events
 			FlowEvent.EnableLock: 'input',
 			FlowEvent.DisableLock: 'input',
-			# Preview Events
-			FlowEvent.ShowPreview: 'input',
-			FlowEvent.ShowPlot: 'input',
 			# Data Events
 			FlowEvent.LinkChanged: 'output',
 			FlowEvent.DataChanged: 'output',

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/__init__.py

@@ -21,6 +21,7 @@ from .info import InfoFlow
 from .lazy_func import FuncFlow
 from .lazy_range import RangeFlow, ScalingMode
 from .params import ParamsFlow
+from .previews import PreviewsFlow
 from .value import ValueFlow
 
 __all__ = [
@@ -32,5 +33,6 @@ __all__ = [
 	'ScalingMode',
 	'FuncFlow',
 	'ParamsFlow',
+	'PreviewsFlow',
 	'ValueFlow',
 ]

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/array.py

@@ -21,7 +21,6 @@ import typing as typ
 import jaxtyping as jtyp
 import numpy as np
 import sympy as sp
-import sympy.physics.units as spu
 
 from blender_maxwell.utils import extra_sympy_units as spux
 from blender_maxwell.utils import logger
@@ -117,13 +116,19 @@ class ArrayFlow:
 			new_unit: An (optional) new unit to scale the result to.
 		"""
 		# Compile JAX-Compatible Rescale Function
+		## -> Generally, we try to keep things nice and rational.
+		## -> However, too-large ints may cause JAX to suffer from an overflow.
+		## -> Jax works in 32-bit domain by default, for performance.
+		## -> While it can be adjusted, that would also have tradeoffs.
+		## -> Instead, a quick .n() turns all the big-ints into floats.
+		## -> Not super satisfying, but hey - it's all numerical anyway.
 		a = self.mathtype.sp_symbol_a
 		rescale_expr = (
 			spux.scale_to_unit(rescale_func(a * self.unit), new_unit)
 			if self.unit is not None
 			else rescale_func(a)
 		)
-		_rescale_func = sp.lambdify(a, rescale_expr, 'jax')
+		_rescale_func = sp.lambdify(a, rescale_expr.n(), 'jax')
 		values = _rescale_func(self.values)
 
 		# Return ArrayFlow

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/capabilities.py

@@ -24,9 +24,30 @@ from .flow_kinds import FlowKind
 
 @dataclasses.dataclass(frozen=True, kw_only=True)
 class CapabilitiesFlow:
+	"""Describes the compatibility relationship between two sockets, which governs whether they can be linked.
+
+	By default, socket type (which may impact color) and active `FlowKind` (which impacts shape) must match in order for two sockets to be compatible.
+
+	However, in many cases, more expressiveness beyond this naive constraint is desirable.
+	For example:
+
+	- Allow any socket to be linked to the `ViewerNode` input.
+	- Allow only _angled_ sources to be passed as inputs to the input-derived `BlochBoundCond` node.
+	- Allow `Expr:Value` to connect to `Expr:Func`, but only allow the converse if `PhysicalType`, `MathType`, and `Size` match.
+
+	In many cases, it's desirable
+
+	"""
+
+	# Defaults
 	socket_type: SocketType
 	active_kind: FlowKind
+
+	# Relationships
 	allow_out_to_in: dict[FlowKind, FlowKind] = dataclasses.field(default_factory=dict)
+	allow_out_to_in_if_matches: dict[FlowKind, (FlowKind, bool)] = dataclasses.field(
+		default_factory=dict
+	)
 
 	is_universal: bool = False
 
@@ -41,12 +62,19 @@ class CapabilitiesFlow:
 
 	def is_compatible_with(self, other: typ.Self) -> bool:
 		return other.is_universal or (
-			self.socket_type == other.socket_type
+			self.socket_type is other.socket_type
 			and (
-				self.active_kind == other.active_kind
+				self.active_kind is other.active_kind
 				or (
 					other.active_kind in other.allow_out_to_in
-					and self.active_kind == other.allow_out_to_in[other.active_kind]
+					and self.active_kind is other.allow_out_to_in[other.active_kind]
+				)
+				or (
+					other.active_kind in other.allow_out_to_in_if_matches
+					and self.active_kind
+					is other.allow_out_to_in_if_matches[other.active_kind][0]
+					and self.allow_out_to_in_if_matches[other.active_kind][1]
+					== other.allow_out_to_in_if_matches[other.active_kind][1]
 				)
 			)
 			# == Constraint

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/flow_kinds.py

@@ -15,6 +15,7 @@
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
 import enum
+import functools
 import typing as typ
 
 from blender_maxwell.utils import extra_sympy_units as spux
@@ -23,6 +24,17 @@ from blender_maxwell.utils.staticproperty import staticproperty
 
 log = logger.get(__name__)
 
+_PROPERTY_NAMES = {
+	'capabilities',
+	'previews',
+	'value',
+	'array',
+	'lazy_range',
+	'lazy_func',
+	'params',
+	'info',
+}
+
 
 class FlowKind(enum.StrEnum):
 	"""Defines a kind of data that can flow between nodes.
@@ -50,14 +62,15 @@ class FlowKind(enum.StrEnum):
 	"""
 
 	Capabilities = enum.auto()
+	Previews = enum.auto()
 
 	# Values
 	Value = enum.auto()  ## 'value'
 	Array = enum.auto()  ## 'array'
 
 	# Lazy
-	Func = enum.auto()  ## 'lazy_func'
 	Range = enum.auto()  ## 'lazy_range'
+	Func = enum.auto()  ## 'lazy_func'
 
 	# Auxiliary
 	Params = enum.auto()  ## 'params'
@@ -70,12 +83,13 @@ class FlowKind(enum.StrEnum):
 	def to_name(v: typ.Self) -> str:
 		return {
 			FlowKind.Capabilities: 'Capabilities',
+			FlowKind.Previews: 'Previews',
 			# Values
 			FlowKind.Value: 'Value',
 			FlowKind.Array: 'Array',
 			# Lazy
-			FlowKind.Range: 'Range',
 			FlowKind.Func: 'Func',
+			FlowKind.Range: 'Range',
 			# Auxiliary
 			FlowKind.Params: 'Params',
 			FlowKind.Info: 'Info',
@@ -88,6 +102,48 @@ class FlowKind(enum.StrEnum):
 	####################
 	# - Static Properties
 	####################
+	@staticproperty
+	def property_names() -> set[str]:
+		"""Set of strings for (socket) properties associated with a `FlowKind`.
+
+		Usable for optimized O(1) lookup, to check whether a property name can be converted to a `FlowKind`.
+		To actually retrieve the `FlowKind` from one of these names, use `FlowKind.from_property_name()`.
+		"""
+		return _PROPERTY_NAMES
+
+	@functools.cache
+	@staticmethod
+	def from_property_name(prop_name: str) -> typ.Self:
+		"""Retrieve the `FlowKind` associated with a particular property name.
+
+		Parameters:
+			prop_name: The name of the property.
+				**Must** be a string defined in `FlowKind.property_names`.
+		"""
+		return {
+			'capabilities': FlowKind.Capabilities,
+			'previews': FlowKind.Previews,
+			'value': FlowKind.Value,
+			'array': FlowKind.Array,
+			'lazy_range': FlowKind.Range,
+			'lazy_func': FlowKind.Func,
+			'params': FlowKind.Params,
+			'info': FlowKind.Info,
+		}[prop_name]
+
+	@functools.cached_property
+	def property_name(self) -> typ.Self:
+		"""Retrieve the `FlowKind` associated with a particular property name.
+
+		Parameters:
+			prop_name: The name of the property.
+				**Must** be a string defined in `FlowKind.property_names`.
+		"""
+		return {
+			FlowKind.from_property_name(prop_name): prop_name
+			for prop_name in FlowKind.property_names
+		}[self]
+
 	@staticproperty
 	def active_kinds() -> list[typ.Self]:
 		"""Return a list of `FlowKind`s that are able to be considered "active".
@@ -121,6 +177,7 @@ class FlowKind(enum.StrEnum):
 	####################
 	# - Class Methods
 	####################
+	## TODO: Remove this (only events uses it).
 	@classmethod
 	def scale_to_unit_system(
 		cls,

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/info.py

@@ -93,7 +93,7 @@ class InfoFlow:
 			return list(self.dims.keys())[idx]
 		return None
 
-	def dim_by_name(self, dim_name: str) -> int:
+	def dim_by_name(self, dim_name: str, optional: bool = False) -> int | None:
 		"""The integer axis occupied by the dimension.
 
 		Can be used to index `.shape` of the represented raw array.
@@ -102,6 +102,9 @@ class InfoFlow:
 		if len(dims_with_name) == 1:
 			return dims_with_name[0]
 
+		if optional:
+			return None
+
 		msg = f'Dim name {dim_name} not found in InfoFlow (or >1 found)'
 		raise ValueError(msg)
 
@@ -127,14 +130,15 @@ class InfoFlow:
 		return False
 
 	def is_idx_uniform(self, dim: sim_symbols.SimSymbol) -> bool:
-		"""Whether the (int) dim has explicitly uniform indexing.
+		"""Whether the given dim has explicitly uniform indexing.
 
 		This is needed primarily to check whether a Fourier Transform can be meaningfully performed on the data over the dimension's axis.
 
 		In practice, we've decided that only `RangeFlow` really truly _guarantees_ uniform indexing.
 		While `ArrayFlow` may be uniform in practice, it's a very expensive to check, and it's far better to enforce that the user perform that check and opt for a `RangeFlow` instead, at the time of dimension definition.
 		"""
-		return isinstance(self.dims[dim], RangeFlow) and self.dims[dim].scaling == 'lin'
+		dim_idx = self.dims[dim]
+		return isinstance(dim_idx, RangeFlow) and dim_idx.scaling == 'lin'
 
 	def dim_axis(self, dim: sim_symbols.SimSymbol) -> int:
 		"""The integer axis occupied by the dimension.
@@ -194,7 +198,7 @@ class InfoFlow:
 		return {
 			dim.name_pretty: {
 				'length': str(len(dim_idx)) if dim_idx is not None else '∞',
-				'mathtype': dim.mathtype.label_pretty,
+				'mathtype': dim.mathtype_size_label,
 				'unit': dim.unit_label,
 			}
 			for dim, dim_idx in self.dims.items()
@@ -315,27 +319,23 @@ class InfoFlow:
 		op: typ.Callable[[spux.SympyExpr, spux.SympyExpr], spux.SympyExpr],
 		unit_op: typ.Callable[[spux.SympyExpr, spux.SympyExpr], spux.SympyExpr],
 	) -> spux.SympyExpr:
-		if self.dims == other.dims:
-			sym_name = sim_symbols.SimSymbolName.Expr
-			expr = op(self.output.sp_symbol_phy, other.output.sp_symbol_phy)
-			unit_expr = unit_op(self.output.unit_factor, other.output.unit_factor)
+		sym_name = sim_symbols.SimSymbolName.Expr
+		expr = op(self.output.sp_symbol_phy, other.output.sp_symbol_phy)
+		unit_expr = unit_op(self.output.unit_factor, other.output.unit_factor)
+		## TODO: Handle per-cell matrix units?
 
-			return InfoFlow(
-				dims=self.dims,
-				output=sim_symbols.SimSymbol.from_expr(sym_name, expr, unit_expr),
-				pinned_values=self.pinned_values,
-			)
-
-		msg = f'InfoFlow: operate_output cannot be used when dimensions are not identical ({self.dims} | {other.dims}).'
-		raise ValueError(msg)
+		return InfoFlow(
+			dims=self.dims,
+			output=sim_symbols.SimSymbol.from_expr(sym_name, expr, unit_expr),
+			pinned_values=self.pinned_values,
+		)
 
 	####################
 	# - Operations: Fold
 	####################
 	def fold_last_input(self):
 		"""Fold the last input dimension into the output."""
-		last_key = list(self.dims.keys())[-1]
-		last_idx = list(self.dims.values())[-1]
+		last_idx = self.dims[self.last_dim]
 
 		rows = self.output.rows
 		cols = self.output.cols
@@ -351,7 +351,9 @@ class InfoFlow:
 
 		return InfoFlow(
 			dims={
-				dim: dim_idx for dim, dim_idx in self.dims.items() if dim != last_key
+				dim: dim_idx
+				for dim, dim_idx in self.dims.items()
+				if dim != self.last_dim
 			},
 			output=new_output,
 			pinned_values=self.pinned_values,

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/lazy_func.py

@@ -20,10 +20,14 @@ import typing as typ
 from types import MappingProxyType
 
 import jax
+import jaxtyping as jtyp
 
 from blender_maxwell.utils import extra_sympy_units as spux
 from blender_maxwell.utils import logger, sim_symbols
 
+from .array import ArrayFlow
+from .info import InfoFlow
+from .lazy_range import RangeFlow
 from .params import ParamsFlow
 
 log = logger.get(__name__)
@@ -314,14 +318,66 @@ class FuncFlow:
 	) -> typ.Self:
 		if self.supports_jax:
 			return self.func_jax(
-				*params.scaled_func_args(self.func_args, symbol_values),
-				*params.scaled_func_kwargs(self.func_args, symbol_values),
+				*params.scaled_func_args(symbol_values),
+				**params.scaled_func_kwargs(symbol_values),
 			)
 		return self.func(
-			*params.scaled_func_args(self.func_kwargs, symbol_values),
-			*params.scaled_func_kwargs(self.func_kwargs, symbol_values),
+			*params.scaled_func_args(symbol_values),
+			**params.scaled_func_kwargs(symbol_values),
 		)
 
+	def realize_as_data(
+		self,
+		info: InfoFlow,
+		params: ParamsFlow,
+		symbol_values: dict[sim_symbols.SimSymbol, spux.SympyExpr] = MappingProxyType(
+			{}
+		),
+	) -> dict[sim_symbols.SimSymbol, jtyp.Inexact[jtyp.Array, '...']]:
+		"""Realize as an ordered dictionary mapping each realized `self.dims` entry, with the last entry containing all output data as mapped from the `self.output`."""
+		data = {}
+		for dim, dim_idx in info.dims.items():
+			# Continuous Index (*)
+			## -> Continuous dimensions **must** be symbols in ParamsFlow.
+			## -> ...Since the output data shape is parameterized by it.
+			if info.has_idx_cont(dim):
+				if dim in params.symbols:
+					# Scalar Realization
+					## -> Conform & cast the sympy expr to the dimension.
+					if isinstance(symbol_values[dim], spux.SympyType):
+						data |= {dim: dim.scale(symbol_values[dim])}
+
+					# Array Realization
+					## -> Scale the array to the dimension's unit & get values.
+					if isinstance(symbol_values[dim], RangeFlow | ArrayFlow):
+						data |= {
+							dim: symbol_values[dim].rescale_to_unit(dim.unit).values
+						}
+				else:
+					msg = f'ParamsFlow does not contain dimension symbol {dim} (info={info}, params={params})'
+					raise RuntimeError(msg)
+
+			# Discrete Index (Q|R)
+			## -> Realize ArrayFlow|RangeFlow
+			if info.has_idx_discrete(dim):
+				data |= {dim: dim_idx.values}
+
+			# Labelled Index (Z)
+			## -> Passthrough the string labels.
+			if info.has_idx_labels(dim):
+				data |= {dim: dim_idx}
+
+		return data | {info.output: self.realize(params, symbol_values=symbol_values)}
+
+		# return {
+		# dim: (
+		# dim_idx
+		# if info.has_idx_cont(dim) or info.has_idx_labels(dim)
+		# else ??
+		# )
+		# for dim, dim_idx in self.dims
+		# } | {info.output: output_data}
+
 	####################
 	# - Composition Operations
 	####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/lazy_range.py

@@ -218,9 +218,6 @@ class RangeFlow:
 		)
 		return combined_mathtype
 
-	####################
-	# - Methods
-	####################
 	@property
 	def ideal_midpoint(self) -> spux.SympyExpr:
 		return (self.stop + self.start) / 2
@@ -229,6 +226,41 @@ class RangeFlow:
 	def ideal_range(self) -> spux.SympyExpr:
 		return self.stop - self.start
 
+	####################
+	# - Methods
+	####################
+	@staticmethod
+	def try_from_array(
+		array: ArrayFlow, uniformity_tolerance: float = 1e-9
+	) -> ArrayFlow | typ.Self:
+		"""Attempt to create a RangeFlow from a potentially uniform ArrayFlow, falling back to that same ArrayFlow if it isn't uniform.
+
+		For functional (ex. Fourier Transform) and memory-related reasons, it's important to be explicit about the uniformity of index elements.
+		For this reason, only `RangeFlow`s are considered uniform - `ArrayFlow`s are not, as it's expensive to check in a hot loop, while `RangeFlow`s have this property simply by existing.
+
+		Of course, real-world data sources may not come in a memory-efficient configuration, even if they are, in fact, monotonically increasing with uniform finite differences.
+		This method bridges that gap: If (within `uniformity_tolerance`) **all** finite differences are the same, then the `ArrayFlow` can be converted losslessly to a `RangeFlow.
+		**Otherwise**, the `ArrayFlow` is returned verbatim.
+
+		Notes:
+			A few other checks are also performed to guarantee the semantics of a resulting `RangeFlow`: The array must be sorted, there must be at least two values, and the first value must be strictly smaller than the last value.
+		"""
+		diffs = jnp.diff(array.values)
+
+		if (
+			jnp.all(jnp.abs(diffs - diffs[0]) < uniformity_tolerance)
+			and len(array.values) > 2  # noqa: PLR2004
+			and array.values[0] < array.values[-1]
+			and array.is_sorted
+		):
+			return RangeFlow(
+				start=sp.S(array.values[0]),
+				stop=sp.S(array.values[-1]),
+				steps=len(array.values),
+				unit=array.unit,
+			)
+		return array
+
 	def rescale(
 		self, rescale_func, reverse: bool = False, new_unit: spux.Unit | None = None
 	) -> typ.Self:
@@ -612,8 +644,8 @@ class RangeFlow:
 				symbols=self.symbols,
 			)
 		return RangeFlow(
-			start=self.start * unit,
-			stop=self.stop * unit,
+			start=self.start,
+			stop=self.stop,
 			steps=self.steps,
 			scaling=self.scaling,
 			unit=unit,

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/params.py

@@ -31,8 +31,6 @@ from .expr_info import ExprInfo
 from .flow_kinds import FlowKind
 from .lazy_range import RangeFlow
 
-# from .info import InfoFlow
-
 log = logger.get(__name__)
 
 
@@ -44,11 +42,18 @@ class ParamsFlow:
 		All symbols valid for use in the expression.
 	"""
 
+	arg_targets: list[sim_symbols.SimSymbol] = dataclasses.field(default_factory=list)
+	kwarg_targets: list[str, sim_symbols.SimSymbol] = dataclasses.field(
+		default_factory=dict
+	)
+
 	func_args: list[spux.SympyExpr] = dataclasses.field(default_factory=list)
 	func_kwargs: dict[str, spux.SympyExpr] = dataclasses.field(default_factory=dict)
 
 	symbols: frozenset[sim_symbols.SimSymbol] = frozenset()
 
+	is_differentiable: bool = False
+
 	####################
 	# - Symbols
 	####################
@@ -76,8 +81,9 @@ class ParamsFlow:
 	####################
 	# - JIT'ed Callables for Numerical Function Arguments
 	####################
+	@functools.cached_property
 	def func_args_n(
-		self, target_syms: list[sim_symbols.SimSymbol]
+		self,
 	) -> list[
 		typ.Callable[
 			[int | float | complex | jtyp.Inexact[jtyp.Array, '...'], ...],
@@ -86,15 +92,12 @@ class ParamsFlow:
 	]:
 		"""Callable functions for evaluating each `self.func_args` entry numerically.
 
-		Before simplification, each `self.func_args` entry will be conformed to the corresponding (by-index) `SimSymbol` in `target_syms`.
+		Before simplification, each `self.func_args` entry will be conformed to the corresponding (by-index) `SimSymbol` in `self.target_syms`.
 
 		Notes:
 			Before using any `sympy` expressions as arguments to the returned callablees, they **must** be fully conformed and scaled to the corresponding `self.symbols` entry using that entry's `SimSymbol.scale()` method.
 
 			This ensures conformance to the `SimSymbol` properties (like units), as well as adherance to a numerical type identity compatible with `sp.lambdify()`.
-
-		Parameters:
-			target_syms: `SimSymbol`s describing how a particular `ParamsFlow` function argument should be scaled when performing a purely numerical insertion.
 		"""
 		return [
 			sp.lambdify(
@@ -102,11 +105,14 @@ class ParamsFlow:
 				target_sym.conform(func_arg, strip_unit=True),
 				'jax',
 			)
-			for func_arg, target_sym in zip(self.func_args, target_syms, strict=True)
+			for func_arg, target_sym in zip(
+				self.func_args, self.arg_targets, strict=True
+			)
 		]
 
+	@functools.cached_property
 	def func_kwargs_n(
-		self, target_syms: dict[str, sim_symbols.SimSymbol]
+		self,
 	) -> dict[
 		str,
 		typ.Callable[
@@ -120,12 +126,12 @@ class ParamsFlow:
 		This ensures conformance to the `SimSymbol` properties, as well as adherance to a numerical type identity compatible with `sp.lambdify()`
 		"""
 		return {
-			func_arg_key: sp.lambdify(
+			key: sp.lambdify(
 				self.sorted_sp_symbols,
-				target_syms[func_arg_key].scale(func_arg),
+				self.kwarg_targets[key].conform(func_arg, strip_unit=True),
 				'jax',
 			)
-			for func_arg_key, func_arg in self.func_kwargs.items()
+			for key, func_arg in self.func_kwargs.items()
 		}
 
 	####################
@@ -182,7 +188,6 @@ class ParamsFlow:
 	####################
 	def scaled_func_args(
 		self,
-		target_syms: list[sim_symbols.SimSymbol] = (),
 		symbol_values: dict[sim_symbols.SimSymbol, spux.SympyExpr] = MappingProxyType(
 			{}
 		),
@@ -196,32 +201,24 @@ class ParamsFlow:
 		1. Conform Symbols: Arbitrary `sympy` expressions passed as `symbol_values` must first be conformed to match the ex. units of `SimSymbol`s found in `self.symbols`, before they can be used.
 
 		2. Conform Function Arguments: Arbitrary `sympy` expressions encoded in `self.func_args` must, **after** inserting the conformed numerical symbols, themselves be conformed to the expected ex. units of the function that they are to be used within.
-			**`ParamsFlow` doesn't contain information about the `SimSymbol`s that `self.func_args` are expected to conform to** (on purpose).
-			Therefore, the user is required to pass a `target_syms` with identical length to `self.func_args`, describing the `SimSymbol`s to conform the function arguments to.
 
 		Our implementation attempts to utilize simple, powerful primitives to accomplish this in roughly three steps:
 
 		1. **Realize Symbols**: Particular passed symbolic values `symbol_values`, which are arbitrary `sympy` expressions, are conformed to the definitions in `self.symbols` (ex. to match units), then cast to numerical values (pure Python / jax array).
 
-		2. **Lazy Function Arguments**: Stored function arguments `self.func_args`, which are arbitrary `sympy` expressions, are conformed to the definitions in `target_syms` (ex. to match units), then cast to numerical values (pure Python / jax array).
+		2. **Lazy Function Arguments**: Stored function arguments `self.func_args`, which are arbitrary `sympy` expressions, are conformed to the definitions in `self.target_syms` (ex. to match units), then cast to numerical values (pure Python / jax array).
 			_Technically, this happens as part of `self.func_args_n`._
 
 		3. **Numerical Evaluation**: The numerical values for each symbol are passed as parameters to each (callable) element of `self.func_args_n`, which produces a correct numerical value for each function argument.
 
 		Parameters:
-			target_syms: `SimSymbol`s describing how the function arguments returned by this method are intended to be used.
-				**Generally**, the parallel `FuncFlow.func_args` should be inserted here, and guarantees correct results when this output is inserted into `FuncFlow.func(...)`.
-			symbol_values: Particular values for all symbols in `self.symbols`, which will be conformed and used to compute the function arguments (before they are conformed to `target_syms`).
+			symbol_values: Particular values for all symbols in `self.symbols`, which will be conformed and used to compute the function arguments (before they are conformed to `self.target_syms`).
 		"""
 		realized_symbols = list(self.realize_symbols(symbol_values).values())
-		return [
-			func_arg_n(*realized_symbols)
-			for func_arg_n in self.func_args_n(target_syms)
-		]
+		return [func_arg_n(*realized_symbols) for func_arg_n in self.func_args_n]
 
 	def scaled_func_kwargs(
 		self,
-		target_syms: list[sim_symbols.SimSymbol] = (),
 		symbol_values: dict[spux.Symbol, spux.SympyExpr] = MappingProxyType({}),
 	) -> dict[
 		str, int | float | Fraction | float | complex | jtyp.Shaped[jtyp.Array, '...']
@@ -233,7 +230,7 @@ class ParamsFlow:
 		realized_symbols = self.realize_symbols(symbol_values)
 		return {
 			func_arg_name: func_arg_n(**realized_symbols)
-			for func_arg_name, func_arg_n in self.func_kwargs_n(target_syms).items()
+			for func_arg_name, func_arg_n in self.func_kwargs_n.items()
 		}
 
 	####################
@@ -249,27 +246,41 @@ class ParamsFlow:
 		The next composed function will receive a tuple of two arrays, instead of just one, allowing binary operations to occur.
 		"""
 		return ParamsFlow(
+			arg_targets=self.arg_targets + other.arg_targets,
+			kwarg_targets=self.kwarg_targets | other.kwarg_targets,
 			func_args=self.func_args + other.func_args,
 			func_kwargs=self.func_kwargs | other.func_kwargs,
 			symbols=self.symbols | other.symbols,
+			is_differentiable=self.is_differentiable & other.is_differentiable,
 		)
 
 	def compose_within(
 		self,
+		enclosing_arg_targets: list[sim_symbols.SimSymbol] = (),
+		enclosing_kwarg_targets: list[sim_symbols.SimSymbol] = (),
 		enclosing_func_args: list[spux.SympyExpr] = (),
 		enclosing_func_kwargs: dict[str, spux.SympyExpr] = MappingProxyType({}),
-		enclosing_symbols: frozenset[spux.Symbol] = frozenset(),
+		enclosing_symbols: frozenset[sim_symbols.SimSymbol] = frozenset(),
+		enclosing_is_differentiable: bool = False,
 	) -> typ.Self:
 		return ParamsFlow(
+			arg_targets=self.arg_targets + list(enclosing_arg_targets),
+			kwarg_targets=self.kwarg_targets | dict(enclosing_kwarg_targets),
 			func_args=self.func_args + list(enclosing_func_args),
 			func_kwargs=self.func_kwargs | dict(enclosing_func_kwargs),
 			symbols=self.symbols | enclosing_symbols,
+			is_differentiable=(
+				self.is_differentiable
+				if not enclosing_symbols
+				else (self.is_differentiable & enclosing_is_differentiable)
+			),
 		)
 
 	####################
 	# - Generate ExprSocketDef
 	####################
-	def sym_expr_infos(self, use_range: bool = False) -> dict[str, ExprInfo]:
+	@functools.cached_property
+	def sym_expr_infos(self) -> dict[str, ExprInfo]:
 		"""Generate keyword arguments for defining all `ExprSocket`s needed to realize all `self.symbols`.
 
 		Many nodes need actual data, and as such, they require that the user select actual values for any symbols in the `ParamsFlow`.
@@ -284,28 +295,16 @@ class ParamsFlow:
 			}
 			```
 
-		Parameters:
-			info: The InfoFlow associated with the `Expr` being realized.
-				Each symbol in `self.symbols` **must** have an associated same-named dimension in `info`.
-			use_range: Causes the
-
 		The `ExprInfo`s can be directly defererenced `**expr_info`)
 		"""
 		for sym in self.sorted_symbols:
-			if use_range and sym.mathtype is spux.MathType.Complex:
-				msg = 'No support for complex range in ExprInfo'
-				raise NotImplementedError(msg)
-			if use_range and (sym.rows > 1 or sym.cols > 1):
-				msg = 'No support for non-scalar elements of range in ExprInfo'
-				raise NotImplementedError(msg)
 			if sym.rows > 3 or sym.cols > 1:
 				msg = 'No support for >Vec3 / Matrix values in ExprInfo'
 				raise NotImplementedError(msg)
 
 		return {
-			sym.name: {
-				'active_kind': FlowKind.Value if not use_range else FlowKind.Range,
-				'default_steps': 50,
+			sym: {
+				'default_steps': 25,
 			}
 			| sym.expr_info
 			for sym in self.sorted_symbols

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/previews.py

@@ -0,0 +1,193 @@
+# blender_maxwell
+# Copyright (C) 2024 blender_maxwell Project Contributors
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Affero General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Affero General Public License for more details.
+#
+# You should have received a copy of the GNU Affero General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+import typing as typ
+
+import bpy
+import pydantic as pyd
+
+from blender_maxwell.utils import logger
+
+IMAGE_AREA_TYPE = 'IMAGE_EDITOR'
+IMAGE_SPACE_TYPE = 'IMAGE_EDITOR'
+
+log = logger.get(__name__)
+
+####################
+# - Global Collection Handling
+####################
+MANAGED_COLLECTION_NAME = 'BLMaxwell'
+PREVIEW_COLLECTION_NAME = 'BLMaxwell Visible'
+
+
+def collection(collection_name: str, view_layer_exclude: bool) -> bpy.types.Collection:
+	# Init the "Managed Collection"
+	# Ensure Collection exists (and is in the Scene collection)
+	if collection_name not in bpy.data.collections:
+		collection = bpy.data.collections.new(collection_name)
+		bpy.context.scene.collection.children.link(collection)
+	else:
+		collection = bpy.data.collections[collection_name]
+
+	## Ensure synced View Layer exclusion
+	if (
+		layer_collection := bpy.context.view_layer.layer_collection.children[
+			collection_name
+		]
+	).exclude != view_layer_exclude:
+		layer_collection.exclude = view_layer_exclude
+
+	return collection
+
+
+def managed_collection() -> bpy.types.Collection:
+	return collection(MANAGED_COLLECTION_NAME, view_layer_exclude=True)
+
+
+def preview_collection() -> bpy.types.Collection:
+	return collection(PREVIEW_COLLECTION_NAME, view_layer_exclude=False)
+
+
+####################
+# - Global Collection Handling
+####################
+class PreviewsFlow(pyd.BaseModel):
+	"""Represents global references to previewable entries."""
+
+	model_config = pyd.ConfigDict(frozen=True)
+
+	bl_image_name: str | None = None
+	bl_object_names: frozenset[str] = frozenset()
+
+	####################
+	# - Operations
+	####################
+	def __or__(self, other: typ.Self) -> typ.Self:
+		return PreviewsFlow(
+			bl_image_name=other.bl_image_name,
+			bl_object_names=self.bl_object_names | other.bl_object_names,
+		)
+
+	####################
+	# - Image Editor UX
+	####################
+	@classmethod
+	def preview_area(cls) -> bpy.types.Area | None:
+		"""Deduces a Blender UI area that can be used for image preview.
+
+		Returns:
+			A Blender UI area, if an appropriate one is visible; else `None`,
+		"""
+		valid_areas = [
+			area for area in bpy.context.screen.areas if area.type == IMAGE_AREA_TYPE
+		]
+		if valid_areas:
+			return valid_areas[0]
+		return None
+
+	@classmethod
+	def preview_space(cls) -> bpy.types.SpaceProperties | None:
+		"""Deduces a Blender UI space, within `self.preview_area`, that can be used for image preview.
+
+		Returns:
+			A Blender UI space within `self.preview_area`, if it isn't None; else, `None`.
+		"""
+		preview_area = cls.preview_area()
+		if preview_area is not None:
+			valid_spaces = [
+				space for space in preview_area.spaces if space.type == IMAGE_SPACE_TYPE
+			]
+			if valid_spaces:
+				return valid_spaces[0]
+			return None
+		return None
+
+	####################
+	# - Preview Plot
+	####################
+	@classmethod
+	def hide_image_preview(cls) -> None:
+		"""Show all image previews in the first available image editor.
+
+		If no image editors are visible, then nothing happens.
+		"""
+		preview_space = cls.preview_space()
+		if preview_space is not None and preview_space.image is not None:
+			cls.preview_space().image = None
+
+	def update_image_preview(self) -> None:
+		"""Show the image preview in the first available image editor.
+
+		If no image editors are visible, then nothing happens.
+		"""
+		preview_space = self.preview_space()
+		if self.bl_image_name is not None:
+			bl_image = bpy.data.images.get(self.bl_image_name)
+
+			# Replace Preview Space Image
+			if (
+				bl_image is not None
+				and preview_space is not None
+				and preview_space.image is not bl_image
+			):
+				preview_space.image = bl_image
+
+			# Remove Image
+			if bl_image is None and preview_space.image is not None:
+				preview_space.image = None
+		elif preview_space.image is not None:
+			preview_space.image = None
+
+	####################
+	# - Preview Objects
+	####################
+	@classmethod
+	def hide_bl_object_previews(cls) -> None:
+		"""Hide all previewed Blender objects."""
+		for bl_object_name in [obj.name for obj in preview_collection().objects]:
+			bl_object = bpy.data.objects.get(bl_object_name)
+			if bl_object is not None and bl_object.name in preview_collection().objects:
+				preview_collection().objects.unlink(bl_object)
+
+	def update_bl_object_previews(self) -> frozenset[str]:
+		"""Preview objects that need previewing and unpreview objects that need unpreviewing.
+
+		Designed to utilize the least possible amount of operations to achieve a desired set of previewed objects, from the current set of previewed objects.
+		"""
+		# Deduce Change in Previewed Objects
+		## -> Examine the preview collection for all currently previewed names.
+		## -> Preview names that shouldn't exist should be added.
+		## -> Preview names that should exist should be removed.
+		previewed_bl_objects = {obj.name for obj in preview_collection().objects}
+		bl_objects_to_remove = previewed_bl_objects - self.bl_object_names
+		bl_objects_to_add = self.bl_object_names - previewed_bl_objects
+
+		# Remove Previews
+		## -> Never presume that bl_object is already defined.
+		for bl_object_name in bl_objects_to_remove:
+			bl_object = bpy.data.objects.get(bl_object_name)
+			if bl_object is not None and bl_object.name in preview_collection().objects:
+				preview_collection().objects.unlink(bl_object)
+
+		# Add Previews
+		## -> Never presume that bl_object is already defined.
+		for bl_object_name in bl_objects_to_add:
+			bl_object = bpy.data.objects.get(bl_object_name)
+			if (
+				bl_object is not None
+				and bl_object.name not in preview_collection().objects
+			):
+				preview_collection().objects.link(bl_object)

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/node_types.py

@@ -38,6 +38,7 @@ class NodeType(blender_type_enum.BlenderTypeEnum):
 	Scene = enum.auto()
 	## Inputs / Constants
 	ExprConstant = enum.auto()
+	SymbolConstant = enum.auto()
 	ScientificConstant = enum.auto()
 	UnitSystemConstant = enum.auto()
 	BlenderConstant = enum.auto()

src/blender_maxwell/node_trees/maxwell_sim_nodes/node_tree.py

@@ -19,7 +19,7 @@ import typing as typ
 
 import bpy
 
-from blender_maxwell.utils import logger
+from blender_maxwell.utils import logger, serialize
 
 from . import contracts as ct
 from .managed_objs.managed_bl_image import ManagedBLImage

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/extract_data.py

@@ -86,11 +86,13 @@ def extract_info(monitor_data, monitor_attr: str) -> ct.InfoFlow | None:  # noqa
 	if xarr is None:
 		return None
 
-	def mk_idx_array(axis: str) -> ct.ArrayFlow:
-		return ct.ArrayFlow(
-			values=xarr.get_index(axis).values,
-			unit=symbols[axis].unit,
-			is_sorted=True,
+	def mk_idx_array(axis: str) -> ct.RangeFlow | ct.ArrayFlow:
+		return ct.RangeFlow.try_from_array(
+			ct.ArrayFlow(
+				values=xarr.get_index(axis).values,
+				unit=symbols[axis].unit,
+				is_sorted=True,
+			)
 		)
 
 	# Compute InfoFlow from XArray

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/filter_math.py

@@ -124,12 +124,12 @@ class FilterOperation(enum.StrEnum):
 	# - Computed Properties
 	####################
 	@property
-	def func_args(self) -> list[spux.MathType]:
+	def func_args(self) -> list[sim_symbols.SimSymbol]:
 		FO = FilterOperation
 		return {
 			# Pin
-			FO.Pin: [spux.MathType.Integer],
-			FO.PinIdx: [spux.MathType.Integer],
+			FO.Pin: [sim_symbols.idx(None)],
+			FO.PinIdx: [sim_symbols.idx(None)],
 		}.get(self, [])
 
 	####################
@@ -155,10 +155,10 @@ class FilterOperation(enum.StrEnum):
 		match self:
 			# Slice
 			case FO.Slice:
-				return [dim for dim in info.dims if not dim.has_idx_labels(dim)]
+				return [dim for dim in info.dims if not info.has_idx_labels(dim)]
 
 			case FO.SliceIdx:
-				return [dim for dim in info.dims if not dim.has_idx_labels(dim)]
+				return [dim for dim in info.dims if not info.has_idx_labels(dim)]
 
 			# Pin
 			case FO.PinLen1:
@@ -272,10 +272,15 @@ class FilterMathNode(base.MaxwellSimNode):
 	# - Properties: Expr InfoFlow
 	####################
 	@events.on_value_changed(
+		# Trigger
 		socket_name={'Expr'},
+		# Loaded
 		input_sockets={'Expr'},
 		input_socket_kinds={'Expr': ct.FlowKind.Info},
 		input_sockets_optional={'Expr': True},
+		# Flow
+		## -> See docs in TransformMathNode
+		stop_propagation=True,
 	)
 	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
 		has_info = not ct.FlowSignal.check(input_sockets['Expr'])
@@ -593,11 +598,17 @@ class FilterMathNode(base.MaxwellSimNode):
 					pinned_value, require_sorted=True
 				)
 
-				return params.compose_within(enclosing_func_args=[nearest_idx_to_value])
+				return params.compose_within(
+					enclosing_arg_targets=[sim_symbols.idx(None)],
+					enclosing_func_args=[sp.S(nearest_idx_to_value)],
+				)
 
 			# Pin by-Index
 			if props['operation'] is FilterOperation.PinIdx and has_pinned_axis:
-				return params.compose_within(enclosing_func_args=[pinned_axis])
+				return params.compose_within(
+					enclosing_arg_targets=[sim_symbols.idx(None)],
+					enclosing_func_args=[sp.S(pinned_axis)],
+				)
 
 			return params
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/map_math.py

@@ -236,7 +236,7 @@ class MapOperation(enum.StrEnum):
 			MO.Sinc: lambda expr: sp.sinc(expr),
 			# By Vector
 			# Vector -> Number
-			MO.Norm2: lambda expr: sp.sqrt(expr.T @ expr),
+			MO.Norm2: lambda expr: sp.sqrt(expr.T @ expr)[0],
 			# By Matrix
 			# Matrix -> Number
 			MO.Det: lambda expr: sp.det(expr),
@@ -467,10 +467,15 @@ class MapMathNode(base.MaxwellSimNode):
 	# - Properties
 	####################
 	@events.on_value_changed(
+		# Trigger
 		socket_name={'Expr'},
+		# Loaded
 		input_sockets={'Expr'},
 		input_socket_kinds={'Expr': ct.FlowKind.Info},
 		input_sockets_optional={'Expr': True},
+		# Flow
+		## -> See docs in TransformMathNode
+		stop_propagation=True,
 	)
 	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
 		has_info = not ct.FlowSignal.check(input_sockets['Expr'])

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/operate_math.py

@@ -210,7 +210,7 @@ class BinaryOperation(enum.StrEnum):
 				):
 					ops += [BO.Cross]
 
-				return ops
+				return ops_el_el + ops
 
 			## Vector | Matrix
 			case (1, 2):
@@ -374,10 +374,15 @@ class OperateMathNode(base.MaxwellSimNode):
 	# - Properties
 	####################
 	@events.on_value_changed(
+		# Trigger
 		socket_name={'Expr L', 'Expr R'},
+		# Loaded
 		input_sockets={'Expr L', 'Expr R'},
 		input_socket_kinds={'Expr L': ct.FlowKind.Info, 'Expr R': ct.FlowKind.Info},
 		input_sockets_optional={'Expr L': True, 'Expr R': True},
+		# Flow
+		## -> See docs in TransformMathNode
+		stop_propagation=True,
 	)
 	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
 		has_info_l = not ct.FlowSignal.check(input_sockets['Expr L'])

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/transform_math.py

@@ -17,7 +17,6 @@
 """Declares `TransformMathNode`."""
 
 import enum
-import functools
 import typing as typ
 
 import bpy
@@ -39,13 +38,25 @@ log = logger.get(__name__)
 # - Operation Enum
 ####################
 class TransformOperation(enum.StrEnum):
-	"""Valid operations for the `MapMathNode`.
+	"""Valid operations for the `TransformMathNode`.
 
 	Attributes:
-		FreqToVacWL: Transform frequency axes to be indexed by vacuum wavelength.
-		VacWLToFreq: Transform vacuum wavelength axes to be indexed by frequency.
-		FFT: Compute the fourier transform of the input expression.
-		InvFFT: Compute the inverse fourier transform of the input expression.
+		FreqToVacWL: Transform an frequency dimension to vacuum wavelength.
+		VacWLToFreq: Transform a vacuum wavelength dimension to frequency.
+		ConvertIdxUnit: Convert the unit of a dimension to a compatible unit.
+		SetIdxUnit: Set all properties of a dimension.
+		FirstColToFirstIdx: Extract the first data column and set the first dimension's index array equal to it.
+			**For 2D integer-indexed data only**.
+
+		IntDimToComplex: Fold a last length-2 integer dimension into the output, transforming it from a real-like type to complex type.
+		DimToVec: Fold the last dimension into the scalar output, creating a vector output type.
+		DimsToMat: Fold the last two dimensions into the scalar output, creating a matrix output type.
+		FT: Compute the 1D fourier transform along a dimension.
+			New dimensional bounds are computing using the Nyquist Limit.
+			For higher dimensions, simply repeat along more dimensions.
+		InvFT1D: Compute the inverse 1D fourier transform along a dimension.
+			New dimensional bounds are computing using the Nyquist Limit.
+			For higher dimensions, simply repeat along more dimensions.
 	"""
 
 	# Covariant Transform
@@ -79,7 +90,7 @@ class TransformOperation(enum.StrEnum):
 			TO.VacWLToFreq: 'λᵥ → 𝑓',
 			TO.ConvertIdxUnit: 'Convert Dim',
 			TO.SetIdxUnit: 'Set Dim',
-			TO.FirstColToFirstIdx: '1st Col → Dim',
+			TO.FirstColToFirstIdx: '1st Col → 1st Dim',
 			# Fold
 			TO.IntDimToComplex: '→ ℂ',
 			TO.DimToVec: '→ Vector',
@@ -87,10 +98,14 @@ class TransformOperation(enum.StrEnum):
 			## TODO: Vector to new last-dim integer
 			## TODO: Matrix to two last-dim integers
 			# Fourier
-			TO.FT1D: '→ 𝑓',
-			TO.InvFT1D: '𝑓 →',
+			TO.FT1D: 'FT',
+			TO.InvFT1D: 'iFT',
 		}[value]
 
+	@property
+	def name(self) -> str:
+		return TransformOperation.to_name(self)
+
 	@staticmethod
 	def to_icon(_: typ.Self) -> str:
 		return ''
@@ -108,49 +123,32 @@ class TransformOperation(enum.StrEnum):
 	####################
 	# - Methods
 	####################
-	@property
-	def num_dim_inputs(self) -> None:
-		"""The number of axes that should be passed as inputs to `func_jax` when evaluating it.
-
-		Especially useful for `ParamFlow`, when deciding whether to pass an integer-axis argument based on a user-selected dimension.
-		"""
-		TO = TransformOperation
-		return {
-			# Covariant Transform
-			TO.FreqToVacWL: 1,
-			TO.VacWLToFreq: 1,
-			TO.ConvertIdxUnit: 1,
-			TO.SetIdxUnit: 1,
-			TO.FirstColToFirstIdx: 0,
-			# Fold
-			TO.IntDimToComplex: 0,
-			TO.DimToVec: 0,
-			TO.DimsToMat: 0,
-			## TODO: Vector to new last-dim integer
-			## TODO: Matrix to two last-dim integers
-			# Fourier
-			TO.FT1D: 1,
-			TO.InvFT1D: 1,
-		}[self]
-
 	def valid_dims(self, info: ct.InfoFlow) -> list[typ.Self]:
 		TO = TransformOperation
 		match self:
-			case TO.FreqToVacWL | TO.FT1D:
+			case TO.FreqToVacWL:
 				return [
 					dim
 					for dim in info.dims
 					if dim.physical_type is spux.PhysicalType.Freq
 				]
 
-			case TO.VacWLToFreq | TO.InvFT1D:
+			case TO.VacWLToFreq:
 				return [
 					dim
 					for dim in info.dims
 					if dim.physical_type is spux.PhysicalType.Length
 				]
 
-			case TO.ConvertIdxUnit | TO.SetIdxUnit:
+			case TO.ConvertIdxUnit:
+				return [
+					dim
+					for dim in info.dims
+					if not info.has_idx_labels(dim)
+					and spux.PhysicalType.from_unit(dim.unit, optional=True) is not None
+				]
+
+			case TO.SetIdxUnit:
 				return [dim for dim in info.dims if not info.has_idx_labels(dim)]
 
 			## ColDimToComplex: Implicit Last Dimension
@@ -198,13 +196,11 @@ class TransformOperation(enum.StrEnum):
 		# Fold
 		## Last Dim -> Complex
 		if (
-			info.dims
-			# Output is Int|Rat|Real
+			len(info.dims) >= 1
 			and (
 				info.output.mathtype
 				in [spux.MathType.Integer, spux.MathType.Rational, spux.MathType.Real]
 			)
-			# Last Axis is Integer of Length 2
 			and info.last_dim.mathtype is spux.MathType.Integer
 			and info.has_idx_labels(info.last_dim)
 			and len(info.dims[info.last_dim]) == 2  # noqa: PLR2004
@@ -231,14 +227,13 @@ class TransformOperation(enum.StrEnum):
 	####################
 	# - Function Properties
 	####################
-	@functools.cached_property
-	def jax_func(self):
+	def jax_func(self, axis: int | None = None):
 		TO = TransformOperation
 		return {
 			# Covariant Transform
 			## -> Freq <-> WL is a rescale (noop) AND flip (not noop).
-			TO.FreqToVacWL: lambda expr, axis: jnp.flip(expr, axis=axis),
-			TO.VacWLToFreq: lambda expr, axis: jnp.flip(expr, axis=axis),
+			TO.FreqToVacWL: lambda expr: jnp.flip(expr, axis=axis),
+			TO.VacWLToFreq: lambda expr: jnp.flip(expr, axis=axis),
 			TO.ConvertIdxUnit: lambda expr: expr,
 			TO.SetIdxUnit: lambda expr: expr,
 			TO.FirstColToFirstIdx: lambda expr: jnp.delete(expr, 0, axis=1),
@@ -250,8 +245,8 @@ class TransformOperation(enum.StrEnum):
 			TO.DimToVec: lambda expr: expr,
 			TO.DimsToMat: lambda expr: expr,
 			# Fourier
-			TO.FT1D: lambda expr, axis: jnp.fft(expr, axis=axis),
-			TO.InvFT1D: lambda expr, axis: jnp.ifft(expr, axis=axis),
+			TO.FT1D: lambda expr: jnp.fft(expr, axis=axis),
+			TO.InvFT1D: lambda expr: jnp.ifft(expr, axis=axis),
 		}[self]
 
 	def transform_info(
@@ -268,25 +263,21 @@ class TransformOperation(enum.StrEnum):
 			# Covariant Transform
 			TO.FreqToVacWL: lambda: info.replace_dim(
 				(f_dim := dim),
-				[
-					sim_symbols.wl(unit),
-					info.dims[f_dim].rescale(
-						lambda el: sci_constants.vac_speed_of_light / el,
-						reverse=True,
-						new_unit=unit,
-					),
-				],
+				sim_symbols.wl(unit),
+				info.dims[f_dim].rescale(
+					lambda el: sci_constants.vac_speed_of_light / el,
+					reverse=True,
+					new_unit=unit,
+				),
 			),
 			TO.VacWLToFreq: lambda: info.replace_dim(
 				(wl_dim := dim),
-				[
-					sim_symbols.freq(unit),
-					info.dims[wl_dim].rescale(
-						lambda el: sci_constants.vac_speed_of_light / el,
-						reverse=True,
-						new_unit=unit,
-					),
-				],
+				sim_symbols.freq(unit),
+				info.dims[wl_dim].rescale(
+					lambda el: sci_constants.vac_speed_of_light / el,
+					reverse=True,
+					new_unit=unit,
+				),
 			),
 			TO.ConvertIdxUnit: lambda: info.replace_dim(
 				dim,
@@ -300,7 +291,9 @@ class TransformOperation(enum.StrEnum):
 			TO.SetIdxUnit: lambda: info.replace_dim(
 				dim,
 				dim.update(
-					sym_name=new_dim_name, physical_type=physical_type, unit=unit
+					sym_name=new_dim_name,
+					physical_type=physical_type,
+					unit=unit,
 				),
 				(
 					info.dims[dim].correct_unit(unit)
@@ -311,10 +304,12 @@ class TransformOperation(enum.StrEnum):
 			TO.FirstColToFirstIdx: lambda: info.replace_dim(
 				info.first_dim,
 				info.first_dim.update(
+					sym_name=new_dim_name,
 					mathtype=spux.MathType.from_jax_array(data_col),
+					physical_type=physical_type,
 					unit=unit,
 				),
-				ct.ArrayFlow(values=data_col, unit=unit),
+				ct.RangeFlow.try_from_array(ct.ArrayFlow(values=data_col, unit=unit)),
 			).slice_dim(info.last_dim, (1, len(info.dims[info.last_dim]), 1)),
 			# Fold
 			TO.IntDimToComplex: lambda: info.delete_dim(info.last_dim).update_output(
@@ -380,10 +375,18 @@ class TransformMathNode(base.MaxwellSimNode):
 	# - Properties: Expr InfoFlow
 	####################
 	@events.on_value_changed(
+		# Trigger
 		socket_name={'Expr'},
+		# Loaded
 		input_sockets={'Expr'},
 		input_socket_kinds={'Expr': ct.FlowKind.Info},
 		input_sockets_optional={'Expr': True},
+		# Flow
+		## -> Expr wants to emit DataChanged, which is usually fine.
+		## -> However, this node sets `expr_info`, which causes DC to emit.
+		## -> One action should emit one DataChanged pipe.
+		## -> Therefore, defer responsibility for DataChanged to self.expr_info.
+		stop_propagation=True,
 	)
 	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
 		has_info = not ct.FlowSignal.check(input_sockets['Expr'])
@@ -440,7 +443,7 @@ class TransformMathNode(base.MaxwellSimNode):
 	@bl_cache.cached_bl_property(depends_on={'expr_info', 'active_dim'})
 	def dim(self) -> sim_symbols.SimSymbol | None:
 		if self.expr_info is not None and self.active_dim is not None:
-			return self.expr_info.dim_by_name(self.active_dim)
+			return self.expr_info.dim_by_name(self.active_dim, optional=True)
 		return None
 
 	####################
@@ -454,48 +457,52 @@ class TransformMathNode(base.MaxwellSimNode):
 	)
 	active_new_unit: enum.StrEnum = bl_cache.BLField(
 		enum_cb=lambda self, _: self.search_units(),
-		cb_depends_on={'dim', 'new_physical_type'},
+		cb_depends_on={'dim', 'new_physical_type', 'operation'},
 	)
 
 	def search_units(self) -> list[ct.BLEnumElement]:
-		if self.dim is not None:
-			if self.dim.physical_type is not spux.PhysicalType.NonPhysical:
-				unit_name = sp.sstr(self.dim.unit)
-				return [
-					(
-						sp.sstr(unit),
-						spux.sp_to_str(unit),
-						sp.sstr(unit),
-						'',
-						0,
-					)
-					for unit in self.dim.physical_type.valid_units
-				]
-
-			if self.dim.unit is not None:
-				unit_name = sp.sstr(self.dim.unit)
-				return [
-					(
-						unit_name,
-						spux.sp_to_str(self.dim.unit),
-						unit_name,
-						'',
-						0,
-					)
-				]
-		if self.new_physical_type is not spux.PhysicalType.NonPhysical:
-			return [
-				(
-					sp.sstr(unit),
-					spux.sp_to_str(unit),
-					sp.sstr(unit),
-					'',
-					i,
+		TO = TransformOperation
+		match self.operation:
+			# Covariant Transform
+			case TO.ConvertIdxUnit if self.dim is not None:
+				physical_type = spux.PhysicalType.from_unit(
+					self.dim.unit, optional=True
 				)
-				for i, unit in enumerate(self.new_physical_type.valid_units)
-			]
+				if physical_type is not None:
+					valid_units = physical_type.valid_units
+				else:
+					valid_units = []
 
-		return []
+			case TO.FreqToVacWL if self.dim is not None:
+				valid_units = spux.PhysicalType.Length.valid_units
+
+			case TO.VacWLToFreq if self.dim is not None:
+				valid_units = spux.PhysicalType.Freq.valid_units
+
+			case TO.SetIdxUnit if (
+				self.dim is not None
+				and self.new_physical_type is not spux.PhysicalType.NonPhysical
+			):
+				valid_units = self.new_physical_type.valid_units
+
+			case TO.FirstColToFirstIdx if (
+				self.new_physical_type is not spux.PhysicalType.NonPhysical
+			):
+				valid_units = self.new_physical_type.valid_units
+
+			case _:
+				valid_units = []
+
+		return [
+			(
+				sp.sstr(unit),
+				spux.sp_to_str(unit),
+				sp.sstr(unit),
+				'',
+				i,
+			)
+			for i, unit in enumerate(valid_units)
+		]
 
 	@bl_cache.cached_bl_property(depends_on={'active_new_unit'})
 	def new_unit(self) -> spux.Unit:
@@ -507,30 +514,85 @@ class TransformMathNode(base.MaxwellSimNode):
 	####################
 	# - UI
 	####################
-	def draw_label(self):
-		if self.operation is not None:
-			return 'T: ' + TransformOperation.to_name(self.operation)
+	@bl_cache.cached_bl_property(depends_on={'new_unit'})
+	def new_unit_str(self) -> str:
+		if self.new_unit is None:
+			return ''
+		return spux.sp_to_str(self.new_unit)
 
-		return self.bl_label
+	def draw_label(self):
+		TO = TransformOperation
+		match self.operation:
+			case TO.FreqToVacWL if self.dim is not None:
+				return f'T: {self.dim.name_pretty} | 𝑓 → {self.new_unit_str}'
+
+			case TO.VacWLToFreq if self.dim is not None:
+				return f'T: {self.dim.name_pretty} | λᵥ → {self.new_unit_str}'
+
+			case TO.ConvertIdxUnit if self.dim is not None:
+				return f'T: {self.dim.name_pretty} → {self.new_unit_str}'
+
+			case TO.SetIdxUnit if self.dim is not None:
+				return f'T: {self.dim.name_pretty} → {self.new_name.name_pretty} | {self.new_unit_str}'
+
+			case (
+				TO.IntDimToComplex
+				| TO.DimToVec
+				| TO.DimsToMat
+			) if self.expr_info is not None and self.expr_info.dims:
+				return f'T: {self.expr_info.last_dim.name_unit_label} {self.operation.name}'
+
+			case TO.FT1D if self.dim is not None:
+				return f'T: FT[{self.dim.name_unit_label}]'
+
+			case TO.InvFT1D if self.dim is not None:
+				return f'T: iFT[{self.dim.name_unit_label}]'
+
+			case _:
+				if self.operation is not None:
+					return f'T: {self.operation.name}'
+				return self.bl_label
 
 	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout) -> None:
 		layout.prop(self, self.blfields['operation'], text='')
 
-		if self.operation is not None and self.operation.num_dim_inputs == 1:
-			TO = TransformOperation
-			layout.prop(self, self.blfields['active_dim'], text='')
+		TO = TransformOperation
+		match self.operation:
+			case TO.ConvertIdxUnit:
+				row = layout.row(align=True)
+				row.prop(self, self.blfields['active_dim'], text='')
+				row.prop(self, self.blfields['active_new_unit'], text='')
 
-			if self.operation in [TO.ConvertIdxUnit, TO.SetIdxUnit]:
+			case TO.FreqToVacWL:
+				row = layout.row(align=True)
+				row.prop(self, self.blfields['active_dim'], text='')
+				row.prop(self, self.blfields['active_new_unit'], text='')
+
+			case TO.VacWLToFreq:
+				row = layout.row(align=True)
+				row.prop(self, self.blfields['active_dim'], text='')
+				row.prop(self, self.blfields['active_new_unit'], text='')
+
+			case TO.SetIdxUnit:
+				row = layout.row(align=True)
+				row.prop(self, self.blfields['active_dim'], text='')
+				row.prop(self, self.blfields['new_name'], text='')
+
+				row = layout.row(align=True)
+				row.prop(self, self.blfields['new_physical_type'], text='')
+				row.prop(self, self.blfields['active_new_unit'], text='')
+
+			case TO.FirstColToFirstIdx:
 				col = layout.column(align=True)
-				if self.operation is TransformOperation.ConvertIdxUnit:
-					col.prop(self, self.blfields['active_new_unit'], text='')
+				row = col.row(align=True)
+				row.prop(self, self.blfields['new_name'], text='')
+				row.prop(self, self.blfields['active_new_unit'], text='')
 
-				if self.operation is TransformOperation.SetIdxUnit:
-					col.prop(self, self.blfields['new_physical_type'], text='')
+				row = col.row(align=True)
+				row.prop(self, self.blfields['new_physical_type'], text='')
 
-					row = col.row(align=True)
-					row.prop(self, self.blfields['new_name'], text='')
-					row.prop(self, self.blfields['active_new_unit'], text='')
+			case TO.FT1D | TO.InvFT1D:
+				layout.prop(self, self.blfields['active_dim'], text='')
 
 	####################
 	# - Compute: Func / Array
@@ -538,23 +600,43 @@ class TransformMathNode(base.MaxwellSimNode):
 	@events.computes_output_socket(
 		'Expr',
 		kind=ct.FlowKind.Func,
-		props={'operation'},
+		# Loaded
+		props={'operation', 'dim'},
 		input_sockets={'Expr'},
 		input_socket_kinds={
-			'Expr': ct.FlowKind.Func,
+			'Expr': {ct.FlowKind.Func, ct.FlowKind.Info},
 		},
 	)
 	def compute_func(self, props, input_sockets) -> ct.FuncFlow | ct.FlowSignal:
+		"""Transform the input `InfoFlow` depending on the transform operation."""
+		TO = TransformOperation
 		operation = props['operation']
-		lazy_func = input_sockets['Expr']
+		lazy_func = input_sockets['Expr'][ct.FlowKind.Func]
+		info = input_sockets['Expr'][ct.FlowKind.Info]
 
+		has_info = not ct.FlowSignal.check(info)
 		has_lazy_func = not ct.FlowSignal.check(lazy_func)
 
-		if has_lazy_func and operation is not None:
-			return lazy_func.compose_within(
-				operation.jax_func,
-				supports_jax=True,
-			)
+		if operation is not None and has_lazy_func and has_info:
+			# Retrieve Properties
+			dim = props['dim']
+
+			# Match Pattern by Operation
+			match operation:
+				case TO.FreqToVacWL | TO.VacWLToFreq | TO.FT1D | TO.InvFT1D:
+					if dim is not None and info.has_idx_discrete(dim):
+						return lazy_func.compose_within(
+							operation.jax_func(axis=info.dim_axis(dim)),
+							supports_jax=True,
+						)
+					return ct.FlowSignal.FlowPending
+
+				case _:
+					return lazy_func.compose_within(
+						operation.jax_func(),
+						supports_jax=True,
+					)
+
 		return ct.FlowSignal.FlowPending
 
 	####################
@@ -563,54 +645,101 @@ class TransformMathNode(base.MaxwellSimNode):
 	@events.computes_output_socket(
 		'Expr',
 		kind=ct.FlowKind.Info,
+		# Loaded
 		props={'operation', 'dim', 'new_name', 'new_unit', 'new_physical_type'},
 		input_sockets={'Expr'},
 		input_socket_kinds={
 			'Expr': {ct.FlowKind.Func, ct.FlowKind.Info, ct.FlowKind.Params}
 		},
 	)
-	def compute_info(
+	def compute_info(  # noqa: PLR0911
 		self, props: dict, input_sockets: dict
 	) -> ct.InfoFlow | typ.Literal[ct.FlowSignal.FlowPending]:
+		"""Transform the input `InfoFlow` depending on the transform operation."""
+		TO = TransformOperation
 		operation = props['operation']
 		info = input_sockets['Expr'][ct.FlowKind.Info]
 
 		has_info = not ct.FlowSignal.check(info)
-
-		dim = props['dim']
-		new_name = props['new_name']
-		new_unit = props['new_unit']
-		new_physical_type = props['new_physical_type']
 		if has_info and operation is not None:
-			# First Column to First Index
-			## -> We have to evaluate the lazy function at this point.
-			## -> It's the only way to get at the column data.
-			if operation is TransformOperation.FirstColToFirstIdx:
-				lazy_func = input_sockets['Expr'][ct.FlowKind.Func]
-				params = input_sockets['Expr'][ct.FlowKind.Params]
-				has_lazy_func = not ct.FlowSignal.check(lazy_func)
-				has_params = not ct.FlowSignal.check(lazy_func)
+			# Retrieve Properties
+			dim = props['dim']
+			new_name = props['new_name']
+			new_unit = props['new_unit']
+			new_physical_type = props['new_physical_type']
 
-				if has_lazy_func and has_params and not params.symbols:
+			# Retrieve Expression Data
+			lazy_func = input_sockets['Expr'][ct.FlowKind.Func]
+			params = input_sockets['Expr'][ct.FlowKind.Params]
+
+			has_lazy_func = not ct.FlowSignal.check(lazy_func)
+			has_params = not ct.FlowSignal.check(lazy_func)
+
+			# Match Pattern by Operation
+			match operation:
+				# Covariant Transform
+				## -> Needs: Dim, Unit
+				case TO.ConvertIdxUnit if dim is not None and new_unit is not None:
+					physical_type = spux.PhysicalType.from_unit(dim.unit, optional=True)
+					if (
+						physical_type is not None
+						and new_unit in physical_type.valid_units
+					):
+						return operation.transform_info(info, dim=dim, unit=new_unit)
+					return ct.FlowSignal.FlowPending
+
+				case TO.FreqToVacWL if dim is not None and new_unit is not None and new_unit in spux.PhysicalType.Length.valid_units:
+					return operation.transform_info(info, dim=dim, unit=new_unit)
+
+				case TO.VacWLToFreq if dim is not None and new_unit is not None and new_unit in spux.PhysicalType.Freq.valid_units:
+					return operation.transform_info(info, dim=dim, unit=new_unit)
+
+				## -> Needs: Dim, Unit, Physical Type
+				case TO.SetIdxUnit if (
+					dim is not None
+					and new_physical_type is not None
+					and new_unit in new_physical_type.valid_units
+				):
+					return operation.transform_info(
+						info,
+						dim=dim,
+						new_dim_name=new_name,
+						unit=new_unit,
+						physical_type=new_physical_type,
+					)
+
+				## -> Needs: Data Column, Name, Unit, Physical Type
+				## -> We have to evaluate the lazy function at this point.
+				## -> It's the only way to get at the column's data.
+				case TO.FirstColToFirstIdx if (
+					has_lazy_func
+					and has_params
+					and not params.symbols
+					and new_name is not None
+					and new_physical_type is not None
+					and new_unit in new_physical_type.valid_units
+				):
 					data = lazy_func.realize(params)
-					if data.shape is not None and len(data.shape) == 2:
+					if data.shape is not None and len(data.shape) == 2:  # noqa: PLR2004
 						data_col = data[:, 0]
-						return operation.transform_info(info, data_col=data_col)
-				return ct.FlowSignal.FlowPending
+						return operation.transform_info(
+							info,
+							new_dim_name=new_name,
+							data_col=data_col,
+							unit=new_unit,
+							physical_type=new_physical_type,
+						)
 
-			# Check Not-Yet-Updated Dimension
-			## - Operation changes before dimensions.
-			## - If InfoFlow is requested in this interim, big problem.
-			if dim is None and operation.num_dim_inputs > 0:
-				return ct.FlowSignal.FlowPending
+				# Fold
+				## -> Needs: Nothing
+				case TO.IntDimToComplex | TO.DimToVec | TO.DimsToMat:
+					return operation.transform_info(info)
+
+				# Fourier
+				## -> Needs: Dimension
+				case TO.FT1D | TO.InvFT1D if dim is not None:
+					return operation.transform_info(info, dim=dim)
 
-			return operation.transform_info(
-				info,
-				dim=dim,
-				new_dim_name=new_name,
-				unit=new_unit,
-				physical_type=new_physical_type,
-			)
 		return ct.FlowSignal.FlowPending
 
 	####################
@@ -619,30 +748,19 @@ class TransformMathNode(base.MaxwellSimNode):
 	@events.computes_output_socket(
 		'Expr',
 		kind=ct.FlowKind.Params,
-		props={'operation', 'dim'},
+		# Loaded
+		props={'operation'},
 		input_sockets={'Expr'},
-		input_socket_kinds={'Expr': {ct.FlowKind.Params, ct.FlowKind.Info}},
+		input_socket_kinds={'Expr': ct.FlowKind.Params},
 	)
 	def compute_params(self, props, input_sockets) -> ct.ParamsFlow | ct.FlowSignal:
-		info = input_sockets['Expr'][ct.FlowKind.Info]
-		params = input_sockets['Expr'][ct.FlowKind.Params]
-
-		has_info = not ct.FlowSignal.check(info)
-		has_params = not ct.FlowSignal.check(params)
-
 		operation = props['operation']
-		dim = props['dim']
-		if has_info and has_params and operation is not None:
-			# Axis Required: Insert by-Dimension
-			## -> Some transformations ex. FT require setting an axis.
-			## -> The user selects which dimension the op should be done along.
-			## -> This dimension is converted to an axis integer.
-			## -> Finally, we pass the argument via params.
-			if operation.num_dim_inputs == 1:
-				axis = info.dim_axis(dim) if dim is not None else None
-				return params.compose_within(enclosing_func_args=[axis])
+		params = input_sockets['Expr']
 
+		has_params = not ct.FlowSignal.check(params)
+		if has_params and operation is not None:
 			return params
+
 		return ct.FlowSignal.FlowPending
 
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/viz.py

@@ -104,6 +104,7 @@ class VizMode(enum.StrEnum):
 		"""Given the input `InfoFlow`, deduce which visualization modes are valid to use with the described data."""
 		Z = spux.MathType.Integer
 		R = spux.MathType.Real
+		C = spux.MathType.Complex
 		VM = VizMode
 
 		return {
@@ -115,6 +116,9 @@ class VizMode(enum.StrEnum):
 				VM.Points2D,
 				VM.Bar,
 			],
+			((R,), (1, 1, C)): [
+				VM.Curve2D,
+			],
 			((R, Z), (1, 1, R)): [
 				VM.Curves2D,
 				VM.FilledCurves2D,
@@ -231,10 +235,15 @@ class VizNode(base.MaxwellSimNode):
 	## - Properties
 	#####################
 	@events.on_value_changed(
+		# Trigger
 		socket_name={'Expr'},
+		# Loaded
 		input_sockets={'Expr'},
 		input_socket_kinds={'Expr': ct.FlowKind.Info},
 		input_sockets_optional={'Expr': True},
+		# Flow
+		## -> See docs in TransformMathNode
+		stop_propagation=True,
 	)
 	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
 		has_info = not ct.FlowSignal.check(input_sockets['Expr'])
@@ -326,7 +335,7 @@ class VizNode(base.MaxwellSimNode):
 		if self.viz_target is VizTarget.Plot2D:
 			row = col.row(align=True)
 			row.alignment = 'CENTER'
-			row.label(text='Width/Height/DPI')
+			row.label(text='Width | Height | DPI')
 
 			row = col.row(align=True)
 			row.prop(self, self.blfields['plot_width'], text='')
@@ -339,8 +348,10 @@ class VizNode(base.MaxwellSimNode):
 	# - Events
 	####################
 	@events.on_value_changed(
+		# Trigger
 		socket_name='Expr',
 		run_on_init=True,
+		# Loaded
 		input_sockets={'Expr'},
 		input_socket_kinds={'Expr': {ct.FlowKind.Info, ct.FlowKind.Params}},
 		input_sockets_optional={'Expr': True},
@@ -355,14 +366,19 @@ class VizNode(base.MaxwellSimNode):
 		# Declare Loose Sockets that Realize Symbols
 		## -> This happens if Params contains not-yet-realized symbols.
 		if has_info and has_params and params.symbols:
-			if set(self.loose_input_sockets) != {
-				sym.name for sym in params.symbols if sym in info.dims
-			}:
+			if set(self.loose_input_sockets) != {sym.name for sym in params.symbols}:
 				self.loose_input_sockets = {
-					dim_name: sockets.ExprSocketDef(**expr_info)
-					for dim_name, expr_info in params.sym_expr_infos(
-						use_range=True
-					).items()
+					sym.name: sockets.ExprSocketDef(
+						**(
+							expr_info
+							| {
+								'active_kind': ct.FlowKind.Range
+								if sym in info.dims
+								else ct.FlowKind.Value
+							}
+						)
+					)
+					for sym, expr_info in params.sym_expr_infos.items()
 				}
 
 		elif self.loose_input_sockets:
@@ -373,9 +389,10 @@ class VizNode(base.MaxwellSimNode):
 	#####################
 	@events.computes_output_socket(
 		'Preview',
-		kind=ct.FlowKind.Value,
+		kind=ct.FlowKind.Previews,
 		# Loaded
 		props={
+			'sim_node_name',
 			'viz_mode',
 			'viz_target',
 			'colormap',
@@ -391,7 +408,7 @@ class VizNode(base.MaxwellSimNode):
 	)
 	def compute_dummy_value(self, props, input_sockets, loose_input_sockets):
 		"""Needed for the plot to regenerate in the viewer."""
-		return ct.FlowSignal.NoFlow
+		return ct.PreviewsFlow(bl_image_name=props['sim_node_name'])
 
 	#####################
 	## - On Show Plot
@@ -416,6 +433,7 @@ class VizNode(base.MaxwellSimNode):
 	def on_show_plot(
 		self, managed_objs, props, input_sockets, loose_input_sockets
 	) -> None:
+		log.critical('Show Plot (too many times)')
 		lazy_func = input_sockets['Expr'][ct.FlowKind.Func]
 		info = input_sockets['Expr'][ct.FlowKind.Info]
 		params = input_sockets['Expr'][ct.FlowKind.Params]
@@ -427,23 +445,17 @@ class VizNode(base.MaxwellSimNode):
 		viz_mode = props['viz_mode']
 		viz_target = props['viz_target']
 		if has_info and has_params and viz_mode is not None and viz_target is not None:
-			# Realize Data w/Realized Symbols
+			# Retrieve Data
 			## -> The loose input socket values are user-selected symbol values.
-			## -> These expressions are used to realize the lazy data.
-			## -> `.realize()` ensures all ex. units  are correctly conformed.
-			realized_syms = {
-				sym: loose_input_sockets[sym.name] for sym in params.sorted_symbols
-			}
-			output_data = lazy_func.realize(params, symbol_values=realized_syms)
-
-			data = {
-				dim: (
-					realized_syms[dim].values
-					if dim in realized_syms
-					else info.dims[dim]
-				)
-				for dim in info.dims
-			} | {info.output: output_data}
+			## -> These are used to get rid of symbols in the ParamsFlow.
+			## -> What's left is a dictionary from SimSymbol -> Data
+			data = lazy_func.realize_as_data(
+				info,
+				params,
+				symbol_values={
+					sym: loose_input_sockets[sym.name] for sym in params.sorted_symbols
+				},
+			)
 
 			# Match Viz Type & Perform Visualization
 			## -> Viz Target determines how to plot.
@@ -459,7 +471,6 @@ class VizNode(base.MaxwellSimNode):
 						width_inches=plot_width,
 						height_inches=plot_height,
 						dpi=plot_dpi,
-						bl_select=True,
 					)
 
 				case VizTarget.Pixels:
@@ -468,7 +479,6 @@ class VizNode(base.MaxwellSimNode):
 						plot.map_2d_to_image(
 							data,
 							colormap=colormap,
-							bl_select=True,
 						)
 
 				case VizTarget.PixelsPlane:

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/base.py

@@ -21,6 +21,7 @@ Attributes:
 """
 
 import enum
+import functools
 import typing as typ
 from collections import defaultdict
 from types import MappingProxyType
@@ -62,7 +63,6 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 			Used as a node-specific cache index.
 		sim_node_name: A unique human-readable name identifying the node.
 			Used when naming managed objects and exporting.
-		preview_active: Whether the preview (if any) is currently active.
 		locked: Whether the node is currently 'locked' aka. non-editable.
 	"""
 
@@ -98,7 +98,6 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 	loose_output_sockets: dict[str, sockets.base.SocketDef] = bl_cache.BLField({})
 
 	# UI Options
-	preview_active: bool = bl_cache.BLField(False)
 	locked: bool = bl_cache.BLField(False, use_prop_update=False)
 
 	# Active Socket Set
@@ -264,35 +263,6 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 				## TODO: Account for FlowKind
 				bl_socket.value = socket_value
 
-	####################
-	# - Events: Preview | Plot
-	####################
-	@events.on_show_plot(stop_propagation=False)
-	def _on_show_plot(self):
-		node_tree = self.id_data
-		if len(self.event_methods_by_event[ct.FlowEvent.ShowPlot]) > 1:
-			## TODO: Is this check good enough?
-			## TODO: Set icon/indicator/something to make it clear which node is being previewed.
-			node_tree.report_show_plot(self)
-
-	@events.on_show_preview()
-	def _on_show_preview(self):
-		node_tree = self.id_data
-		node_tree.report_show_preview(self)
-
-		# Set Preview to Active
-		## Implicitly triggers any @on_value_changed for preview_active.
-		if not self.preview_active:
-			self.preview_active = True
-
-	@events.on_value_changed(
-		prop_name='preview_active', props={'preview_active'}, stop_propagation=True
-	)
-	def _on_preview_changed(self, props):
-		if not props['preview_active']:
-			for mobj in self.managed_objs.values():
-				mobj.hide_preview()
-
 	####################
 	# - Events: Lock
 	####################
@@ -521,14 +491,17 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 		return {
 			ct.FlowEvent.EnableLock: lambda *_: True,
 			ct.FlowEvent.DisableLock: lambda *_: True,
-			ct.FlowEvent.DataChanged: lambda event_method, socket_name, prop_name, _: (
+			ct.FlowEvent.DataChanged: lambda event_method, socket_name, prop_names, _: (
 				(
 					socket_name
 					and socket_name in event_method.callback_info.on_changed_sockets
 				)
 				or (
-					prop_name
-					and prop_name in event_method.callback_info.on_changed_props
+					prop_names
+					and any(
+						prop_name in event_method.callback_info.on_changed_props
+						for prop_name in prop_names
+					)
 				)
 				or (
 					socket_name
@@ -536,6 +509,7 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 					and socket_name in self.loose_input_sockets
 				)
 			),
+			# Non-Triggered
 			ct.FlowEvent.OutputRequested: lambda output_socket_method,
 			output_socket_name,
 			_,
@@ -546,7 +520,6 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 					== output_socket_method.callback_info.output_socket_name
 				)
 			),
-			ct.FlowEvent.ShowPreview: lambda *_: True,
 			ct.FlowEvent.ShowPlot: lambda *_: True,
 		}
 
@@ -595,6 +568,9 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 		bl_socket = self.inputs.get(input_socket_name)
 		if bl_socket is not None:
 			if bl_socket.instance_id:
+				if kind is ct.FlowKind.Previews:
+					return bl_socket.compute_data(kind=kind)
+
 				return (
 					ct.FlowKind.scale_to_unit_system(
 						kind,
@@ -610,12 +586,10 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 			## -> Anyone needing results will need to wait on preinit().
 			return ct.FlowSignal.FlowInitializing
 
-		# if optional:
+		if kind is ct.FlowKind.Previews:
+			return ct.PreviewsFlow()
 		return ct.FlowSignal.NoFlow
 
-		msg = f'{self.sim_node_name}: Input socket "{input_socket_name}" cannot be computed, as it is not an active input socket'
-		raise ValueError(msg)
-
 	####################
 	# - Compute Event: Output Socket
 	####################
@@ -638,33 +612,64 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 			The value of the output socket, as computed by the dedicated method
 			registered using the `@computes_output_socket` decorator.
 		"""
-		if self.outputs.get(output_socket_name) is None:
-			if optional:
-				return None
+		# Previews: Aggregate All Input Sockets
+		## -> All PreviewsFlows on all input sockets are combined.
+		## -> Output Socket Methods can add additional PreviewsFlows.
+		if kind is ct.FlowKind.Previews:
+			input_previews = functools.reduce(
+				lambda a, b: a | b,
+				[
+					self._compute_input(
+						socket, kind=ct.FlowKind.Previews, unit_system=None
+					)
+					for socket in [bl_socket.name for bl_socket in self.inputs]
+				],
+				ct.PreviewsFlow(),
+			)
 
-			msg = f"Can't compute nonexistent output socket name {output_socket_name}, as it's not currently active"
-			raise RuntimeError(msg)
+		# No Output Socket: No Flow
+		## -> All PreviewsFlows on all input sockets are combined.
+		## -> Output Socket Methods can add additional PreviewsFlows.
+		if self.outputs.get(output_socket_name) is None:
+			return ct.FlowSignal.NoFlow
 
 		output_socket_methods = self.filtered_event_methods_by_event(
 			ct.FlowEvent.OutputRequested,
 			(output_socket_name, None, kind),
 		)
 
-		# Run (=1) Method
-		if output_socket_methods:
-			if len(output_socket_methods) > 1:
-				msg = f'More than one method found for ({output_socket_name}, {kind.value!s}.'
-				raise RuntimeError(msg)
+		# Exactly One Output Socket Method
+		## -> All PreviewsFlows on all input sockets are combined.
+		## -> Output Socket Methods can add additional PreviewsFlows.
+		if len(output_socket_methods) == 1:
+			res = output_socket_methods[0](self)
 
-			return output_socket_methods[0](self)
+			# Res is PreviewsFlow: Concatenate
+			## -> This will add the elements within the returned PreviewsFluw.
+			if kind is ct.FlowKind.Previews and not ct.FlowSignal.check(res):
+				input_previews |= res
 
-		# Auxiliary Fallbacks
+			return res
+
+		# > One Output Socket Method: Error
+		if len(output_socket_methods) > 1:
+			msg = (
+				f'More than one method found for ({output_socket_name}, {kind.value!s}.'
+			)
+			raise RuntimeError(msg)
+
+		if kind is ct.FlowKind.Previews:
+			return input_previews
 		return ct.FlowSignal.NoFlow
-		# if optional or kind in [ct.FlowKind.Info, ct.FlowKind.Params]:
-		# return ct.FlowSignal.NoFlow
 
-		# msg = f'No output method for ({output_socket_name}, {kind})'
-		# raise ValueError(msg)
+	####################
+	# - Plot
+	####################
+	def compute_plot(self):
+		plot_methods = self.filtered_event_methods_by_event(ct.FlowEvent.ShowPlot, ())
+
+		for plot_method in plot_methods:
+			plot_method(self)
 
 	####################
 	# - Event Trigger
@@ -674,11 +679,11 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 		method_info: events.InfoOutputRequested,
 		input_socket_name: ct.SocketName | None,
 		input_socket_kinds: set[ct.FlowKind] | None,
-		prop_name: str | None,
+		prop_names: set[str] | None,
 	) -> bool:
 		return (
-			prop_name is not None
-			and prop_name in method_info.depon_props
+			prop_names is not None
+			and any(prop_name in method_info.depon_props for prop_name in prop_names)
 			or input_socket_name is not None
 			and (
 				input_socket_name in method_info.depon_input_sockets
@@ -704,41 +709,63 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 		)
 
 	@bl_cache.cached_bl_property()
-	def _dependent_outputs(
+	def output_socket_invalidates(
 		self,
 	) -> dict[
 		tuple[ct.SocketName, ct.FlowKind], set[tuple[ct.SocketName, ct.FlowKind]]
 	]:
-		## TODO: Cleanup
-		## TODO: Detect cycles?
-		## TODO: Networkx?
+		"""Deduce which output socket | `FlowKind` combos are altered in response to a given output socket | `FlowKind` combo.
+
+		Returns:
+			A dictionary, wher eeach key is a tuple representing an output socket name and its flow kind that has been altered, and each value is a set of tuples representing output socket names and flow kind.
+
+			Indexing by any particular `(output_socket_name, flow_kind)` will produce a set of all `{(output_socket_name, flow_kind)}` that rely on it.
+		"""
 		altered_to_invalidated = defaultdict(set)
+
+		# Iterate ALL Methods that Compute Output Sockets
+		## -> We call it the "altered method".
+		## -> Our approach will be to deduce what relies on it.
 		output_requested_methods = self.event_methods_by_event[
 			ct.FlowEvent.OutputRequested
 		]
-
 		for altered_method in output_requested_methods:
 			altered_info = altered_method.callback_info
 			altered_key = (altered_info.output_socket_name, altered_info.kind)
 
+			# Inner: Iterate ALL Methods that Compute Output Sockets
+			## -> We call it the "invalidated method".
+			## -> While O(n^2), it runs only once per-node, and is then cached.
+			## -> `n` is rarely so large as to be a startup-time concern.
+			## -> Thus, in this case, using a simple implementation is better.
 			for invalidated_method in output_requested_methods:
 				invalidated_info = invalidated_method.callback_info
 
+				# Check #0: Inv. Socket depends on Altered Socket
+				## -> Simply check if the altered name is in the dependencies.
 				if (
 					altered_info.output_socket_name
 					in invalidated_info.depon_output_sockets
 				):
+					# Check #2: FlowKinds Match
+					## -> Case 1: Single Altered Kind was Requested by Inv
+					## -> Case 2: Altered Kind in set[Requested Kinds] is
+					## -> Case 3: Altered Kind is FlowKind.Value
+					## This encapsulates the actual events decorator semantics.
 					is_same_kind = (
 						altered_info.kind
-						== (
+						is (
 							_kind := invalidated_info.depon_output_socket_kinds.get(
 								altered_info.output_socket_name
 							)
 						)
 						or (isinstance(_kind, set) and altered_info.kind in _kind)
-						or altered_info.kind == ct.FlowKind.Value
+						or altered_info.kind is ct.FlowKind.Value
 					)
 
+					# Check Success: Add Invalidated (name,kind) to Altered Set
+					## -> We've now confirmed a dependency.
+					## -> Thus, this name|kind should be included.
 					if is_same_kind:
 						invalidated_key = (
 							invalidated_info.output_socket_name,
@@ -753,7 +780,7 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 		event: ct.FlowEvent,
 		socket_name: ct.SocketName | None = None,
 		socket_kinds: set[ct.FlowKind] | None = None,
-		prop_name: ct.SocketName | None = None,
+		prop_names: set[str] | None = None,
 	) -> None:
 		"""Recursively triggers events forwards or backwards along the node tree, allowing nodes in the update path to react.
 
@@ -770,124 +797,141 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 			socket_name: The input socket that was altered, if any, in order to trigger this event.
 			pop_name: The property that was altered, if any, in order to trigger this event.
 		"""
-		log.debug(
-			'%s: Triggered Event %s (socket_name=%s, socket_kinds=%s, prop_name=%s)',
-			self.sim_node_name,
-			event,
-			str(socket_name),
-			str(socket_kinds),
-			str(prop_name),
-		)
-		# Outflow Socket Kinds
-		## -> Something has happened!
-		## -> The effect is yet to be determined...
-		## -> We will watch for which kinds actually invalidate.
-		## -> ...Then ONLY propagate kinds that have an invalidated outsck.
-		## -> This way, kinds get "their own" invalidation chains.
-		## -> ...While still respecting "crossovers".
-		altered_socket_kinds = set()
+		# log.debug(
+		# '[%s] [%s] Triggered (socket_name=%s, socket_kinds=%s, prop_names=%s)',
+		# self.sim_node_name,
+		# event,
+		# str(socket_name),
+		# str(socket_kinds),
+		# str(prop_names),
+		# )
 
 		# Invalidate Caches on DataChanged
+		## -> socket_kinds MUST NOT be None
+		## -> Trigger direction is always 'forwards' for DataChanged
+		## -> Track which FlowKinds are actually altered per-output-socket.
+		altered_socket_kinds: dict[ct.SocketName, set[ct.FlowKind]] = defaultdict(set)
 		if event is ct.FlowEvent.DataChanged:
-			input_socket_name = socket_name  ## Trigger direction is forwards
+			in_sckname = socket_name
 
-			# Invalidate Input Socket Cache
-			if input_socket_name is not None:
-				if socket_kinds is None:
+			# Clear Input Socket Cache(s)
+			## -> The input socket cache for each altered FlowKinds is cleared.
+			## -> Since it's non-persistent, it will be lazily re-filled.
+			if in_sckname is not None:
+				for in_kind in socket_kinds:
+					# log.debug(
+					# '![%s] Clear Input Socket Cache (%s, %s)',
+					# self.sim_node_name,
+					# in_sckname,
+					# in_kind,
+					# )
 					self._compute_input.invalidate(
-						input_socket_name=input_socket_name,
-						kind=...,
+						input_socket_name=in_sckname,
+						kind=in_kind,
 						unit_system=...,
 					)
-				else:
-					for socket_kind in socket_kinds:
-						self._compute_input.invalidate(
-							input_socket_name=input_socket_name,
-							kind=socket_kind,
-							unit_system=...,
-						)
 
-			# Invalidate Output Socket Cache
+			# Clear Output Socket Cache(s)
 			for output_socket_method in self.event_methods_by_event[
 				ct.FlowEvent.OutputRequested
 			]:
+				# Determine Consequences of Changed (Socket|Kind) / Prop
+				## -> Each '@computes_output_socket' declares data to load.
+				## -> Compare what was changed to what each output socket needs.
+				## -> IF what is needed, was changed, THEN:
+				## --- The output socket needs recomputing.
 				method_info = output_socket_method.callback_info
 				if self._should_recompute_output_socket(
-					method_info, socket_name, socket_kinds, prop_name
+					method_info, socket_name, socket_kinds, prop_names
 				):
 					out_sckname = method_info.output_socket_name
-					kind = method_info.kind
+					out_kind = method_info.kind
 
-					# Invalidate Output Directly
-					# log.critical(
-					# '[%s] Invalidating: (%s, %s)',
+					# log.debug(
+					# '![%s] Clear Output Socket Cache (%s, %s)',
 					# self.sim_node_name,
 					# out_sckname,
-					# str(kind),
+					# out_kind,
 					# )
-					altered_socket_kinds.add(kind)
 					self.compute_output.invalidate(
 						output_socket_name=out_sckname,
-						kind=kind,
+						kind=out_kind,
 					)
+					altered_socket_kinds[out_sckname].add(out_kind)
 
-					# Invalidate Any Dependent Outputs
-					if (
-						dep_outs := self._dependent_outputs.get((out_sckname, kind))
-					) is not None:
-						for dep_out in dep_outs:
-							# log.critical(
-							# '![%s] Invalidating: (%s, %s)',
+					# Invalidate Dependent Output Sockets
+					## -> Other outscks may depend on the altered outsck.
+					## -> The property 'output_socket_invalidates' encodes this.
+					## -> The property 'output_socket_invalidates' encodes this.
+					cleared_outscks_kinds = self.output_socket_invalidates.get(
+						(out_sckname, out_kind)
+					)
+					if cleared_outscks_kinds is not None:
+						for dep_out_sckname, dep_out_kind in cleared_outscks_kinds:
+							# log.debug(
+							# '!![%s] Clear Output Socket Cache (%s, %s)',
 							# self.sim_node_name,
-							# dep_out[0],
-							# dep_out[1],
+							# out_sckname,
+							# out_kind,
 							# )
-							altered_socket_kinds.add(dep_out[1])
 							self.compute_output.invalidate(
-								output_socket_name=dep_out[0],
-								kind=dep_out[1],
+								output_socket_name=dep_out_sckname,
+								kind=dep_out_kind,
 							)
+							altered_socket_kinds[dep_out_sckname].add(dep_out_kind)
 
 		# Run Triggered Event Methods
+		## -> A triggered event method may request to stop propagation.
+		## -> A triggered event method may request to stop propagation.
 		stop_propagation = False
 		triggered_event_methods = self.filtered_event_methods_by_event(
-			event, (socket_name, prop_name, None)
+			event, (socket_name, prop_names, None)
 		)
 		for event_method in triggered_event_methods:
 			stop_propagation |= event_method.stop_propagation
-			# log.critical(
-			# '%s: Running %s',
+			# log.debug(
+			# '![%s] Running: %s',
 			# self.sim_node_name,
 			# str(event_method.callback_info),
 			# )
 			event_method(self)
 
-		# DataChanged Propagation Stop: No Altered Socket Kinds
-		## -> If no FlowKinds were altered, then propagation makes no sense.
-		## -> Semantically, **nothing has changed** == no DataChanged!
-		if event is ct.FlowEvent.DataChanged and not altered_socket_kinds:
-			return
-
-		# Constrain ShowPlot to First Node: Workaround
-		if event is ct.FlowEvent.ShowPlot:
-			return
-
-		# Propagate Event to All Sockets in "Trigger Direction"
+		# Propagate Event
+		## -> If 'stop_propagation' was tripped, don't propagate.
+		## -> If no sockets were altered during DataChanged, don't propagate.
+		## -> Each FlowEvent decides whether to flow forwards/backwards.
 		## -> The trigger chain goes node/socket/socket/node/socket/...
+		## -> Unlinked sockets naturally stop the propagation.
 		if not stop_propagation:
 			direc = ct.FlowEvent.flow_direction[event]
-			triggered_sockets = self._bl_sockets(direc=direc)
-			for bl_socket in triggered_sockets:
-				if direc == 'output' and not bl_socket.is_linked:
-					continue
+			for bl_socket in self._bl_sockets(direc=direc):
+				# DataChanged: Propagate Altered SocketKinds
+				## -> Only altered FlowKinds for the socket will propagate.
+				## -> In this way, we guarantee no extraneous (noop) flow.
+				if event is ct.FlowEvent.DataChanged:
+					if bl_socket.name in altered_socket_kinds:
+						# log.debug(
+						# '![%s] [%s] Propagating (direction=%s, altered_socket_kinds=%s)',
+						# self.sim_node_name,
+						# event,
+						# direc,
+						# altered_socket_kinds[bl_socket.name],
+						# )
+						bl_socket.trigger_event(
+							event, socket_kinds=altered_socket_kinds[bl_socket.name]
+						)
 
-				# log.critical(
-				# '![%s] Propagating: (%s, %s)',
-				# self.sim_node_name,
-				# event,
-				# altered_socket_kinds,
-				# )
-				bl_socket.trigger_event(event, socket_kinds=altered_socket_kinds)
+					## -> Otherwise, do nothing - guarantee no extraneous flow.
+
+				# Propagate Normally
+				else:
+					# log.debug(
+					# '![%s] [%s] Propagating (direction=%s)',
+					# self.sim_node_name,
+					# event,
+					# direc,
+					# )
+					bl_socket.trigger_event(event)
 
 	####################
 	# - Property Event: On Update
@@ -903,18 +947,22 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 		Parameters:
 			prop_name: The name of the property that changed.
 		"""
-		# All Attributes: Trigger Event
-		## -> This declares that the single property has changed.
-		## -> This should happen first, in case dependents need a cache.
-		if hasattr(self, prop_name):
-			self.trigger_event(ct.FlowEvent.DataChanged, prop_name=prop_name)
-
 		# BLField Attributes: Invalidate BLField Dependents
-		## -> Dependent props will generally also trigger on_prop_changed.
-		## -> The recursion ends with the depschain.
+		## -> All invalidated blfields will have their caches cleared.
+		## -> The (topologically) ordered list of cleared blfields is returned.
 		## -> WARNING: The chain is not checked for ex. cycles.
 		if prop_name in self.blfields:
-			self.invalidate_blfield_deps(prop_name)
+			cleared_blfields = self.clear_blfields_after(prop_name)
+
+			# log.debug(
+			# '%s (Node): Set of Cleared BLFields: %s',
+			# self.bl_label,
+			# str(cleared_blfields),
+			# )
+			self.trigger_event(
+				ct.FlowEvent.DataChanged,
+				prop_names={prop_name for prop_name, _ in cleared_blfields},
+			)
 
 	####################
 	# - UI Methods

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/constants/__init__.py

@@ -18,15 +18,18 @@ from . import (
 	blender_constant,
 	expr_constant,
 	scientific_constant,
+	symbol_constant,
 )
 
 BL_REGISTER = [
 	*expr_constant.BL_REGISTER,
+	*symbol_constant.BL_REGISTER,
 	*scientific_constant.BL_REGISTER,
 	*blender_constant.BL_REGISTER,
 ]
 BL_NODES = {
 	**expr_constant.BL_NODES,
+	**symbol_constant.BL_NODES,
 	**scientific_constant.BL_NODES,
 	**blender_constant.BL_NODES,
 }

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/constants/scientific_constant.py

@@ -76,13 +76,13 @@ class ScientificConstantNode(base.MaxwellSimNode):
 		"""Retrieve a symbol for the scientific constant."""
 		if self.sci_constant is not None and self.sci_constant_info is not None:
 			unit = self.sci_constant_info['units']
-			return sim_symbols.SimSymbol(
-				sym_name=self.sci_constant_name,
-				mathtype=spux.MathType.from_expr(self.sci_constant),
-				# physical_type=  ## TODO: Formalize unit w/o physical_type
-				unit=unit,
+			return sim_symbols.SimSymbol.from_expr(
+				self.sci_constant_name,
+				self.sci_constant,
+				unit,
 				is_constant=True,
 			)
+
 		return None
 
 	####################
@@ -125,7 +125,7 @@ class ScientificConstantNode(base.MaxwellSimNode):
 		if self.sci_constant_info:
 			row = _col.row(align=True)
 			# row.alignment = 'CENTER'
-			row.label(text=f'{self.sci_constant_info["units"]}')
+			row.label(text=f'{spux.sp_to_str(self.sci_constant_info["units"].n(4))}')
 
 			row = _col.row(align=True)
 			# row.alignment = 'CENTER'
@@ -184,13 +184,18 @@ class ScientificConstantNode(base.MaxwellSimNode):
 	@events.computes_output_socket(
 		'Expr',
 		kind=ct.FlowKind.Params,
-		props={'sci_constant'},
+		props={'sci_constant', 'sci_constant_sym'},
 	)
 	def compute_params(self, props: dict) -> typ.Any:
 		sci_constant = props['sci_constant']
+		sci_constant_sym = props['sci_constant_sym']
 
-		if sci_constant is not None:
-			return ct.ParamsFlow(func_args=[sci_constant])
+		if sci_constant is not None and sci_constant_sym is not None:
+			return ct.ParamsFlow(
+				arg_targets=[sci_constant_sym],
+				func_args=[sci_constant],
+				is_differentiable=True,
+			)
 		return ct.FlowSignal.FlowPending
 
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/constants/symbol_constant.py

@@ -0,0 +1,266 @@
+# blender_maxwell
+# Copyright (C) 2024 blender_maxwell Project Contributors
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Affero General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Affero General Public License for more details.
+#
+# You should have received a copy of the GNU Affero General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+import enum
+import typing as typ
+
+import bpy
+import sympy as sp
+
+from blender_maxwell.utils import bl_cache, logger, sim_symbols
+from blender_maxwell.utils import extra_sympy_units as spux
+
+from .... import contracts as ct
+from .... import sockets
+from ... import base, events
+
+log = logger.get(__name__)
+
+
+class SymbolConstantNode(base.MaxwellSimNode):
+	node_type = ct.NodeType.SymbolConstant
+	bl_label = 'Symbol'
+
+	input_sockets: typ.ClassVar = {}
+	output_sockets: typ.ClassVar = {
+		'Expr': sockets.ExprSocketDef(
+			active_kind=ct.FlowKind.Func,
+			show_info_columns=True,
+		),
+	}
+
+	####################
+	# - Socket Interface
+	####################
+	sym_name: sim_symbols.SimSymbolName = bl_cache.BLField(
+		sim_symbols.SimSymbolName.Constant
+	)
+
+	size: spux.NumberSize1D = bl_cache.BLField(spux.NumberSize1D.Scalar)
+	mathtype: spux.MathType = bl_cache.BLField(spux.MathType.Real)
+	physical_type: spux.PhysicalType = bl_cache.BLField(spux.PhysicalType.NonPhysical)
+
+	####################
+	# - Properties: Unit
+	####################
+	active_unit: enum.StrEnum = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_valid_units(),
+		cb_depends_on={'physical_type'},
+	)
+
+	def search_valid_units(self) -> list[ct.BLEnumElement]:
+		"""Compute Blender enum elements of valid units for the current `physical_type`."""
+		if self.physical_type is not spux.PhysicalType.NonPhysical:
+			return [
+				(sp.sstr(unit), spux.sp_to_str(unit), sp.sstr(unit), '', i)
+				for i, unit in enumerate(self.physical_type.valid_units)
+			]
+		return []
+
+	@bl_cache.cached_bl_property(depends_on={'active_unit'})
+	def unit(self) -> spux.Unit | None:
+		"""Gets the current active unit.
+
+		Returns:
+			The current active `sympy` unit.
+
+			If the socket expression is unitless, this returns `None`.
+		"""
+		if self.active_unit is not None:
+			return spux.unit_str_to_unit(self.active_unit)
+
+		return None
+
+	@property
+	def unit_factor(self) -> spux.Unit | None:
+		"""Like `self.unit`, except `1` instead of `None` when unitless."""
+		return sp.Integer(1) if self.unit is None else self.unit
+
+	####################
+	# - Domain
+	####################
+	interval_finite_z: tuple[int, int] = bl_cache.BLField((0, 1))
+	interval_finite_q: tuple[tuple[int, int], tuple[int, int]] = bl_cache.BLField(
+		((0, 1), (1, 1))
+	)
+	interval_finite_re: tuple[float, float] = bl_cache.BLField((0.0, 1.0))
+	interval_inf: tuple[bool, bool] = bl_cache.BLField((True, True))
+	interval_closed: tuple[bool, bool] = bl_cache.BLField((True, True))
+
+	interval_finite_im: tuple[float, float] = bl_cache.BLField((0.0, 1.0))
+	interval_inf_im: tuple[bool, bool] = bl_cache.BLField((True, True))
+	interval_closed_im: tuple[bool, bool] = bl_cache.BLField((True, True))
+
+	####################
+	# - Computed Properties
+	####################
+	@bl_cache.cached_bl_property(
+		depends_on={
+			'sym_name',
+			'size',
+			'mathtype',
+			'physical_type',
+			'unit',
+			'interval_finite_z',
+			'interval_finite_q',
+			'interval_finite_re',
+			'interval_inf',
+			'interval_closed',
+			'interval_finite_im',
+			'interval_inf_im',
+			'interval_closed_im',
+		}
+	)
+	def symbol(self) -> sim_symbols.SimSymbol:
+		return sim_symbols.SimSymbol(
+			sym_name=self.sym_name,
+			mathtype=self.mathtype,
+			physical_type=self.physical_type,
+			unit=self.unit,
+			rows=self.size.rows,
+			cols=self.size.cols,
+			interval_finite_z=self.interval_finite_z,
+			interval_finite_q=self.interval_finite_q,
+			interval_finite_re=self.interval_finite_re,
+			interval_inf=self.interval_inf,
+			interval_closed=self.interval_closed,
+			interval_finite_im=self.interval_finite_im,
+			interval_inf_im=self.interval_inf_im,
+			interval_closed_im=self.interval_closed_im,
+		)
+
+	####################
+	# - UI
+	####################
+	def draw_label(self):
+		return self.symbol.def_label
+
+	def draw_props(self, _: bpy.types.Context, col: bpy.types.UILayout) -> None:
+		col.prop(self, self.blfields['sym_name'], text='')
+
+		row = col.row(align=True)
+		row.alignment = 'CENTER'
+		row.label(text='Assumptions')
+
+		row = col.row(align=True)
+		row.prop(self, self.blfields['mathtype'], text='')
+
+		row = col.row(align=True)
+		row.prop(self, self.blfields['size'], text='')
+		row.prop(self, self.blfields['active_unit'], text='')
+
+		col.prop(self, self.blfields['physical_type'], text='')
+
+		row = col.row(align=True)
+		row.alignment = 'CENTER'
+		row.label(text='Domain')
+
+		match self.mathtype:
+			case spux.MathType.Integer:
+				col.prop(self, self.blfields['interval_finite_z'], text='')
+				col.prop(self, self.blfields['interval_inf'], text='Infinite')
+				col.prop(self, self.blfields['interval_closed'], text='Closed')
+
+			case spux.MathType.Rational:
+				col.prop(self, self.blfields['interval_finite_q'], text='')
+				col.prop(self, self.blfields['interval_inf'], text='Infinite')
+				col.prop(self, self.blfields['interval_closed'], text='Closed')
+
+			case spux.MathType.Real:
+				col.prop(self, self.blfields['interval_finite_re'], text='')
+				col.prop(self, self.blfields['interval_inf'], text='Infinite')
+				col.prop(self, self.blfields['interval_closed'], text='Closed')
+
+			case spux.MathType.Complex:
+				col.prop(self, self.blfields['interval_finite_re'], text='ℝ')
+				col.prop(self, self.blfields['interval_inf'], text='ℝ Infinite')
+				col.prop(self, self.blfields['interval_closed'], text='ℝ Closed')
+
+				col.separator()
+
+				col.prop(self, self.blfields['interval_finite_im'], text='𝕀')
+				col.prop(self, self.blfields['interval_inf'], text='𝕀 Infinite')
+				col.prop(self, self.blfields['interval_closed'], text='𝕀 Closed')
+
+	####################
+	# - FlowKinds
+	####################
+	@events.computes_output_socket(
+		# Trigger
+		'Expr',
+		kind=ct.FlowKind.Value,
+		# Loaded
+		props={'symbol'},
+	)
+	def compute_value(self, props) -> typ.Any:
+		return props['symbol'].sp_symbol
+
+	@events.computes_output_socket(
+		# Trigger
+		'Expr',
+		kind=ct.FlowKind.Func,
+		# Loaded
+		props={'symbol'},
+	)
+	def compute_lazy_func(self, props) -> typ.Any:
+		sp_sym = props['symbol'].sp_symbol
+		return ct.FuncFlow(
+			func=sp.lambdify(sp_sym, sp_sym, 'jax'),
+			func_args=[sp_sym],
+			supports_jax=True,
+		)
+
+	####################
+	# - FlowKinds: Auxiliary
+	####################
+	@events.computes_output_socket(
+		# Trigger
+		'Expr',
+		kind=ct.FlowKind.Info,
+		# Loaded
+		props={'symbol'},
+	)
+	def compute_info(self, props) -> typ.Any:
+		return ct.InfoFlow(
+			output=props['symbol'],
+		)
+
+	@events.computes_output_socket(
+		# Trigger
+		'Expr',
+		kind=ct.FlowKind.Params,
+		# Loaded
+		props={'symbol'},
+	)
+	def compute_params(self, props) -> typ.Any:
+		sym = props['symbol']
+		return ct.ParamsFlow(
+			arg_targets=[sym],
+			func_args=[sym.sp_symbol],
+			symbols={sym},
+			is_differentiable=(
+				sym.mathtype in [spux.MathType.Real, spux.MathType.Complex]
+			),
+		)
+
+
+####################
+# - Blender Registration
+####################
+BL_REGISTER = [
+	SymbolConstantNode,
+]
+BL_NODES = {ct.NodeType.SymbolConstant: (ct.NodeCategory.MAXWELLSIM_INPUTS_CONSTANTS)}

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/file_importers/data_file_importer.py

@@ -50,10 +50,15 @@ class DataFileImporterNode(base.MaxwellSimNode):
 	# - Properties
 	####################
 	@events.on_value_changed(
+		# Trigger
 		socket_name={'File Path'},
+		# Loaded
 		input_sockets={'File Path'},
 		input_socket_kinds={'File Path': ct.FlowKind.Value},
 		input_sockets_optional={'File Path': True},
+		# Flow
+		## -> See docs in TransformMathNode
+		stop_propagation=True,
 	)
 	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
 		has_file_path = not ct.FlowSignal.check(input_sockets['File Path'])
@@ -83,7 +88,15 @@ class DataFileImporterNode(base.MaxwellSimNode):
 	####################
 	# - Output Info
 	####################
-	@bl_cache.cached_bl_property(depends_on={'file_path'})
+	@bl_cache.cached_bl_property(
+		depends_on={
+			'output_name',
+			'output_mathtype',
+			'output_physical_type',
+			'output_unit',
+		}
+		| {f'dim_{i}_name' for i in range(6)}
+	)
 	def expr_info(self) -> ct.InfoFlow | None:
 		"""Retrieve the output expression's `InfoFlow`."""
 		info = self.compute_output('Expr', kind=ct.FlowKind.Info)
@@ -184,19 +197,19 @@ class DataFileImporterNode(base.MaxwellSimNode):
 	@events.computes_output_socket(
 		'Expr',
 		kind=ct.FlowKind.Func,
+		# Loaded
 		input_sockets={'File Path'},
 	)
-	def compute_func(self, input_sockets: dict) -> td.Simulation:
+	def compute_func(self, input_sockets) -> td.Simulation:
 		"""Declare a lazy, composable function that returns the loaded data.
 
 		Returns:
 			A completely empty `ParamsFlow`, ready to be composed.
 		"""
 		file_path = input_sockets['File Path']
+		has_file_path = not ct.FlowSignal.check(file_path)
 
-		has_file_path = not ct.FlowSignal.check(input_sockets['File Path'])
-
-		if has_file_path:
+		if has_file_path and file_path is not None:
 			data_file_format = ct.DataFileFormat.from_path(file_path)
 			if data_file_format is not None:
 				# Jax Compatibility: Lazy Data Loading

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/monitors/eh_field_monitor.py

@@ -195,18 +195,23 @@ class EHFieldMonitorNode(base.MaxwellSimNode):
 	####################
 	# - Preview
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Time Monitor',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews_time(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
+
+	@events.computes_output_socket(
+		'Freq Monitor',
+		kind=ct.FlowKind.Previews,
+		# Loaded
+		props={'sim_node_name'},
+	)
+	def compute_previews_freq(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		# Trigger

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/monitors/field_power_flux_monitor.py

@@ -170,18 +170,23 @@ class PowerFluxMonitorNode(base.MaxwellSimNode):
 	####################
 	# - Preview - Changes to Input Sockets
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Time Monitor',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews_time(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
+
+	@events.computes_output_socket(
+		'Freq Monitor',
+		kind=ct.FlowKind.Previews,
+		# Loaded
+		props={'sim_node_name'},
+	)
+	def compute_previews_freq(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		# Trigger

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/monitors/permittivity_monitor.py

@@ -119,18 +119,14 @@ class PermittivityMonitorNode(base.MaxwellSimNode):
 	####################
 	# - Preview
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Permittivity Monitor',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews_freq(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		# Trigger

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/outputs/file_exporters/data_file_exporter.py

@@ -232,8 +232,17 @@ class DataFileExporterNode(base.MaxwellSimNode):
 				dim.name for dim in params.symbols if dim in info.dims
 			}:
 				self.loose_input_sockets = {
-					dim_name: sockets.ExprSocketDef(**expr_info)
-					for dim_name, expr_info in params.sym_expr_infos(info).items()
+					sym.name: sockets.ExprSocketDef(
+						**(
+							expr_info
+							| {
+								'active_kind': ct.FlowKind.Range
+								if sym in info.dims
+								else ct.FlowKind.Value
+							}
+						)
+					)
+					for sym, expr_info in params.sym_expr_infos.items()
 				}
 
 		elif self.loose_input_sockets:

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/outputs/viewer.py

@@ -18,6 +18,7 @@ import typing as typ
 
 import bpy
 import sympy as sp
+import tidy3d as td
 
 from blender_maxwell.utils import bl_cache, logger
 from blender_maxwell.utils import extra_sympy_units as spux
@@ -88,32 +89,79 @@ class ViewerNode(base.MaxwellSimNode):
 		socket_name='Any',
 	)
 	def on_input_changed(self) -> None:
-		self.input_flow = bl_cache.Signal.InvalidateCache
-
-	@bl_cache.cached_bl_property()
-	def input_flow(self) -> dict[ct.FlowKind, typ.Any | None]:
-		input_flow = {}
+		"""Lightweight invalidator, which invalidates the more specific `cached_bl_property` used to determine when something ex. plot-related has changed.
 
+		Calls `get_flow`, which will be called again when regenerating the `cached_bl_property`s.
+		This **does not** call the flow twice, as `self._compute_input()` will be cached the first time.
+		"""
 		for flow_kind in list(ct.FlowKind):
+			flow = self.get_flow(
+				flow_kind, always_load=flow_kind is ct.FlowKind.Previews
+			)
+			if flow is not None:
+				setattr(
+					self,
+					'input_' + flow_kind.property_name,
+					bl_cache.Signal.InvalidateCache,
+				)
+
+	@bl_cache.cached_bl_property(depends_on={'auto_expr'})
+	def input_capabilities(self) -> ct.CapabilitiesFlow | None:
+		return self.get_flow(ct.FlowKind.Capabilities)
+
+	@bl_cache.cached_bl_property(depends_on={'auto_expr'})
+	def input_previews(self) -> ct.PreviewsFlow | None:
+		return self.get_flow(ct.FlowKind.Previews, always_load=True)
+
+	@bl_cache.cached_bl_property(depends_on={'auto_expr'})
+	def input_value(self) -> ct.ValueFlow | None:
+		return self.get_flow(ct.FlowKind.Value)
+
+	@bl_cache.cached_bl_property(depends_on={'auto_expr'})
+	def input_array(self) -> ct.ArrayFlow | None:
+		return self.get_flow(ct.FlowKind.Array)
+
+	@bl_cache.cached_bl_property(depends_on={'auto_expr'})
+	def input_lazy_range(self) -> ct.RangeFlow | None:
+		return self.get_flow(ct.FlowKind.Range)
+
+	@bl_cache.cached_bl_property(depends_on={'auto_expr'})
+	def input_lazy_func(self) -> ct.FuncFlow | None:
+		return self.get_flow(ct.FlowKind.Func)
+
+	@bl_cache.cached_bl_property(depends_on={'auto_expr'})
+	def input_params(self) -> ct.ParamsFlow | None:
+		return self.get_flow(ct.FlowKind.Params)
+
+	@bl_cache.cached_bl_property(depends_on={'auto_expr'})
+	def input_info(self) -> ct.InfoFlow | None:
+		return self.get_flow(ct.FlowKind.Info)
+
+	def get_flow(
+		self, flow_kind: ct.FlowKind, always_load: bool = False
+	) -> typ.Any | None:
+		"""Generic interface to simplify getting `FlowKind` properties on the viewer node."""
+		if self.auto_expr or always_load:
 			flow = self._compute_input('Any', kind=flow_kind)
 			has_flow = not ct.FlowSignal.check(flow)
 
 			if has_flow:
-				input_flow |= {flow_kind: flow}
-			else:
-				input_flow |= {flow_kind: None}
-
-		return input_flow
+				return flow
+			return None
+		return None
 
 	####################
 	# - Property: Input Expression String Lines
 	####################
-	@bl_cache.cached_bl_property(depends_on={'input_flow'})
+	@bl_cache.cached_bl_property(depends_on={'input_value'})
 	def input_expr_str_entries(self) -> list[list[str]] | None:
-		value = self.input_flow.get(ct.FlowKind.Value)
+		value = self.input_value
+		if value is None:
+			return None
 
+		# Parse SympyType
 		def sp_pretty(v: spux.SympyExpr) -> spux.SympyExpr:
-			## sp.pretty makes new lines and wreaks havoc.
+			## -> The real sp.pretty makes new lines and wreaks havoc.
 			return spux.sp_to_str(v.n(4))
 
 		if isinstance(value, spux.SympyType):
@@ -124,6 +172,25 @@ class ViewerNode(base.MaxwellSimNode):
 				]
 
 			return [[sp_pretty(value)]]
+
+		# Parse Tidy3D Types
+		if isinstance(value, td.Structure):
+			return [
+				[str(key), str(value)]
+				for key, value in dict(value).items()
+				if key not in ['type', 'geometry', 'medium']
+			] + [
+				[str(key), str(value)]
+				for key, value in dict(value.geometry).items()
+				if key != 'type'
+			]
+		if isinstance(value, td.components.base.Tidy3dBaseModel):
+			return [
+				[str(key), str(value)]
+				for key, value in dict(value).items()
+				if key != 'type'
+			]
+
 		return None
 
 	####################
@@ -132,12 +199,12 @@ class ViewerNode(base.MaxwellSimNode):
 	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout):
 		row = layout.row(align=True)
 
+		# Automatic Expression Printing
+		row.prop(self, self.blfields['auto_expr'], text='Live', toggle=True)
+
 		# Debug Mode On/Off
 		row.prop(self, self.blfields['debug_mode'], text='Debug', toggle=True)
 
-		# Automatic Expression Printing
-		row.prop(self, self.blfields['auto_expr'], text='Expr', toggle=True)
-
 		# Debug Mode Operators
 		if self.debug_mode:
 			layout.prop(self, self.blfields['console_print_kind'], text='')
@@ -210,47 +277,47 @@ class ViewerNode(base.MaxwellSimNode):
 	# - Methods
 	####################
 	def print_data_to_console(self):
-		if not self.inputs['Any'].is_linked:
-			return
+		flow = self._compute_input('Any', kind=self.console_print_kind)
 
 		log.info('Printing to Console')
-		data = self._compute_input('Any', kind=self.console_print_kind, optional=True)
-
-		if isinstance(data, spux.SympyType):
-			console.print(sp.pretty(data, use_unicode=True))
+		if isinstance(flow, spux.SympyType):
+			console.print(sp.pretty(flow, use_unicode=True))
 		else:
-			console.print(data)
+			console.print(flow)
 
 	####################
 	# - Event Methods
 	####################
 	@events.on_value_changed(
-		socket_name='Any',
-		prop_name='auto_plot',
-		props={'auto_plot'},
+		# Trigger
+		prop_name={'input_previews', 'auto_plot'},
+		# Loaded
+		props={'input_previews', 'auto_plot'},
 	)
 	def on_changed_plot_preview(self, props):
-		node_tree = self.id_data
+		previews = props['input_previews']
+		if previews is not None:
+			if props['auto_plot']:
+				bl_socket = self.inputs['Any']
+				if bl_socket.is_linked:
+					bl_socket.links[0].from_node.compute_plot()
 
-		# Unset Plot if Nothing Plotted
-		with node_tree.replot():
-			if props['auto_plot'] and self.inputs['Any'].is_linked:
-				self.inputs['Any'].links[0].from_socket.node.trigger_event(
-					ct.FlowEvent.ShowPlot
-				)
+			previews.update_image_preview()
+		else:
+			ct.PreviewsFlow.hide_image_preview()
 
 	@events.on_value_changed(
-		socket_name='Any',
-		prop_name='auto_3d_preview',
-		props={'auto_3d_preview'},
+		# Trigger
+		prop_name={'input_previews', 'auto_3d_preview'},
+		# Loaded
+		props={'input_previews', 'auto_3d_preview'},
 	)
 	def on_changed_3d_preview(self, props):
-		node_tree = self.id_data
-
-		# Remove Non-Repreviewed Previews on Close
-		with node_tree.repreview_all():
-			if props['auto_3d_preview']:
-				self.trigger_event(ct.FlowEvent.ShowPreview)
+		previews = props['input_previews']
+		if previews is not None and props['auto_3d_preview']:
+			previews.update_bl_object_previews()
+		else:
+			ct.PreviewsFlow.hide_bl_object_previews()
 
 
 ####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/simulations/fdtd_sim.py

@@ -64,20 +64,22 @@ class FDTDSimNode(base.MaxwellSimNode):
 		},
 	)
 	def compute_fdtd_sim(self, input_sockets: dict) -> sp.Expr:
-		## TODO: Visualize the boundary conditions on top of the sim domain
+		if any(ct.FlowSignal.check(inp) for inp in input_sockets):
+			return ct.FlowSignal.FlowPending
+
 		sim_domain = input_sockets['Domain']
 		sources = input_sockets['Sources']
 		structures = input_sockets['Structures']
 		bounds = input_sockets['BCs']
 		monitors = input_sockets['Monitors']
-
 		return td.Simulation(
-			**sim_domain,  ## run_time=, size=, grid=, medium=
+			**sim_domain,
 			structures=structures,
 			sources=sources,
 			monitors=monitors,
 			boundary_spec=bounds,
 		)
+		## TODO: Visualize the boundary conditions on top of the sim domain
 
 
 ####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/simulations/sim_domain.py

@@ -93,18 +93,14 @@ class SimDomainNode(base.MaxwellSimNode):
 	####################
 	# - Preview
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Domain',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		## Trigger

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/sources/gaussian_beam_source.py

@@ -165,18 +165,14 @@ class GaussianBeamSourceNode(base.MaxwellSimNode):
 	####################
 	# - Preview - Changes to Input Sockets
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Angled Source',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		# Trigger

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/sources/plane_wave_source.py

@@ -129,18 +129,14 @@ class PlaneWaveSourceNode(base.MaxwellSimNode):
 	####################
 	# - Preview - Changes to Input Sockets
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Angled Source',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		# Trigger

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/sources/point_dipole_source.py

@@ -104,18 +104,14 @@ class PointDipoleSourceNode(base.MaxwellSimNode):
 	####################
 	# - Preview
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Source',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		socket_name={'Center'},

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/structures/geonodes_structure.py

@@ -132,18 +132,14 @@ class GeoNodesStructureNode(base.MaxwellSimNode):
 	####################
 	# - Events: Preview
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Structure',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		# Trigger

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/structures/primitives/box_structure.py

@@ -16,13 +16,15 @@
 
 import typing as typ
 
+import bpy
 import sympy as sp
 import sympy.physics.units as spu
 import tidy3d as td
+import tidy3d.plugins.adjoint as tdadj
 
 from blender_maxwell.assets.geonodes import GeoNodes, import_geonodes
+from blender_maxwell.utils import bl_cache, logger
 from blender_maxwell.utils import extra_sympy_units as spux
-from blender_maxwell.utils import logger
 
 from .... import contracts as ct
 from .... import managed_objs, sockets
@@ -62,41 +64,172 @@ class BoxStructureNode(base.MaxwellSimNode):
 	}
 
 	####################
-	# - Outputs
+	# - Properties
+	####################
+	differentiable: bool = bl_cache.BLField(False)
+
+	####################
+	# - UI
+	####################
+	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout):
+		layout.prop(
+			self,
+			self.blfields['differentiable'],
+			text='Differentiable',
+			toggle=True,
+		)
+
+	####################
+	# - FlowKind.Value
 	####################
 	@events.computes_output_socket(
 		'Structure',
+		kind=ct.FlowKind.Value,
+		# Loaded
+		props={'differentiable'},
 		input_sockets={'Medium', 'Center', 'Size'},
-		unit_systems={'Tidy3DUnits': ct.UNITS_TIDY3D},
-		scale_input_sockets={
-			'Center': 'Tidy3DUnits',
-			'Size': 'Tidy3DUnits',
+		output_sockets={'Structure'},
+		output_socket_kinds={'Structure': ct.FlowKind.Params},
+	)
+	def compute_value(self, props, input_sockets, output_sockets) -> td.Box:
+		output_params = output_sockets['Structure']
+		center = input_sockets['Center']
+		size = input_sockets['Size']
+		medium = input_sockets['Medium']
+
+		has_output_params = not ct.FlowSignal.check(output_params)
+		has_center = not ct.FlowSignal.check(center)
+		has_size = not ct.FlowSignal.check(size)
+		has_medium = not ct.FlowSignal.check(medium)
+
+		if (
+			has_center
+			and has_size
+			and has_medium
+			and has_output_params
+			and not props['differentiable']
+			and not output_params.symbols
+		):
+			return td.Structure(
+				geometry=td.Box(
+					center=spux.scale_to_unit_system(center, ct.UNITS_TIDY3D),
+					size=spux.scale_to_unit_system(size, ct.UNITS_TIDY3D),
+				),
+				medium=medium,
+			)
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind.Func
+	####################
+	@events.computes_output_socket(
+		'Structure',
+		kind=ct.FlowKind.Func,
+		# Loaded
+		props={'differentiable'},
+		input_sockets={'Medium', 'Center', 'Size'},
+		input_socket_kinds={
+			'Medium': ct.FlowKind.Func,
+			'Center': ct.FlowKind.Func,
+			'Size': ct.FlowKind.Func,
+		},
+		output_sockets={'Structure'},
+		output_socket_kinds={'Structure': ct.FlowKind.Params},
+	)
+	def compute_lazy_structure(self, props, input_sockets, output_sockets) -> td.Box:
+		output_params = output_sockets['Structure']
+		center = input_sockets['Center']
+		size = input_sockets['Size']
+		medium = input_sockets['Medium']
+
+		has_output_params = not ct.FlowSignal.check(output_params)
+		has_center = not ct.FlowSignal.check(center)
+		has_size = not ct.FlowSignal.check(size)
+		has_medium = not ct.FlowSignal.check(medium)
+
+		differentiable = props['differentiable']
+		if (
+			has_output_params
+			and has_center
+			and has_size
+			and has_medium
+			and differentiable == output_params.is_differentiable
+		):
+			if differentiable:
+				return (center | size | medium).compose_within(
+					enclosing_func=lambda els: tdadj.JaxStructure(
+						geometry=tdadj.JaxBox(
+							center=tuple(els[0][0].flatten()),
+							size=tuple(els[0][1].flatten()),
+						),
+						medium=els[1],
+					),
+					supports_jax=True,
+				)
+			return (center | size | medium).compose_within(
+				enclosing_func=lambda els: td.Structure(
+					geometry=td.Box(
+						center=tuple(els[0][0].flatten()),
+						size=tuple(els[0][1].flatten()),
+					),
+					medium=els[1],
+				),
+				supports_jax=False,
+			)
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind.Params
+	####################
+	@events.computes_output_socket(
+		'Structure',
+		kind=ct.FlowKind.Params,
+		# Loaded
+		props={'differentiable'},
+		input_sockets={'Medium', 'Center', 'Size'},
+		input_socket_kinds={
+			'Medium': ct.FlowKind.Params,
+			'Center': ct.FlowKind.Params,
+			'Size': ct.FlowKind.Params,
 		},
 	)
-	def compute_structure(self, input_sockets, unit_systems) -> td.Box:
-		return td.Structure(
-			geometry=td.Box(
-				center=input_sockets['Center'],
-				size=input_sockets['Size'],
-			),
-			medium=input_sockets['Medium'],
-		)
+	def compute_params(self, props, input_sockets) -> td.Box:
+		center = input_sockets['Center']
+		size = input_sockets['Size']
+		medium = input_sockets['Medium']
+
+		has_center = not ct.FlowSignal.check(center)
+		has_size = not ct.FlowSignal.check(size)
+		has_medium = not ct.FlowSignal.check(medium)
+
+		if has_center and has_size and has_medium:
+			if props['differentiable'] == (
+				center.is_differentiable
+				& size.is_differentiable
+				& medium.is_differentiable
+			):
+				return center | size | medium
+			return ct.FlowSignal.FlowPending
+		return ct.FlowSignal.FlowPending
 
 	####################
 	# - Events: Preview
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Structure',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
+		output_sockets={'Structure'},
+		output_socket_kinds={'Structure': ct.FlowKind.Params},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews(self, props, output_sockets):
+		output_params = output_sockets['Structure']
+		has_output_params = not ct.FlowSignal.check(output_params)
+
+		if has_output_params and not output_params.symbols:
+			return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
+		return ct.PreviewsFlow()
 
 	@events.on_value_changed(
 		# Trigger
@@ -105,29 +238,26 @@ class BoxStructureNode(base.MaxwellSimNode):
 		# Loaded
 		input_sockets={'Center', 'Size'},
 		managed_objs={'modifier'},
-		unit_systems={'BlenderUnits': ct.UNITS_BLENDER},
-		scale_input_sockets={
-			'Center': 'BlenderUnits',
-		},
+		output_sockets={'Structure'},
+		output_socket_kinds={'Structure': ct.FlowKind.Params},
 	)
-	def on_inputs_changed(
-		self,
-		managed_objs,
-		input_sockets,
-		unit_systems,
-	):
-		# Push Loose Input Values to GeoNodes Modifier
-		managed_objs['modifier'].bl_modifier(
-			'NODES',
-			{
-				'node_group': import_geonodes(GeoNodes.StructurePrimitiveBox),
-				'unit_system': unit_systems['BlenderUnits'],
-				'inputs': {
-					'Size': input_sockets['Size'],
+	def on_inputs_changed(self, managed_objs, input_sockets, output_sockets):
+		output_params = output_sockets['Structure']
+		has_output_params = not ct.FlowSignal.check(output_params)
+		if has_output_params and not output_params.symbols:
+			# Push Loose Input Values to GeoNodes Modifier
+			center = input_sockets['Center']
+			managed_objs['modifier'].bl_modifier(
+				'NODES',
+				{
+					'node_group': import_geonodes(GeoNodes.StructurePrimitiveBox),
+					'unit_system': ct.UNITS_BLENDER,
+					'inputs': {
+						'Size': input_sockets['Size'],
+					},
 				},
-			},
-			location=input_sockets['Center'],
-		)
+				location=spux.scale_to_unit_system(center, ct.UNITS_BLENDER),
+			)
 
 
 ####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/structures/primitives/cylinder_structure.py

@@ -89,18 +89,14 @@ class CylinderStructureNode(base.MaxwellSimNode):
 	####################
 	# - Preview
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Structure',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		# Trigger

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/structures/primitives/sphere_structure.py

@@ -83,18 +83,14 @@ class SphereStructureNode(base.MaxwellSimNode):
 	####################
 	# - Preview
 	####################
-	@events.on_value_changed(
-		# Trigger
-		prop_name='preview_active',
+	@events.computes_output_socket(
+		'Structure',
+		kind=ct.FlowKind.Previews,
 		# Loaded
-		managed_objs={'modifier'},
-		props={'preview_active'},
+		props={'sim_node_name'},
 	)
-	def on_preview_changed(self, managed_objs, props):
-		if props['preview_active']:
-			managed_objs['modifier'].show_preview()
-		else:
-			managed_objs['modifier'].hide_preview()
+	def compute_previews(self, props):
+		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
 		# Trigger

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/base.py

@@ -50,8 +50,10 @@ class SocketDef(pyd.BaseModel, abc.ABC):
 		Parameters:
 			bl_socket: The Blender node socket to alter using data from this SocketDef.
 		"""
+		log.debug('%s: Start Socket Preinit', bl_socket.bl_label)
 		bl_socket.reset_instance_id()
 		bl_socket.regenerate_dynamic_field_persistance()
+		log.debug('%s: End Socket Preinit', bl_socket.bl_label)
 
 	def postinit(self, bl_socket: bpy.types.NodeSocket) -> None:
 		"""Pre-initialize a real Blender node socket from this socket definition.
@@ -59,8 +61,12 @@ class SocketDef(pyd.BaseModel, abc.ABC):
 		Parameters:
 			bl_socket: The Blender node socket to alter using data from this SocketDef.
 		"""
+		log.debug('%s: Start Socket Postinit', bl_socket.bl_label)
 		bl_socket.is_initializing = False
 		bl_socket.on_active_kind_changed()
+		bl_socket.on_socket_props_changed(set(bl_socket.blfields))
+		bl_socket.on_data_changed(set(ct.FlowKind))
+		log.debug('%s: End Socket Postinit', bl_socket.bl_label)
 
 	@abc.abstractmethod
 	def init(self, bl_socket: bpy.types.NodeSocket) -> None:
@@ -135,6 +141,8 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 	socket_type: ct.SocketType
 	bl_label: str
 
+	use_linked_capabilities: bool = bl_cache.BLField(False, use_prop_update=False)
+
 	## Computed by Subclass
 	bl_idname: str
 
@@ -181,17 +189,17 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 		"""
 		self.display_shape = self.active_kind.socket_shape
 
-	def on_socket_prop_changed(self, prop_name: str) -> None:
-		"""Called when a property has been updated.
+	def on_socket_props_changed(self, prop_names: set[str]) -> None:
+		"""Called when a set of properties has been updated.
 
 		Notes:
-			Can be overridden if a socket needs to respond to a property change.
+			Can be overridden if a socket needs to respond to property changes.
 
 			**Always prefer using node events instead of overriding this in a socket**.
 			Think **very carefully** before using this, and use it with the greatest of care.
 
 		Attributes:
-			prop_name: The name of the property that was changed.
+			prop_names: The set of property names that were changed.
 		"""
 
 	def on_prop_changed(self, prop_name: str) -> None:
@@ -207,30 +215,49 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 		Attributes:
 			prop_name: The name of the property that was changed.
 		"""
-		# All Attributes: Trigger Local Event
-		## -> While initializing, only `DataChanged` won't trigger.
-		if hasattr(self, prop_name):
-			# Property Callbacks: Active Kind
-			## -> WARNING: May NOT rely on flow.
-			if prop_name == 'active_kind':
+		# BLField Attributes: Invalidate BLField Dependents
+		## -> All invalidated blfields will have their caches cleared.
+		## -> The (topologically) ordered list of cleared blfields is returned.
+		## -> WARNING: The chain is not checked for ex. cycles.
+		if not self.is_initializing and prop_name in self.blfields:
+			cleared_blfields = self.clear_blfields_after(prop_name)
+			set_of_cleared_blfields = set(cleared_blfields)
+
+			# Property Callbacks: Internal
+			## -> NOTE: May NOT recurse on_prop_changed.
+			if ('active_kind', 'invalidate') in set_of_cleared_blfields:
+				# log.debug(
+				# '%s (NodeSocket): Changed Active Kind',
+				# self.bl_label,
+				# )
 				self.on_active_kind_changed()
 
 			# Property Callbacks: Per-Socket
-			## -> WARNING: May NOT rely on flow.
-			self.on_socket_prop_changed(prop_name)
+			## -> NOTE: User-defined handlers might recurse on_prop_changed.
+			self.is_initializing = True
+			self.on_socket_props_changed(set_of_cleared_blfields)
+			self.is_initializing = False
 
-			# Not Initializing: Trigger Event
-			## -> This declares that the socket has changed.
-			## -> This should happen first, in case dependents need a cache.
-			if not self.is_initializing:
-				self.trigger_event(ct.FlowEvent.DataChanged)
-
-		# BLField Attributes: Invalidate BLField Dependents
-		## -> Dependent props will generally also trigger on_prop_changed.
-		## -> The recursion ends with the depschain.
-		## -> WARNING: The chain is not checked for ex. cycles.
-		if prop_name in self.blfields:
-			self.invalidate_blfield_deps(prop_name)
+			# Trigger Event
+			## -> Before SocketDef.postinit(), never emit DataChanged.
+			## -> ONLY emit DataChanged if a FlowKind-bound prop was cleared.
+			## -> ONLY emit a single DataChanged w/set of altered FlowKinds.
+			## w/node's trigger_event, we've guaranteed a minimal action.
+			socket_kinds = {
+				ct.FlowKind.from_property_name(prop_name)
+				for prop_name in {
+					prop_name
+					for prop_name, clear_method in set_of_cleared_blfields
+					if clear_method == 'invalidate'
+				}.intersection(ct.FlowKind.property_names)
+			}
+			# log.debug(
+			# '%s (NodeSocket): Computed SocketKind Frontier: %s',
+			# self.bl_label,
+			# str(socket_kinds),
+			# )
+			if socket_kinds:
+				self.trigger_event(ct.FlowEvent.DataChanged, socket_kinds=socket_kinds)
 
 	####################
 	# - Link Event: Consent / On Change
@@ -273,11 +300,29 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 			return False
 
 		# Capability Check
-		if not link.from_socket.capabilities.is_compatible_with(self.capabilities):
+		## -> "Use Linked Capabilities" allow sockets flow-dependent caps.
+		## -> The tradeoff: No link if there is no InfoFlow.
+		if self.use_linked_capabilities:
+			info = self.compute_data(kind=ct.FlowKind.Info)
+			has_info = not ct.FlowSignal.check(info)
+			if has_info:
+				incoming_capabilities = link.from_socket.linked_capabilities(info)
+			else:
+				log.error(
+					'Attempted to link output socket "%s" to input socket "%s" (%s), but linked capabilities of the output socket could not be determined',
+					link.from_socket.bl_label,
+					self.bl_label,
+					self.capabilities,
+				)
+				return False
+		else:
+			incoming_capabilities = link.from_socket.capabilities
+
+		if not incoming_capabilities.is_compatible_with(self.capabilities):
 			log.error(
 				'Attempted to link output socket "%s" (%s) to input socket "%s" (%s), but capabilities are incompatible',
 				link.from_socket.bl_label,
-				link.from_socket.capabilities,
+				incoming_capabilities,
 				self.bl_label,
 				self.capabilities,
 			)
@@ -288,6 +333,8 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 	def on_link_added(self, link: bpy.types.NodeLink) -> None:  # noqa: ARG002
 		"""Triggers a `ct.FlowEvent.LinkChanged` event when a link is added.
 
+		Calls `self.trigger_event()` with `FlowKind`s, since an added link requires recomputing **all** data that depends on flow.
+
 		Notes:
 			Called by the node tree, generally (but not guaranteed) after `self.allow_add_link()` has given consent to add the link.
 
@@ -295,7 +342,7 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 			link: The node link that was added.
 				Currently unused.
 		"""
-		self.trigger_event(ct.FlowEvent.LinkChanged)
+		self.trigger_event(ct.FlowEvent.LinkChanged, socket_kinds=set(ct.FlowKind))
 
 	def allow_remove_link(self, from_socket: bpy.types.NodeSocket) -> bool:  # noqa: ARG002
 		"""Called to ask whether a link may be removed from this `to_socket`.
@@ -333,6 +380,8 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 	def on_link_removed(self, from_socket: bpy.types.NodeSocket) -> None:  # noqa: ARG002
 		"""Triggers a `ct.FlowEvent.LinkChanged` event when a link is removed.
 
+		Calls `self.trigger_event()` with `FlowKind`s, since a removed link requires recomputing **all** data that depends on flow.
+
 		Notes:
 			Called by the node tree, generally (but not guaranteed) after `self.allow_remove_link()` has given consent to remove the link.
 
@@ -340,7 +389,7 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 			from_socket: The node socket that was attached to before link removal.
 				Currently unused.
 		"""
-		self.trigger_event(ct.FlowEvent.LinkChanged)
+		self.trigger_event(ct.FlowEvent.LinkChanged, socket_kinds=set(ct.FlowKind))
 
 	def remove_invalidated_links(self) -> None:
 		"""Reevaluates the capabilities of all socket links, and removes any that no longer match.
@@ -371,6 +420,41 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 	####################
 	# - Event Chain
 	####################
+	def on_data_changed(self, socket_kinds: set[ct.FlowKind]) -> None:
+		"""Called when `ct.FlowEvent.DataChanged` flows through this socket.
+
+		Parameters:
+			socket_kinds: The altered `ct.FlowKind`s flowing through.
+		"""
+		self.on_socket_data_changed(socket_kinds)
+
+	def on_socket_data_changed(self, socket_kinds: set[ct.FlowKind]) -> None:
+		"""Called when `ct.FlowEvent.DataChanged` flows through this socket.
+
+		Notes:
+			Can be overridden if a socket needs to respond to `DataChanged` in a custom way.
+
+			**Always prefer using node events instead of overriding this in a socket**.
+			Think **very carefully** before using this, and use it with the greatest of care.
+
+		Parameters:
+			socket_kinds: The altered `ct.FlowKind`s flowing through.
+		"""
+
+	def on_link_changed(self) -> None:
+		"""Called when `ct.FlowEvent.LinkChanged` flows through this socket."""
+		self.on_socket_link_changed()
+
+	def on_socket_link_changed(self) -> None:
+		"""Called when `ct.FlowEvent.LinkChanged` flows through this socket.
+
+		Notes:
+			Can be overridden if a socket needs to respond to `LinkChanged` in a custom way.
+
+			**Always prefer using node events instead of overriding this in a socket**.
+			Think **very carefully** before using this, and use it with the greatest of care.
+		"""
+
 	def trigger_event(
 		self,
 		event: ct.FlowEvent,
@@ -384,7 +468,6 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 		- **Output Socket -> Input**: Trigger event on node (w/`socket_name`).
 		- **Output Socket -> Output**: Trigger event on `to_socket`s along output links.
 
-
 		Notes:
 			This can be an unpredictably heavy function, depending on the node graph topology.
 
@@ -395,11 +478,41 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 			event: The event to report along the node tree.
 				The value of `ct.FlowEvent.flow_direction[event]` (`input` or `output`) determines the direction that an event flows.
 		"""
+		# log.debug(
+		# '[%s] [%s] Triggered (socket_kinds=%s)',
+		# self.name,
+		# event,
+		# str(socket_kinds),
+		# )
+		# Local DataChanged Callbacks
+		## -> socket_kinds MUST NOT be None
+		if event is ct.FlowEvent.DataChanged:
+			# WORKAROUND
+			## -> Altering value/lazy_range like this causes MANY DataChanged
+			## -> If we pretend we're initializing, we can block on_prop_changed
+			## -> This works because _unit conversion doesn't change the value_
+			## -> Only the displayed values change - which are inv. on __set__.
+			## -> For this reason alone, we can get away with it :)
+			## -> TODO: This is not clean :)
+			self.is_initializing = True
+			self.on_data_changed(socket_kinds)
+			self.is_initializing = False
+
+		# Local LinkChanged Callbacks
+		## -> socket_kinds MUST NOT be None
+		if event is ct.FlowEvent.LinkChanged:
+			self.is_initializing = True
+			self.on_link_changed()
+			self.on_data_changed(socket_kinds)
+			self.is_initializing = False
+
 		flow_direction = ct.FlowEvent.flow_direction[event]
 
 		# Locking
-		if event in [ct.FlowEvent.EnableLock, ct.FlowEvent.DisableLock]:
-			self.locked = event == ct.FlowEvent.EnableLock
+		if event is ct.FlowEvent.EnableLock:
+			self.locked = True
+		elif event is ct.FlowEvent.DisableLock:
+			self.locked = False
 
 		# Event by Socket Orientation | Flow Direction
 		match (self.is_output, flow_direction):
@@ -408,7 +521,7 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 					link.from_socket.trigger_event(event, socket_kinds=socket_kinds)
 
 			case (False, 'output'):
-				if event == ct.FlowEvent.LinkChanged:
+				if event is ct.FlowEvent.LinkChanged:
 					self.node.trigger_event(
 						ct.FlowEvent.DataChanged,
 						socket_name=self.name,
@@ -432,6 +545,10 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 	# - FlowKind: Auxiliary
 	####################
 	# Capabilities
+	def linked_capabilities(self, info: ct.InfoFlow) -> ct.CapabilitiesFlow:
+		"""Try this first when `is_linked and use_linked_capabilities`."""
+		raise NotImplementedError
+
 	@property
 	def capabilities(self) -> None:
 		"""By default, the socket is linkeable with any other socket of the same type and active kind.
@@ -592,21 +709,16 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 		Raises:
 			ValueError: When referencing a socket that's meant to be directly referenced.
 		"""
-		kind_data_map = {
+		return {
 			ct.FlowKind.Capabilities: lambda: self.capabilities,
+			ct.FlowKind.Previews: lambda: ct.PreviewsFlow(),
 			ct.FlowKind.Value: lambda: self.value,
 			ct.FlowKind.Array: lambda: self.array,
 			ct.FlowKind.Func: lambda: self.lazy_func,
 			ct.FlowKind.Range: lambda: self.lazy_range,
 			ct.FlowKind.Params: lambda: self.params,
 			ct.FlowKind.Info: lambda: self.info,
-		}
-		if kind in kind_data_map:
-			return kind_data_map[kind]()
-
-		## TODO: Reflect this constraint in the type
-		msg = f'Socket {self.bl_label} ({self.socket_type}): Kind {kind} cannot be computed within a socket "compute_data", as it is meant to be referenced directly'
-		raise ValueError(msg)
+		}[kind]()
 
 	def compute_data(
 		self,
@@ -635,7 +747,7 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 			return self.node.compute_output(self.name, kind=kind)
 
 		# Compute Input Socket
-		## Unlinked: Retrieve Socket Value
+		## -> Unlinked: Retrieve Socket Value
 		if not self.is_linked:
 			return self._compute_data(kind)
 
@@ -645,7 +757,8 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 		linked_values = [link.from_socket.compute_data(kind) for link in self.links]
 
 		# Return Single Value / List of Values
-		if len(linked_values) == 1:
+		## -> Multi-input sockets are not yet supported.
+		if linked_values:
 			return linked_values[0]
 
 		# Edge Case: While Dragging Link (but not yet removed)
@@ -653,11 +766,7 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 		## - self.is_linked = True, since the user hasn't confirmed anything.
 		## - self.links will be empty, since the link object was freed.
 		## When this particular condition is met, pretend that we're not linked.
-		if len(linked_values) == 0:
-			return self._compute_data(kind)
-
-		msg = f'Socket {self.bl_label} ({self.socket_type}): Multi-input sockets are not yet supported'
-		raise NotImplementedError(msg)
+		return self._compute_data(kind)
 
 	####################
 	# - UI - Color

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/basic/any.py

@@ -14,6 +14,8 @@
 # You should have received a copy of the GNU Affero General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
+from blender_maxwell.utils import bl_cache
+
 from ... import contracts as ct
 from .. import base
 
@@ -25,8 +27,8 @@ class AnyBLSocket(base.MaxwellSimSocket):
 	socket_type = ct.SocketType.Any
 	bl_label = 'Any'
 
-	@property
-	def capabilities(self):
+	@bl_cache.cached_bl_property(depends_on={'active_kind'})
+	def capabilities(self) -> ct.CapabilitiesFlow:
 		return ct.CapabilitiesFlow(
 			socket_type=self.socket_type,
 			active_kind=self.active_kind,

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/basic/bool.py

@@ -16,7 +16,7 @@
 
 import bpy
 
-from blender_maxwell.utils import bl_cache, logger
+from blender_maxwell.utils import bl_cache
 
 from ... import contracts as ct
 from .. import base
@@ -43,7 +43,7 @@ class BoolBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Computation of Default Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'raw_value'})
 	def value(self) -> bool:
 		return self.raw_value
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/basic/file_path.py

@@ -48,7 +48,7 @@ class FilePathBLSocket(base.MaxwellSimSocket):
 	####################
 	# - FlowKind: Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'raw_value'})
 	def value(self) -> Path:
 		return self.raw_value
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/basic/string.py

@@ -16,6 +16,8 @@
 
 import bpy
 
+from blender_maxwell.utils import bl_cache
+
 from ... import contracts as ct
 from .. import base
 
@@ -30,12 +32,7 @@ class StringBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Properties
 	####################
-	raw_value: bpy.props.StringProperty(
-		name='String',
-		description='Represents a string',
-		default='',
-		update=(lambda self, context: self.on_prop_changed('raw_value', context)),
-	)
+	raw_value: str = bl_cache.BLField('')
 
 	####################
 	# - Socket UI
@@ -46,7 +43,7 @@ class StringBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Computation of Default Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'raw_value'})
 	def value(self) -> str:
 		return self.raw_value
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/blender/geonodes.py

@@ -71,7 +71,7 @@ class BlenderGeoNodesBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Default Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'raw_value'})
 	def value(self) -> bpy.types.NodeTree | ct.FlowSignal:
 		return self.raw_value if self.raw_value is not None else ct.FlowSignal.NoFlow
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/blender/image.py

@@ -16,6 +16,8 @@
 
 import bpy
 
+from blender_maxwell.utils import bl_cache, logger
+
 from ... import contracts as ct
 from .. import base
 
@@ -30,12 +32,7 @@ class BlenderImageBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Properties
 	####################
-	raw_value: bpy.props.PointerProperty(
-		name='Blender Image',
-		description='Represents a Blender Image',
-		type=bpy.types.Image,
-		update=(lambda self, context: self.on_prop_changed('raw_value', context)),
-	)
+	raw_value: bpy.types.Image = bl_cache.BLField()
 
 	####################
 	# - UI
@@ -46,7 +43,7 @@ class BlenderImageBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Default Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'raw_value'})
 	def value(self) -> bpy.types.Image | None:
 		return self.raw_value
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/blender/material.py

@@ -16,6 +16,8 @@
 
 import bpy
 
+from blender_maxwell.utils import bl_cache, logger
+
 from ... import contracts as ct
 from .. import base
 
@@ -27,12 +29,7 @@ class BlenderMaterialBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Properties
 	####################
-	raw_value: bpy.props.PointerProperty(
-		name='Blender Material',
-		description='Represents a Blender material',
-		type=bpy.types.Material,
-		update=(lambda self, context: self.on_prop_changed('raw_value', context)),
-	)
+	raw_value: bpy.types.Material = bl_cache.BLField()
 
 	####################
 	# - UI
@@ -43,7 +40,7 @@ class BlenderMaterialBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Default Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'raw_value'})
 	def value(self) -> bpy.types.Material | None:
 		return self.raw_value
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/blender/object.py

@@ -16,29 +16,12 @@
 
 import bpy
 
+from blender_maxwell.utils import bl_cache, logger
+
 from ... import contracts as ct
 from .. import base
 
-
-####################
-# - Create and Assign BL Object
-####################
-class BlenderMaxwellCreateAndAssignBLObject(bpy.types.Operator):
-	bl_idname = 'blender_maxwell.create_and_assign_bl_object'
-	bl_label = 'Create and Assign BL Object'
-
-	node_tree_name = bpy.props.StringProperty(name='Node Tree Name')
-	node_name = bpy.props.StringProperty(name='Node Name')
-	socket_name = bpy.props.StringProperty(name='Socket Name')
-
-	def execute(self, context):
-		node_tree = bpy.data.node_groups[self.node_tree_name]
-		node = node_tree.nodes[self.node_name]
-		socket = node.inputs[self.socket_name]
-
-		socket.create_and_assign_bl_object()
-
-		return {'FINISHED'}
+log = logger.get(__name__)
 
 
 ####################
@@ -51,47 +34,18 @@ class BlenderObjectBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Properties
 	####################
-	raw_value: bpy.props.PointerProperty(
-		name='Blender Object',
-		description='Represents a Blender object',
-		type=bpy.types.Object,
-		update=(lambda self, context: self.on_prop_changed('raw_value', context)),
-	)
+	raw_value: bpy.types.Object = bl_cache.BLField()
 
 	####################
 	# - UI
 	####################
-	def draw_label_row(self, label_col_row, text):
-		label_col_row.label(text=text)
-
-		op = label_col_row.operator(
-			'blender_maxwell.create_and_assign_bl_object',
-			text='',
-			icon='ADD',
-		)
-		op.socket_name = self.name
-		op.node_name = self.node.name
-		op.node_tree_name = self.node.id_data.name
-
 	def draw_value(self, col: bpy.types.UILayout) -> None:
 		col.prop(self, 'raw_value', text='')
 
-	####################
-	# - Methods
-	####################
-	def create_and_assign_bl_object(self):
-		node_tree = self.node.id_data
-		mesh = bpy.data.meshes.new('MaxwellMesh')
-		new_bl_object = bpy.data.objects.new('MaxwellObject', mesh)
-
-		bpy.context.collection.objects.link(new_bl_object)
-
-		self.value = new_bl_object
-
 	####################
 	# - Default Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'raw_value'})
 	def value(self) -> bpy.types.Object | None:
 		return self.raw_value
 
@@ -114,6 +68,5 @@ class BlenderObjectSocketDef(base.SocketDef):
 # - Blender Registration
 ####################
 BL_REGISTER = [
-	BlenderMaxwellCreateAndAssignBLObject,
 	BlenderObjectBLSocket,
 ]

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/blender/text.py

@@ -16,9 +16,13 @@
 
 import bpy
 
+from blender_maxwell.utils import bl_cache, logger
+
 from ... import contracts as ct
 from .. import base
 
+log = logger.get(__name__)
+
 
 ####################
 # - Blender Socket
@@ -30,12 +34,7 @@ class BlenderTextBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Properties
 	####################
-	raw_value: bpy.props.PointerProperty(
-		name='Blender Text',
-		description='Represents a Blender text datablock',
-		type=bpy.types.Text,
-		update=(lambda self, context: self.on_prop_changed('raw_value', context)),
-	)
+	raw_value: bpy.types.Text = bl_cache.BLField()
 
 	####################
 	# - UI
@@ -46,7 +45,7 @@ class BlenderTextBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Default Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'raw_value'})
 	def value(self) -> bpy.types.Text:
 		return self.raw_value
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/expr.py

@@ -64,21 +64,21 @@ class InfoDisplayCol(enum.StrEnum):
 
 	@staticmethod
 	def to_name(value: typ.Self) -> str:
+		"""Friendly, single-letter, human-readable column names.
+
+		Must be concise, as there is not a lot of header space to contain these.
+		"""
 		IDC = InfoDisplayCol
 		return {
 			IDC.Length: 'L',
-			IDC.MathType: '∈',
+			IDC.MathType: 'M',
 			IDC.Unit: 'U',
 		}[value]
 
 	@staticmethod
-	def to_icon(value: typ.Self) -> str:
-		IDC = InfoDisplayCol
-		return {
-			IDC.Length: '',
-			IDC.MathType: '',
-			IDC.Unit: '',
-		}[value]
+	def to_icon(_: typ.Self) -> str:
+		"""No icons."""
+		return ''
 
 
 ####################
@@ -109,6 +109,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 
 	socket_type = ct.SocketType.Expr
 	bl_label = 'Expr'
+	use_socket_color = True
 
 	####################
 	# - Socket Interface
@@ -117,6 +118,58 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	mathtype: spux.MathType = bl_cache.BLField(spux.MathType.Real)
 	physical_type: spux.PhysicalType = bl_cache.BLField(spux.PhysicalType.NonPhysical)
 
+	@bl_cache.cached_bl_property(
+		depends_on={
+			'active_kind',
+			'symbols',
+			'raw_value_spstr',
+			'raw_min_spstr',
+			'raw_max_spstr',
+			'output_name',
+			'mathtype',
+			'physical_type',
+			'unit',
+			'size',
+		}
+	)
+	def output_sym(self) -> sim_symbols.SimSymbol | None:
+		"""Compute an appropriate `SimSymbol` to represent the mathematical and physical properties of the socket's own output.
+
+		For the parsed string expression, functionality is derived heavily from the internal method `self._parse_expr_symbol()`.
+
+		Raises:
+			NotImplementedError: When `active_kind` is neither `Value`, `Func`, or `Range`.
+		"""
+		if self.symbols:
+			if self.active_kind in [ct.FlowKind.Value, ct.FlowKind.Func]:
+				return self._parse_expr_symbol(
+					self._parse_expr_str(self.raw_value_spstr)
+				)
+
+			if self.active_kind is ct.FlowKind.Range:
+				## TODO: Support RangeFlow
+				## -- It's hard; we need a min-span set over bound domains.
+				## -- We... Don't use this anywhere. Yet?
+				# sym_start = self._parse_expr_symbol(
+				# self._parse_expr_str(self.raw_min_spstr)
+				# )
+				# sym_stop = self._parse_expr_symbol(
+				# self._parse_expr_str(self.raw_max_spstr)
+				# )
+				msg = 'RangeFlow support not yet implemented for when self.symbols is not empty'
+				raise NotImplementedError(msg)
+
+			raise NotImplementedError
+
+		return sim_symbols.SimSymbol(
+			sym_name=self.output_name,
+			mathtype=self.mathtype,
+			physical_type=self.physical_type,
+			unit=self.unit,
+			rows=self.size.rows,
+			cols=self.size.cols,
+		)
+
 	####################
 	# - Symbols
 	####################
@@ -140,6 +193,11 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		"""Computes `sympy` symbols from `self.sorted_symbols`."""
 		return [sym.sp_symbol_matsym for sym in self.sorted_symbols]
 
+	@bl_cache.cached_bl_property(depends_on={'symbols'})
+	def sorted_symbol_names(self) -> list[sp.Symbol | sp.MatrixSymbol]:
+		"""Computes the name of symbols in `self.sorted_symbols`."""
+		return [sym.name for sym in self.sorted_symbols]
+
 	####################
 	# - Units
 	####################
@@ -171,8 +229,13 @@ class ExprBLSocket(base.MaxwellSimSocket):
 
 		return None
 
-	@property
+	@bl_cache.cached_bl_property(depends_on={'unit'})
 	def unit_factor(self) -> spux.Unit | None:
+		"""Gets the current active unit as a factor, where unitless is `1`.
+
+		Returns:
+			Same as `self.unit`, except `1` instead of `None` when there is no units.
+		"""
 		return sp.Integer(1) if self.unit is None else self.unit
 
 	prev_unit: str | None = bl_cache.BLField(None)
@@ -228,26 +291,92 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Computed String Expressions
 	####################
-	@bl_cache.cached_bl_property(depends_on={'raw_value_spstr'})
+	@bl_cache.cached_bl_property(
+		depends_on={'raw_value_spstr', 'sorted_symbol_names', 'symbols'}
+	)
 	def raw_value_sp(self) -> spux.SympyExpr:
+		"""Parse the given symbolic `FlowKind.Value` string into a `sympy` expression.
+
+		Notes:
+			The `self.*` properties used by `_parse_expr_str` must be included in the `depends_on` of any `cached_bl_property`s that use it.
+
+		Directly derived from the internal method `self._parse_expr_str()`, which acts on `raw_value_spstr`.
+		"""
 		return self._parse_expr_str(self.raw_value_spstr)
 
-	@bl_cache.cached_bl_property(depends_on={'raw_min_spstr'})
+	@bl_cache.cached_bl_property(
+		depends_on={'raw_min_spstr', 'sorted_symbol_names', 'symbols'}
+	)
 	def raw_min_sp(self) -> spux.SympyExpr:
+		"""Parse the given symbolic `FlowKind.Range` string (for the lower bound) into a `sympy` expression.
+
+		Notes:
+			The `self.*` properties used by `_parse_expr_str` must be included in the `depends_on` of any `cached_bl_property`s that use it.
+
+		Directly derived from the internal method `self._parse_expr_str()`, which acts on `raw_min_spstr`.
+		"""
 		return self._parse_expr_str(self.raw_min_spstr)
 
-	@bl_cache.cached_bl_property(depends_on={'raw_max_spstr'})
+	@bl_cache.cached_bl_property(
+		depends_on={'raw_max_spstr', 'sorted_symbol_names', 'symbols'}
+	)
 	def raw_max_sp(self) -> spux.SympyExpr:
+		"""Parse the given symbolic `FlowKind.Range` string (for the upper bound) into a `sympy` expression.
+
+		Notes:
+			The `self.*` properties used by `_parse_expr_str` must be included in the `depends_on` of any `cached_bl_property`s that use it.
+
+		Directly derived from the internal method `self._parse_expr_str()`, which acts on `raw_max_spstr`.
+		"""
 		return self._parse_expr_str(self.raw_max_spstr)
 
 	####################
-	# - Prop-Change Callback
+	# - Event Callbacks
 	####################
-	def on_socket_prop_changed(self, prop_name: str) -> None:
+	def on_socket_data_changed(self, socket_kinds: set[ct.FlowKind]) -> None:
+		"""Alter the socket's color in response to flow.
+
+		- `FlowKind.Info`: Any change causes the socket color to be updated with the physical type of the output symbol.
+
+		Notes:
+			Overridden method called whenever `FlowEvent.LinkChanged` is generated on this socket, in response to link add/link remove.
+
+			See `MaxwellSimTree` for more detail on the link callbacks.
+		"""
+		## NODE: Depends on suppressed on_prop_changed
+
+		if ct.FlowKind.Info in socket_kinds:
+			info = self.compute_data(kind=ct.FlowKind.Info)
+			has_info = not ct.FlowSignal.check(info)
+
+			# Alter Color
+			pt_color = (
+				info.output.physical_type.color
+				if has_info
+				else self.physical_type.color
+			)
+			if self.socket_color != pt_color:
+				self.socket_color = pt_color
+
+	def on_socket_props_changed(
+		self,
+		cleared_blfields: set[
+			tuple[str, typ.Literal['invalidate', 'reset_enum', 'reset_strsearch']]
+		],
+	) -> None:
+		"""Alter the socket in response to local property changes.
+
+		Notes:
+			Overridden method called whenever `FlowEvent.LinkChanged` is generated on this socket, in response to link add/link remove.
+
+			See `MaxwellSimTree` for more detail on the link callbacks.
+		"""
+		## NODE: Depends on suppressed on_prop_changed
+
 		# Conditional Unit-Conversion
 		## -> This is niche functionality, but the only way to convert units.
 		## -> We can only catch 'unit' since it's at the end of a depschain.
-		if prop_name == 'unit':
+		if ('unit', 'invalidate') in cleared_blfields:
 			# Check Unit Change
 			## -> self.prev_unit only updates here; "lags" behind self.unit.
 			## -> 1. "Laggy" unit must be different than new unit.
@@ -272,37 +401,6 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Value Utilities
 	####################
-	def _parse_expr_info(
-		self, expr: spux.SympyExpr
-	) -> tuple[spux.MathType, tuple[int, ...] | None, spux.UnitDimension]:
-		"""Parse a given expression for mathtype and size information.
-
-		Various compatibility checks are also performed, allowing this method to serve as a generic runtime validator/parser for any expressions that need to enter the socket.
-		"""
-		# Parse MathType
-		mathtype = spux.MathType.from_expr(expr)
-		if not self.mathtype.is_compatible(mathtype):
-			msg = f'MathType is {self.mathtype}, but tried to set expr {expr} with mathtype {mathtype}'
-			raise ValueError(msg)
-
-		# Parse Symbols
-		if expr.free_symbols and not expr.free_symbols.issubset(self.sp_symbols):
-			msg = f'Tried to set expr {expr} with free symbols {expr.free_symbols}, which is incompatible with socket symbols {self.symbols}'
-			raise ValueError(msg)
-
-		# Parse Dimensions
-		shape = spux.parse_shape(expr)
-		if not self.size.supports_shape(shape):
-			msg = f'Expr {expr} has non-1D shape {shape}, which is incompatible with the expr socket (shape {self.shape})'
-			raise ValueError(msg)
-
-		size = spux.NumberSize1D.from_shape(shape)
-		if self.size != size:
-			msg = f'Expr {expr} has 1D size {size}, which is incompatible with the expr socket (size {self.size})'
-			raise ValueError(msg)
-
-		return mathtype, size
-
 	def _to_raw_value(self, expr: spux.SympyExpr, force_complex: bool = False):
 		"""Cast the given expression to the appropriate raw value, with scaling guided by `self.unit`."""
 		if self.unit is not None:
@@ -324,38 +422,117 @@ class ExprBLSocket(base.MaxwellSimSocket):
 
 		return pyvalue
 
+	def _parse_expr_symbol(
+		self, expr: spux.SympyExpr | None
+	) -> sim_symbols.SimSymbol | None:
+		"""Deduce the `SimSymbol` corresponding to the given `expr`, else None."""
+		if expr is not None and (
+			not expr.free_symbols or expr.free_symbols.issubset(self.sp_symbols)
+		):
+			# Compute Units of Expression
+			## -> The output units may not be physically meaningful.
+			## -> However, "weird units" may be a good indicator of problems.
+			## -> So, we let the user shoot their foot off.
+			unit_expr = expr.subs(
+				{sym.sp_symbol: sym.unit_factor for sym in self.symbols}
+			)
+
+			return sim_symbols.SimSymbol.from_expr(
+				self.output_name, expr, unit_expr, optional=True
+			)
+
+		return None
+
 	def _parse_expr_str(self, expr_spstr: str) -> spux.SympyExpr | None:
 		"""Parse an expression string by choosing opinionated options for `sp.sympify`.
 
-		Uses `self._parse_expr_info()` to validate the parsed result.
+		Uses `self._parse_expr_symbol()` to validate the parsed result.
 
 		Returns:
 			The parsed expression, if it manages to validate; else None.
 		"""
-		expr = sp.sympify(
+		expr = sp.parsing.sympy_parser.parse_expr(
 			expr_spstr,
-			locals={sym.name: sym.sp_symbol_matsym for sym in self.symbols},
-			strict=False,
-			convert_xor=True,
-		).subs(spux.UNIT_BY_SYMBOL)
+			local_dict=(
+				{sym.name: sym.sp_symbol_matsym for sym in self.symbols}
+				| {sym.name: unit for sym, unit in spux.UNIT_BY_SYMBOL.items()}
+			),
+			transformations=[
+				# Lambda Notation: Symbolic Anonymous Functions
+				## -> Interpret 'lambda: x/8' to sp.Lambda((), x/0)
+				sp.parsing.sympy_parser.lambda_notation,
+				# Automatic Symbols
+				## -> Interpret known functions as their sympy equivs.
+				## -> Interpret unknown 'x' as sp.Symbol('x')
+				## -> NOTE: Must check for extraneous/unwelcome unknowns.
+				sp.parsing.sympy_parser.auto_symbol,
+				# Repeated Decimals
+				## -> Interpret '0.2[1]' as 0.211111...
+				sp.parsing.sympy_parser.repeated_decimals,
+				# Number Literals
+				## -> Interpret ints/float literals.
+				## -> Interpret 'I' as the imaginary number literal.
+				## -> TODO: Maybe special-case the variable name 'I'?
+				sp.parsing.sympy_parser.auto_number,
+				# Factorial Notation
+				## -> Allow 'x!' to be the factorial of x.
+				sp.parsing.sympy_parser.factorial_notation,
+				# Rationalize Float -> Rational
+				## -> Helps numerical stability for pure-symbolic math.
+				## -> AFTER auto_number
+				sp.parsing.sympy_parser.rationalize,
+				# Carrot Exponentiation
+				## -> Interpret '^' as power, instead of as XOR.
+				sp.parsing.sympy_parser.convert_xor,
+				# Symbol Splitting
+				## -> Interpret 'xyz' as 'x*y*z' for convenience.
+				## -> NEVER split greek character names (ex. theta).
+				## -> NEVER split symbol names in 'self.symbols'.
+				sp.parsing.sympy_parser.split_symbols_custom(
+					predicate=lambda sym_name: (
+						sp.parsing.sympy_parser._token_splittable(sym_name)  # noqa: SLF001
+						if sym_name not in self.sorted_symbol_names
+						else False
+					)
+				),
+				# Implicit Mult/Call
+				## -> Most times, allow '2x' as '2*x' / '2 x y' as '2*x*y'.
+				## -> Sometimes, allow 'sin 2x' as 'sin(2*x)'
+				## -> Allow functions to be exponentiated ex. 'sin^2 x'
+				sp.parsing.sympy_parser.implicit_multiplication,
+				sp.parsing.sympy_parser.implicit_application,
+				sp.parsing.sympy_parser.function_exponentiation,
+			],
+		)
 
-		# Try Parsing and Returning the Expression
-		try:
-			self._parse_expr_info(expr)
-		except ValueError:
-			log.exception(
-				'Couldn\'t parse expression "%s" in Expr socket.',
-				expr_spstr,
-			)
-		else:
+		if self._parse_expr_symbol(expr) is not None:
 			return expr
-
 		return None
 
 	####################
 	# - FlowKind: Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(
+		depends_on={
+			'symbols',
+			'unit',
+			'mathtype',
+			'size',
+			'raw_value_sp',
+			'raw_value_int',
+			'raw_value_rat',
+			'raw_value_float',
+			'raw_value_complex',
+			'raw_value_int2',
+			'raw_value_rat2',
+			'raw_value_float2',
+			'raw_value_complex2',
+			'raw_value_int3',
+			'raw_value_rat3',
+			'raw_value_float3',
+			'raw_value_complex3',
+		}
+	)
 	def value(self) -> spux.SympyExpr:
 		"""Return the expression defined by the socket as `FlowKind.Value`.
 
@@ -382,8 +559,8 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		## -> ExprSocket doesn't support Vec4 (yet?).
 		## -> I mean, have you _seen_ that mess of attributes up top?
 		NS = spux.NumberSize1D
-		if self.size == NS.Vec4:
-			return ct.Flow
+		if self.size is NS.Vec4:
+			return ct.FlowSignal.NoFlow
 
 		MT_Z = spux.MathType.Integer
 		MT_Q = spux.MathType.Rational
@@ -430,7 +607,6 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		Notes:
 			Called to set the internal `FlowKind.Value` of this socket.
 		"""
-		_mathtype, _size = self._parse_expr_info(expr)
 		if self.symbols:
 			self.raw_value_spstr = sp.sstr(expr)
 		else:
@@ -473,7 +649,22 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	####################
 	# - FlowKind: Range
 	####################
-	@property
+	@bl_cache.cached_bl_property(
+		depends_on={
+			'symbols',
+			'unit',
+			'mathtype',
+			'size',
+			'steps',
+			'scaling',
+			'raw_min_sp',
+			'raw_max_sp',
+			'raw_range_int',
+			'raw_range_rat',
+			'raw_range_float',
+			'raw_range_complex',
+		}
+	)
 	def lazy_range(self) -> ct.RangeFlow:
 		"""Return the not-yet-computed uniform array defined by the socket.
 
@@ -519,18 +710,18 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		)
 
 	@lazy_range.setter
-	def lazy_range(self, value: ct.RangeFlow) -> None:
+	def lazy_range(self, lazy_range: ct.RangeFlow) -> None:
 		"""Set the not-yet-computed uniform array defined by the socket.
 
 		Notes:
 			Called to compute the internal `FlowKind.Range` of this socket.
 		"""
-		self.steps = value.steps
-		self.scaling = value.scaling
+		self.steps = lazy_range.steps
+		self.scaling = lazy_range.scaling
 
 		if self.symbols:
-			self.raw_min_spstr = sp.sstr(value.start)
-			self.raw_max_spstr = sp.sstr(value.stop)
+			self.raw_min_spstr = sp.sstr(lazy_range.start)
+			self.raw_max_spstr = sp.sstr(lazy_range.stop)
 
 		else:
 			MT_Z = spux.MathType.Integer
@@ -538,32 +729,40 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			MT_R = spux.MathType.Real
 			MT_C = spux.MathType.Complex
 
-			unit = value.unit if value.unit is not None else 1
+			unit = lazy_range.unit if lazy_range.unit is not None else 1
 			if self.mathtype == MT_Z:
 				self.raw_range_int = [
 					self._to_raw_value(bound * unit)
-					for bound in [value.start, value.stop]
+					for bound in [lazy_range.start, lazy_range.stop]
 				]
 			elif self.mathtype == MT_Q:
 				self.raw_range_rat = [
 					self._to_raw_value(bound * unit)
-					for bound in [value.start, value.stop]
+					for bound in [lazy_range.start, lazy_range.stop]
 				]
 			elif self.mathtype == MT_R:
 				self.raw_range_float = [
 					self._to_raw_value(bound * unit)
-					for bound in [value.start, value.stop]
+					for bound in [lazy_range.start, lazy_range.stop]
 				]
 			elif self.mathtype == MT_C:
 				self.raw_range_complex = [
 					self._to_raw_value(bound * unit, force_complex=True)
-					for bound in [value.start, value.stop]
+					for bound in [lazy_range.start, lazy_range.stop]
 				]
 
 	####################
 	# - FlowKind: Func (w/Params if Constant)
 	####################
-	@property
+	@bl_cache.cached_bl_property(
+		depends_on={
+			'value',
+			'symbols',
+			'sorted_sp_symbols',
+			'sorted_symbols',
+			'output_sym',
+		}
+	)
 	def lazy_func(self) -> ct.FuncFlow:
 		"""Returns a lazy value that computes the expression returned by `self.value`.
 
@@ -574,15 +773,21 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		## -> `self.value` is guaranteed to be an expression with unknowns.
 		## -> The function computes `self.value` with unknowns as arguments.
 		if self.symbols:
-			return ct.FuncFlow(
-				func=sp.lambdify(
-					self.sorted_sp_symbols,
-					spux.strip_unit_system(self.value),
-					'jax',
-				),
-				func_args=list(self.sorted_symbols),
-				supports_jax=True,
-			)
+			value = self.value
+			has_value = not ct.FlowSignal.check(value)
+
+			output_sym = self.output_sym
+			if output_sym is not None and has_value:
+				return ct.FuncFlow(
+					func=sp.lambdify(
+						self.sorted_sp_symbols,
+						output_sym.conform(value, strip_unit=True),
+						'jax',
+					),
+					func_args=list(self.sorted_symbols),
+					supports_jax=True,
+				)
+			return ct.FlowSignal.FlowPending
 
 		# Constant
 		## -> When a `self.value` has no unknowns, use a dummy function.
@@ -591,15 +796,25 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		## -> Generally only useful for operations with other expressions.
 		return ct.FuncFlow(
 			func=lambda v: v,
-			func_args=[
-				sim_symbols.SimSymbol.from_expr(
-					sim_symbols.SimSymbolName.Constant, self.value, self.unit_factor
-				)
-			],
+			func_args=[self.output_sym],
 			supports_jax=True,
 		)
 
-	@property
+	@bl_cache.cached_bl_property(depends_on={'sorted_symbols'})
+	def is_differentiable(self) -> bool:
+		"""Whether all symbols are differentiable.
+
+		If there are no symbols, then there is nothing to differentiate, and thus the expression is differentiable.
+		"""
+		if not self.sorted_symbols:
+			return True
+
+		return all(
+			sym.mathtype in [spux.MathType.Real, spux.MathType.Complex]
+			for sym in self.sorted_symbols
+		)
+
+	@bl_cache.cached_bl_property(depends_on={'sorted_symbols', 'output_sym', 'value'})
 	def params(self) -> ct.ParamsFlow:
 		"""Returns parameter symbols/values to accompany `self.lazy_func`.
 
@@ -611,19 +826,28 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		## -> They should be realized later, ex. in a Viz node.
 		## -> Therefore, we just dump the symbols. Easy!
 		## -> NOTE: func_args must have the same symbol order as was lambdified.
-		if self.symbols:
-			return ct.ParamsFlow(
-				func_args=[sym.sp_symbol_phy for sym in self.sorted_symbols],
-				symbols=self.sorted_symbols,
-			)
+		if self.sorted_symbols:
+			output_sym = self.output_sym
+			if output_sym is not None:
+				return ct.ParamsFlow(
+					arg_targets=list(self.sorted_symbols),
+					func_args=[sym.sp_symbol for sym in self.sorted_symbols],
+					symbols=self.sorted_symbols,
+					is_differentiable=self.is_differentiable,
+				)
+			return ct.FlowSignal.FlowPending
 
 		# Constant
 		## -> Simply pass self.value verbatim as a function argument.
 		## -> Easy dice, easy life!
-		return ct.ParamsFlow(func_args=[self.value])
+		return ct.ParamsFlow(
+			arg_targets=[self.output_sym],
+			func_args=[self.value],
+			is_differentiable=self.is_differentiable,
+		)
 
-	@property
-	def info(self) -> ct.ArrayFlow:
+	@bl_cache.cached_bl_property(depends_on={'sorted_symbols', 'output_sym'})
+	def info(self) -> ct.InfoFlow:
 		r"""Returns parameter symbols/values to accompany `self.lazy_func`.
 
 		The output name/size/mathtype/unit corresponds directly the `ExprSocket`.
@@ -634,37 +858,78 @@ class ExprBLSocket(base.MaxwellSimSocket):
 
 		Otherwise, only the output name/size/mathtype/unit corresponding to the socket is passed along.
 		"""
-		output_sym = sim_symbols.SimSymbol(
-			sym_name=self.output_name,
-			mathtype=self.mathtype,
-			physical_type=self.physical_type,
-			unit=self.unit,
-			rows=self.size.rows,
-			cols=self.size.cols,
-		)
-
 		# Constant
 		## -> The input SimSymbols become continuous dimensional indices.
 		## -> All domain validity information is defined on the SimSymbol keys.
-		if self.symbols:
-			return ct.InfoFlow(
-				dims={sym: None for sym in self.sorted_symbols},
-				output=output_sym,
-			)
+		if self.sorted_symbols:
+			output_sym = self.output_sym
+			if output_sym is not None:
+				return ct.InfoFlow(
+					dims={sym: None for sym in self.sorted_symbols},
+					output=self.output_sym,
+				)
+			return ct.FlowSignal.FlowPending
 
 		# Constant
 		## -> We only need the output symbol to describe the raw data.
-		return ct.InfoFlow(output=output_sym)
+		return ct.InfoFlow(output=self.output_sym)
 
 	####################
 	# - FlowKind: Capabilities
 	####################
-	@property
-	def capabilities(self) -> None:
+	def linked_capabilities(self, info: ct.InfoFlow) -> ct.CapabilitiesFlow:
+		"""When this socket is linked as an output socket, expose these capabilities instead of querying `self.capabilities`.
+
+		Only used when `use_linked_capabilities == True`.
+		"""
 		return ct.CapabilitiesFlow(
 			socket_type=self.socket_type,
 			active_kind=self.active_kind,
-			allow_out_to_in={ct.FlowKind.Func: ct.FlowKind.Value},
+			allow_out_to_in={
+				ct.FlowKind.Func: ct.FlowKind.Value,
+			},
+			allow_out_to_in_if_matches={
+				ct.FlowKind.Value: (
+					ct.FlowKind.Func,
+					(
+						info.output.physical_type,
+						info.output.mathtype,
+						info.output.rows,
+						info.output.cols,
+					),
+				),
+			},
+		)
+
+	@bl_cache.cached_bl_property(depends_on={'active_kind', 'output_sym'})
+	def capabilities(self) -> ct.CapabilitiesFlow:
+		"""Expose capabilities for use when checking socket link compatibility.
+
+		Only used when `use_linked_capabilities == True`.
+		"""
+		output_sym = self.output_sym
+		if output_sym is not None:
+			allow_out_to_in_if_matches = {
+				ct.FlowKind.Value: (
+					ct.FlowKind.Func,
+					(
+						output_sym.physical_type,
+						output_sym.mathtype,
+						output_sym.rows,
+						output_sym.cols,
+					),
+				),
+			}
+		else:
+			allow_out_to_in_if_matches = {}
+
+		return ct.CapabilitiesFlow(
+			socket_type=self.socket_type,
+			active_kind=self.active_kind,
+			allow_out_to_in={
+				ct.FlowKind.Func: ct.FlowKind.Value,
+			},
+			allow_out_to_in_if_matches=allow_out_to_in_if_matches,
 		)
 
 	####################
@@ -692,29 +957,32 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		Notes:
 			Whether information about the expression passing through a linked socket is shown is governed by `self.show_info_columns`.
 		"""
-		info = self.compute_data(kind=ct.FlowKind.Info)
-		has_info = not ct.FlowSignal.check(info)
+		if self.active_kind is ct.FlowKind.Func:
+			info = self.compute_data(kind=ct.FlowKind.Info)
+			has_info = not ct.FlowSignal.check(info)
 
-		if has_info:
-			split = row.split(factor=0.85, align=True)
-			_row = split.row(align=False)
+			if has_info:
+				split = row.split(factor=0.85, align=True)
+				_row = split.row(align=False)
+			else:
+				_row = row
+
+			_row.label(text=text)
+			if has_info:
+				if self.show_info_columns:
+					_row.prop(self, self.blfields['info_columns'])
+
+				_row = split.row(align=True)
+				_row.alignment = 'RIGHT'
+				_row.prop(
+					self,
+					self.blfields['show_info_columns'],
+					toggle=True,
+					text='',
+					icon=ct.Icon.ToggleSocketInfo,
+				)
 		else:
-			_row = row
-
-		_row.label(text=text)
-		if has_info:
-			if self.show_info_columns:
-				_row.prop(self, self.blfields['info_columns'])
-
-			_row = split.row(align=True)
-			_row.alignment = 'RIGHT'
-			_row.prop(
-				self,
-				self.blfields['show_info_columns'],
-				toggle=True,
-				text='',
-				icon=ct.Icon.ToggleSocketInfo,
-			)
+			row.label(text=text)
 
 	def draw_output_label_row(self, row: bpy.types.UILayout, text) -> None:
 		"""Provide a dropdown for enabling the `InfoFlow` UI in the linked output label row.
@@ -724,29 +992,32 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		Notes:
 			Whether information about the expression passing through a linked socket is shown is governed by `self.show_info_columns`.
 		"""
-		info = self.compute_data(kind=ct.FlowKind.Info)
-		has_info = not ct.FlowSignal.check(info)
+		if self.active_kind is ct.FlowKind.Func:
+			info = self.compute_data(kind=ct.FlowKind.Info)
+			has_info = not ct.FlowSignal.check(info)
 
-		if has_info:
-			split = row.split(factor=0.15, align=True)
+			if has_info:
+				split = row.split(factor=0.15, align=True)
 
-			_row = split.row(align=True)
-			_row.prop(
-				self,
-				self.blfields['show_info_columns'],
-				toggle=True,
-				text='',
-				icon=ct.Icon.ToggleSocketInfo,
-			)
+				_row = split.row(align=True)
+				_row.prop(
+					self,
+					self.blfields['show_info_columns'],
+					toggle=True,
+					text='',
+					icon=ct.Icon.ToggleSocketInfo,
+				)
 
-			_row = split.row(align=False)
-			_row.alignment = 'RIGHT'
-			if self.show_info_columns:
-				_row.prop(self, self.blfields['info_columns'])
+				_row = split.row(align=False)
+				_row.alignment = 'RIGHT'
+				if self.show_info_columns:
+					_row.prop(self, self.blfields['info_columns'])
+				else:
+					_col = _row.column()
+					_col.alignment = 'EXPAND'
+					_col.label(text='')
 			else:
-				_col = _row.column()
-				_col.alignment = 'EXPAND'
-				_col.label(text='')
+				_row = row
 		else:
 			_row = row
 
@@ -860,42 +1131,38 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			Uses `draw_value` to draw the base UI
 		"""
 		if self.show_func_ui:
-			# Non-Symbolic: Size/Mathtype Selector
-			## -> Symbols imply str expr input.
-			## -> For arbitrary str exprs, size/mathtype are derived from the expr.
-			## -> Otherwise, size/mathtype must be pre-specified for a nice UI.
-			if not self.symbols:
-				row = col.row(align=True)
-				row.prop(self, self.blfields['size'], text='')
-				row.prop(self, self.blfields['mathtype'], text='')
-
-			# Base UI
-			## -> Draws the UI appropriate for the above choice of constraints.
-			self.draw_value(col)
-
-			# Physical Type Selector
-			## -> Determines whether/which unit-dropdown will be shown.
-			col.prop(self, self.blfields['physical_type'], text='')
-
-			# Symbol UI
-			## -> Draws the UI appropriate for the above choice of constraints.
-			## -> TODO
-
 			# Output Name Selector
 			## -> The name of the output
 			if self.show_name_selector:
 				row = col.row()
+				row.alignment = 'CENTER'
 				row.prop(self, self.blfields['output_name'], text='Name')
 
+			# Non-Symbolic: Size/Mathtype Selector
+			## -> Symbols imply str expr input.
+			## -> For arbitrary str exprs, size/mathtype are derived from the expr.
+			## -> Otherwise, size/mathtype must be pre-specified for a nice UI.
+			if self.symbols:
+				self.draw_value(col)
+
+				# TODO: Symbol UI
+			else:
+				row = col.row(align=True)
+				row.prop(self, self.blfields['size'], text='')
+				row.prop(self, self.blfields['mathtype'], text='')
+
+				self.draw_value(col)
+				col.prop(self, self.blfields['physical_type'], text='')
+
 	####################
 	# - UI: InfoFlow
 	####################
 	def draw_info(self, info: ct.InfoFlow, col: bpy.types.UILayout) -> None:
 		"""Visualize the `InfoFlow` information passing through the socket."""
 		if (
-			self.active_kind == ct.FlowKind.Func
+			self.active_kind is ct.FlowKind.Func
 			and self.show_info_columns
-			and self.is_linked
+			and (self.is_linked or self.is_output)
 		):
 			row = col.row()
 			box = row.box()
@@ -922,7 +1189,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			if InfoDisplayCol.Length in self.info_columns:
 				grid.label(text='', icon=ct.Icon.DataSocketOutput)
 			if InfoDisplayCol.MathType in self.info_columns:
-				grid.label(text=info.output.def_label)
+				grid.label(text=info.output.mathtype_size_label)
 			if InfoDisplayCol.Unit in self.info_columns:
 				grid.label(text=info.output.unit_label)
 
@@ -935,7 +1202,6 @@ class ExprSocketDef(base.SocketDef):
 	active_kind: typ.Literal[
 		ct.FlowKind.Value,
 		ct.FlowKind.Range,
-		ct.FlowKind.Array,
 		ct.FlowKind.Func,
 	] = ct.FlowKind.Value
 	output_name: sim_symbols.SimSymbolName = sim_symbols.SimSymbolName.Expr
@@ -1240,6 +1506,7 @@ class ExprSocketDef(base.SocketDef):
 	def init(self, bl_socket: ExprBLSocket) -> None:
 		bl_socket.active_kind = self.active_kind
 		bl_socket.output_name = self.output_name
+		bl_socket.use_linked_capabilities = True
 
 		# Socket Interface
 		## -> Recall that auto-updates are turned off during init()

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/maxwell/bound_cond.py

@@ -15,6 +15,7 @@
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
 import bpy
+import pydantic as pyd
 import tidy3d as td
 
 from blender_maxwell.utils import bl_cache, logger
@@ -59,7 +60,9 @@ class MaxwellBoundCondBLSocket(base.MaxwellSimSocket):
 	####################
 	# - FlowKind
 	####################
-	@property
+	@bl_cache.cached_bl_property(
+		depends_on={'active_kind', 'allow_axes', 'present_axes'}
+	)
 	def capabilities(self) -> ct.CapabilitiesFlow:
 		return ct.CapabilitiesFlow(
 			socket_type=self.socket_type,
@@ -68,7 +71,7 @@ class MaxwellBoundCondBLSocket(base.MaxwellSimSocket):
 			present_any=self.present_axes,
 		)
 
-	@property
+	@bl_cache.cached_bl_property(depends_on={'default'})
 	def value(self) -> td.BoundaryEdge:
 		return self.default.tidy3d_boundary_edge
 
@@ -84,16 +87,20 @@ class MaxwellBoundCondSocketDef(base.SocketDef):
 	socket_type: ct.SocketType = ct.SocketType.MaxwellBoundCond
 
 	default: ct.BoundCondType = ct.BoundCondType.Pml
-	allow_axes: set[ct.SimSpaceAxis] = {
-		ct.SimSpaceAxis.X,
-		ct.SimSpaceAxis.Y,
-		ct.SimSpaceAxis.Z,
-	}
-	present_axes: set[ct.SimSpaceAxis] = {
-		ct.SimSpaceAxis.X,
-		ct.SimSpaceAxis.Y,
-		ct.SimSpaceAxis.Z,
-	}
+	allow_axes: set[ct.SimSpaceAxis] = pyd.Field(
+		default={
+			ct.SimSpaceAxis.X,
+			ct.SimSpaceAxis.Y,
+			ct.SimSpaceAxis.Z,
+		}
+	)
+	present_axes: set[ct.SimSpaceAxis] = pyd.Field(
+		default={
+			ct.SimSpaceAxis.X,
+			ct.SimSpaceAxis.Y,
+			ct.SimSpaceAxis.Z,
+		}
+	)
 
 	def init(self, bl_socket: MaxwellBoundCondBLSocket) -> None:
 		bl_socket.default = self.default

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/maxwell/bound_conds.py

@@ -86,7 +86,9 @@ class MaxwellBoundCondsBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Computation of Default Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(
+		depends_on={'x_pos', 'x_neg', 'y_pos', 'y_neg', 'z_pos', 'z_neg'}
+	)
 	def value(self) -> td.BoundarySpec:
 		"""Compute a user-defined default value for simulation boundary conditions, from certain common/sensible options.
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/maxwell/medium.py

@@ -18,6 +18,7 @@ import bpy
 import scipy as sc
 import sympy.physics.units as spu
 import tidy3d as td
+import tidy3d.plugins.adjoint as tdadj
 
 from blender_maxwell.utils import bl_cache, logger
 from blender_maxwell.utils import extra_sympy_units as spux
@@ -39,12 +40,14 @@ class MaxwellMediumBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Properties
 	####################
-	rel_permittivity: tuple[float, float] = bl_cache.BLField((1.0, 0.0), float_prec=2)
+	eps_rel: tuple[float, float] = bl_cache.BLField((1.0, 0.0), float_prec=2)
+
+	differentiable: bool = bl_cache.BLField(False)
 
 	####################
 	# - FlowKinds
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'eps_rel', 'differentiable'})
 	def value(self) -> td.Medium:
 		freq = (
 			spu.convert_to(
@@ -53,31 +56,49 @@ class MaxwellMediumBLSocket(base.MaxwellSimSocket):
 			)
 			/ spu.hertz
 		)
+
+		if self.differentiable:
+			return tdadj.JaxMedium.from_nk(
+				n=self.eps_rel[0],
+				k=self.eps_rel[1],
+				freq=freq,
+			)
 		return td.Medium.from_nk(
-			n=self.rel_permittivity[0],
-			k=self.rel_permittivity[1],
+			n=self.eps_rel[0],
+			k=self.eps_rel[1],
 			freq=freq,
 		)
 
 	@value.setter
-	def value(
-		self, value: tuple[spux.ConstrSympyExpr(allow_variables=False), complex]
-	) -> None:
-		rel_permittivity = value
+	def value(self, eps_rel: tuple[float, float]) -> None:
+		self.eps_rel = eps_rel
 
-		self.rel_permittivity = (rel_permittivity.real, rel_permittivity.imag)
+	@bl_cache.cached_bl_property(depends_on={'value', 'differentiable'})
+	def lazy_func(self) -> ct.FuncFlow:
+		return ct.FuncFlow(
+			func=lambda: self.value,
+			supports_jax=self.differentiable,
+		)
+
+	@bl_cache.cached_bl_property(depends_on={'differentiable'})
+	def params(self) -> ct.FuncFlow:
+		return ct.ParamsFlow(is_differentiable=self.differentiable)
 
 	####################
 	# - UI
 	####################
 	def draw_value(self, col: bpy.types.UILayout) -> None:
-		split = col.split(factor=0.35, align=False)
+		col.prop(
+			self, self.blfields['differentiable'], text='Differentiable', toggle=True
+		)
+		col.separator()
+		split = col.split(factor=0.25, align=False)
 
-		col = split.column(align=True)
-		col.label(text='ϵ_r (ℂ)')
+		_col = split.column(align=True)
+		_col.label(text='εᵣ')
 
-		col = split.column(align=True)
-		col.prop(self, self.blfields['rel_permittivity'], text='')
+		_col = split.column(align=True)
+		_col.prop(self, self.blfields['eps_rel'], text='')
 
 
 ####################
@@ -90,7 +111,7 @@ class MaxwellMediumSocketDef(base.SocketDef):
 	default_permittivity_imag: float = 0.0
 
 	def init(self, bl_socket: MaxwellMediumBLSocket) -> None:
-		bl_socket.rel_permittivity = (
+		bl_socket.eps_rel = (
 			self.default_permittivity_real,
 			self.default_permittivity_imag,
 		)

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/maxwell/sim_grid.py

@@ -49,7 +49,7 @@ class MaxwellSimGridBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Computation of Default Value
 	####################
-	@property
+	@bl_cache.cached_bl_property(depends_on={'min_steps_per_wl'})
 	def value(self) -> td.GridSpec:
 		return td.GridSpec.auto(
 			min_steps_per_wvl=self.min_steps_per_wl,

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/tidy3d/cloud_task.py

@@ -50,7 +50,9 @@ class ReloadFolderList(bpy.types.Operator):
 		tdcloud.TidyCloudTasks.update_tasks(bl_socket.existing_folder_id)
 
 		bl_socket.existing_folder_id = bl_cache.Signal.ResetEnumItems
+		bl_socket.existing_folder_id = bl_cache.Signal.InvalidateCache
 		bl_socket.existing_task_id = bl_cache.Signal.ResetEnumItems
+		bl_socket.existing_task_id = bl_cache.Signal.InvalidateCache
 
 		return {'FINISHED'}
 
@@ -77,7 +79,9 @@ class Authenticate(bpy.types.Operator):
 			bl_socket.api_key = ''
 
 			bl_socket.existing_folder_id = bl_cache.Signal.ResetEnumItems
+			bl_socket.existing_folder_id = bl_cache.Signal.InvalidateCache
 			bl_socket.existing_task_id = bl_cache.Signal.ResetEnumItems
+			bl_socket.existing_task_id = bl_cache.Signal.InvalidateCache
 
 		return {'FINISHED'}
 
@@ -102,62 +106,18 @@ class Tidy3DCloudTaskBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Properties
 	####################
-	api_key: str = bl_cache.BLField('', prop_ui=True, str_secret=True)
+	api_key: str = bl_cache.BLField('', str_secret=True)
 	should_exist: bool = bl_cache.BLField(False)
 
+	new_task_name: str = bl_cache.BLField('')
+
+	####################
+	# - Properties: Cloud Folders
+	####################
 	existing_folder_id: enum.StrEnum = bl_cache.BLField(
-		prop_ui=True, enum_cb=lambda self, _: self.search_cloud_folders()
-	)
-	existing_task_id: enum.StrEnum = bl_cache.BLField(
-		prop_ui=True, enum_cb=lambda self, _: self.search_cloud_tasks()
+		enum_cb=lambda self, _: self.search_cloud_folders()
 	)
 
-	new_task_name: str = bl_cache.BLField('', prop_ui=True)
-
-	####################
-	# - FlowKinds
-	####################
-	@property
-	def capabilities(self) -> ct.CapabilitiesFlow:
-		return ct.CapabilitiesFlow(
-			socket_type=self.socket_type,
-			active_kind=self.active_kind,
-			must_match={'should_exist': self.should_exist},
-		)
-
-	@property
-	def value(
-		self,
-	) -> ct.NewSimCloudTask | tdcloud.CloudTask | ct.FlowSignal:
-		if tdcloud.IS_AUTHENTICATED:
-			# Retrieve Folder
-			cloud_folder = tdcloud.TidyCloudFolders.folders().get(
-				self.existing_folder_id
-			)
-			if cloud_folder is None:
-				return ct.FlowSignal.NoFlow  ## Folder deleted somewhere else
-
-			# Case: New Task
-			if not self.should_exist:
-				return ct.NewSimCloudTask(
-					task_name=self.new_task_name, cloud_folder=cloud_folder
-				)
-
-			# Case: Existing Task
-			if self.existing_task_id is not None:
-				cloud_task = tdcloud.TidyCloudTasks.tasks(cloud_folder).get(
-					self.existing_task_id
-				)
-				if cloud_folder is None:
-					return ct.FlowSignal.NoFlow  ## Task deleted somewhere else
-
-				return cloud_task
-
-		return ct.FlowSignal.FlowPending
-
-	####################
-	# - Searchers
-	####################
 	def search_cloud_folders(self) -> list[ct.BLEnumElement]:
 		if tdcloud.IS_AUTHENTICATED:
 			return [
@@ -175,6 +135,13 @@ class Tidy3DCloudTaskBLSocket(base.MaxwellSimSocket):
 
 		return []
 
+	####################
+	# - Properties: Cloud Tasks
+	####################
+	existing_task_id: enum.StrEnum = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_cloud_tasks()
+	)
+
 	def search_cloud_tasks(self) -> list[ct.BLEnumElement]:
 		if self.existing_folder_id is None or not tdcloud.IS_AUTHENTICATED:
 			return []
@@ -228,6 +195,54 @@ class Tidy3DCloudTaskBLSocket(base.MaxwellSimSocket):
 			)
 		]
 
+	####################
+	# - FlowKinds
+	####################
+	@bl_cache.cached_bl_property(depends_on={'active_kind', 'should_exist'})
+	def capabilities(self) -> ct.CapabilitiesFlow:
+		return ct.CapabilitiesFlow(
+			socket_type=self.socket_type,
+			active_kind=self.active_kind,
+			must_match={'should_exist': self.should_exist},
+		)
+
+	@bl_cache.cached_bl_property(
+		depends_on={
+			'should_exist',
+			'new_task_name',
+			'existing_folder_id',
+			'existing_task_id',
+		}
+	)
+	def value(
+		self,
+	) -> ct.NewSimCloudTask | tdcloud.CloudTask | ct.FlowSignal:
+		if tdcloud.IS_AUTHENTICATED:
+			# Retrieve Folder
+			cloud_folder = tdcloud.TidyCloudFolders.folders().get(
+				self.existing_folder_id
+			)
+			if cloud_folder is None:
+				return ct.FlowSignal.NoFlow  ## Folder deleted somewhere else
+
+			# Case: New Task
+			if not self.should_exist:
+				return ct.NewSimCloudTask(
+					task_name=self.new_task_name, cloud_folder=cloud_folder
+				)
+
+			# Case: Existing Task
+			if self.existing_task_id is not None:
+				cloud_task = tdcloud.TidyCloudTasks.tasks(cloud_folder).get(
+					self.existing_task_id
+				)
+				if cloud_folder is None:
+					return ct.FlowSignal.NoFlow  ## Task deleted somewhere else
+
+				return cloud_task
+
+		return ct.FlowSignal.FlowPending
+
 	####################
 	# - UI
 	####################

src/blender_maxwell/utils/bl_cache/bl_field.py

@@ -16,6 +16,7 @@
 
 """Implements various key caches on instances of Blender objects, especially nodes and sockets."""
 
+import contextlib
 import functools
 import inspect
 import typing as typ
@@ -166,7 +167,7 @@ class BLField:
 		self.cb_depends_on: set[str] | None = cb_depends_on
 
 		# Update Suppressing
-		self.suppress_update: dict[str, bool] = {}
+		self.suppressed_update: dict[str, bool] = {}
 
 	####################
 	# - Descriptor Setup
@@ -253,9 +254,38 @@ class BLField:
 			return self.bl_prop.default_value  ## TODO: Good idea?
 		return cached_value
 
-	def suppress_next_update(self, bl_instance) -> None:
-		self.suppress_update[bl_instance.instance_id] = True
-		## TODO: Make it a context manager to prevent the worst of surprises
+	@contextlib.contextmanager
+	def suppress_update(self, bl_instance: bl_instance.BLInstance) -> None:
+		"""A context manager that suppresses all calls to `on_prop_changed()` for fields of the given `bl_instance` while active.
+
+		Any change to a `BLProp` managed by this descriptor inevitably trips `bl_instance.on_bl_prop_changed()`.
+		In response to these changes, `bl_instance.on_bl_prop_changed()` always signals the `Signal.InvalidateCache` via this descriptor.
+		Unless something interferes, this results in a call to `bl_instance.on_prop_changed()`.
+
+		Usually, this is great.
+		But sometimes, like when ex. refreshing enum items, we **want** to be able to set the value of the `BLProp` **without** triggering that `bl_instance.on_prop_changed()`.
+		By default, there is absolutely no way to accomplish this.
+
+		That's where this context manager comes into play.
+		While active, all calls to `bl_instance.on_prop_changed()` will be ignored for the given `bl_instance`, allowing us to freely set persistent properties without side effects.
+
+		Examples:
+			A simple illustrative example could look something like:
+
+			```python
+			with self.suppress_update(bl_instance):
+				self.bl_prop.write(bl_instance, 'I won't trigger an update')
+
+			self.bl_prop.write(bl_instance, 'I will trigger an update')
+			```
+		"""
+		self.suppressed_update[bl_instance.instance_id] = True
+		try:
+			yield
+		finally:
+			self.suppressed_update[bl_instance.instance_id] = False
+			## -> We could .pop(None).
+			## -> But keeping a reused memory location around is GC friendly.
 
 	def __set__(
 		self, bl_instance: bl_instance.BLInstance | None, value: typ.Any
@@ -263,7 +293,7 @@ class BLField:
 		"""Sets the value described by the BLField.
 
 		In general, any BLField modified in the UI will set `InvalidateCache` on this descriptor.
-		If `self.prop_info['use_prop_update']` is set, the method `bl_instance.on_prop_changed(self.bl_prop.name)` will then be called and start a `FlowKind.DataChanged` event chain.
+		If `self.prop_info['use_prop_update']` is set, the method `bl_instance.on_prop_changed(self.bl_prop.name)` will then be called and start a `FlowEvent.DataChanged` event chain.
 
 		Notes:
 			Run by Python when the attribute described by the descriptor is set.
@@ -273,28 +303,29 @@ class BLField:
 			bl_instance: Instance that is accessing the attribute.
 			owner: The class that owns the instance.
 		"""
-		# Perform Update Chain
-		## -> We still respect 'use_prop_update', since it is user-sourced.
-		if value is Signal.DoUpdate:
-			if self.prop_info['use_prop_update']:
-				bl_instance.on_prop_changed(self.bl_prop.name)
-
 		# Invalidate Cache
 		## -> This empties the non-persistent cache.
 		## -> As a result, the value must be reloaded from the property.
 		## The 'on_prop_changed' method on the bl_instance might also be called.
-		elif value is Signal.InvalidateCache or value is Signal.InvalidateCacheNoUpdate:
+		if value is Signal.InvalidateCache or value is Signal.InvalidateCacheNoUpdate:
 			self.bl_prop.invalidate_nonpersist(bl_instance)
 
-			# Update Suppression
-			if self.suppress_update.get(bl_instance.instance_id):
-				self.suppress_update[bl_instance.instance_id] = False
-
-			# ELSE: Trigger Update Chain
-			elif self.prop_info['use_prop_update'] and value is Signal.InvalidateCache:
+			# Trigger Update Chain
+			## -> User can disable w/'use_prop_update=False'.
+			## -> Use InvalidateCacheNoUpdate to explicitly disable update.
+			## -> If 'suppressed_update' context manager is active, don't update.
+			if (
+				self.prop_info['use_prop_update']
+				and value is Signal.InvalidateCache
+				and not self.suppressed_update.get(bl_instance.instance_id, False)
+			):
 				bl_instance.on_prop_changed(self.bl_prop.name)
 
 		# Reset Enum Items
+		## -> If there is no enum items callback, do nothing.
+		## -> Re-run the enum items callback and set it active.
+		## -> If the old item can be retained, then do so.
+		## -> Otherwise, set the first item.
 		elif value is Signal.ResetEnumItems:
 			if self.bl_prop_enum_items is None:
 				return
@@ -335,8 +366,8 @@ class BLField:
 				# Swap Enum Items
 				## -> This is the hot stuff - the enum elements are overwritten.
 				## -> The safe_enum_cb will pick up on this immediately.
-				self.suppress_next_update(bl_instance)
-				self.bl_prop_enum_items.write(bl_instance, current_items)
+				with self.suppress_update(bl_instance):
+					self.bl_prop_enum_items.write(bl_instance, current_items)
 
 				# Old Item in Current Items
 				## -> It's possible that the old enum key is in the new enum.
@@ -344,9 +375,8 @@ class BLField:
 				## -> Thus, we set it - Blender sees a change, user doesn't.
 				## -> DO NOT trigger on_prop_changed (since "nothing changed").
 				if any(raw_old_item == item[0] for item in current_items):
-					self.suppress_next_update(bl_instance)
-					self.bl_prop.write(bl_instance, old_item)
-					## -> TODO: Don't write if not needed.
+					with self.suppress_update(bl_instance):
+						self.bl_prop.write(bl_instance, old_item)
 
 				# Old Item Not in Current Items
 				## -> In this case, fallback to the first current item.
@@ -355,28 +385,27 @@ class BLField:
 					raw_first_current_item = current_items[0][0]
 					first_current_item = self.bl_prop.decode(raw_first_current_item)
 
-					self.suppress_next_update(bl_instance)
-					self.bl_prop.write(bl_instance, first_current_item)
-
-					if self.prop_info['use_prop_update']:
-						bl_instance.on_prop_changed(self.bl_prop.name)
+					with self.suppress_update(bl_instance):
+						self.bl_prop.write(bl_instance, first_current_item)
 
 		# Reset Str Search
+		## -> If there is no string search method, do nothing.
+		## -> Simply invalidate the non-persistent cache
 		elif value is Signal.ResetStrSearch:
 			if self.bl_prop_str_search is None:
 				return
 
 			self.bl_prop_str_search.invalidate_nonpersist(bl_instance)
 
-		# General __set__
+		# Default __set__
 		else:
-			self.bl_prop.write(bl_instance, value)
+			with self.suppress_update(bl_instance):
+				self.bl_prop.write(bl_instance, value)
 
 			# Update Semantics
-			if self.suppress_update.get(bl_instance.instance_id):
-				self.suppress_update[bl_instance.instance_id] = False
-
-			elif self.prop_info['use_prop_update']:
+			if self.prop_info['use_prop_update'] and not self.suppressed_update.get(
+				bl_instance.instance_id, False
+			):
 				bl_instance.on_prop_changed(self.bl_prop.name)
 
 	####################

src/blender_maxwell/utils/bl_cache/cached_bl_property.py

@@ -16,6 +16,7 @@
 
 """Implements various key caches on instances of Blender objects, especially nodes and sockets."""
 
+import contextlib
 import inspect
 import typing as typ
 
@@ -76,7 +77,7 @@ class CachedBLProperty:
 		self.decode_type: type = inspect.signature(getter_method).return_annotation
 
 		# Write Suppressing
-		self.suppress_write: dict[str, bool] = {}
+		self.suppressed_update: dict[str, bool] = {}
 
 		# Check Non-Empty Type Annotation
 		## For now, just presume that all types can be encoded/decoded.
@@ -125,9 +126,38 @@ class CachedBLProperty:
 			return Signal.CacheNotReady
 		return cached_value
 
-	def suppress_next_write(self, bl_instance) -> None:
-		self.suppress_write[bl_instance.instance_id] = True
-		## TODO: Make it a context manager to prevent the worst of surprises
+	@contextlib.contextmanager
+	def suppress_update(self, bl_instance: bl_instance.BLInstance) -> None:
+		"""A context manager that suppresses all calls to `on_prop_changed()` for fields of the given `bl_instance` while active.
+
+		Any change to a `BLProp` managed by this descriptor inevitably trips `bl_instance.on_bl_prop_changed()`.
+		In response to these changes, `bl_instance.on_bl_prop_changed()` always signals the `Signal.InvalidateCache` via this descriptor.
+		Unless something interferes, this results in a call to `bl_instance.on_prop_changed()`.
+
+		Usually, this is great.
+		But sometimes, like when ex. refreshing enum items, we **want** to be able to set the value of the `BLProp` **without** triggering that `bl_instance.on_prop_changed()`.
+		By default, there is absolutely no way to accomplish this.
+
+		That's where this context manager comes into play.
+		While active, all calls to `bl_instance.on_prop_changed()` will be ignored for the given `bl_instance`, allowing us to freely set persistent properties without side effects.
+
+		Examples:
+			A simple illustrative example could look something like:
+
+			```python
+			with self.suppress_update(bl_instance):
+				self.bl_prop.write(bl_instance, 'I won't trigger an update')
+
+			self.bl_prop.write(bl_instance, 'I will trigger an update')
+			```
+		"""
+		self.suppressed_update[bl_instance.instance_id] = True
+		try:
+			yield
+		finally:
+			self.suppressed_update[bl_instance.instance_id] = False
+			## -> We could .pop(None).
+			## -> But keeping a reused memory location around is GC friendly.
 
 	def __set__(
 		self, bl_instance: bl_instance.BLInstance | None, value: typ.Any
@@ -141,44 +171,59 @@ class CachedBLProperty:
 		Parameters:
 			bl_instance: The Blender object this prop
 		"""
-		if value is Signal.DoUpdate:
-			bl_instance.on_prop_changed(self.bl_prop.name)
-
-		elif value is Signal.InvalidateCache or value is Signal.InvalidateCacheNoUpdate:
+		# Invalidate Cache
+		## -> This empties the non-persistent cache.
+		## -> If persist=True, this also writes the persistent cache (no update).
+		## The 'on_prop_changed' method on the bl_instance might also be called.
+		if value is Signal.InvalidateCache or value is Signal.InvalidateCacheNoUpdate:
 			# Invalidate Partner Non-Persistent Caches
 			## -> Only for the invalidation case do we also invalidate partners.
 			if bl_instance is not None:
 				# Fill Caches
-				## -> persist: Fill Persist and Non-Persist Cache
-				## -> else: Fill Non-Persist Cache
-				if self.persist and not self.suppress_write.get(
-					bl_instance.instance_id
-				):
-					self.bl_prop.write(bl_instance, self.getter_method(bl_instance))
+				## -> persist=True: Fill Persist and Non-Persist Cache
+				## -> persist=False: Fill Non-Persist Cache
+				if self.persist:
+					with self.suppress_update(bl_instance):
+						self.bl_prop.write(bl_instance, self.getter_method(bl_instance))
 
 				else:
 					self.bl_prop.write_nonpersist(
 						bl_instance, self.getter_method(bl_instance)
 					)
 
-				if value == Signal.InvalidateCache:
+				# Trigger Update
+				## -> Use InvalidateCacheNoUpdate to explicitly disable update.
+				## -> If 'suppress_update' context manager is active, don't update.
+				if value is Signal.InvalidateCache and not self.suppressed_update.get(
+					bl_instance.instance_id
+				):
 					bl_instance.on_prop_changed(self.bl_prop.name)
 
+		# Call Setter
 		elif self.setter_method is not None:
-			# Run Setter
-			## -> The user-provided setter should do any updating of partners.
-			if self.setter_method is not None:
-				self.setter_method(bl_instance, value)
+			if bl_instance is not None:
+				# Run Setter
+				## -> The user-provided setter can set values as it sees fit.
+				## -> The user-provided setter will not immediately trigger updates.
+				with self.suppress_update(bl_instance):
+					self.setter_method(bl_instance, value)
 
-			# Fill Non-Persistant (and maybe Persistent) Cache
-			if self.persist and not self.suppress_write.get(bl_instance.instance_id):
-				self.bl_prop.write(bl_instance, self.getter_method(bl_instance))
+				# Fill Caches
+				## -> persist=True: Fill Persist and Non-Persist Cache
+				## -> persist=False: Fill Non-Persist Cache
+				if self.persist:
+					with self.suppress_update(bl_instance):
+						self.bl_prop.write(bl_instance, self.getter_method(bl_instance))
 
-			else:
-				self.bl_prop.write_nonpersist(
-					bl_instance, self.getter_method(bl_instance)
-				)
-			bl_instance.on_prop_changed(self.bl_prop.name)
+				else:
+					self.bl_prop.write_nonpersist(
+						bl_instance, self.getter_method(bl_instance)
+					)
+
+				# Trigger Update
+				## -> If 'suppress_update' context manager is active, don't update.
+				if not self.suppressed_update.get(bl_instance.instance_id):
+					bl_instance.on_prop_changed(self.bl_prop.name)
 
 		else:
 			msg = f'Tried to set "{value}" to "{self.prop_name}" on "{bl_instance.bl_label}", but a setter was not defined'

src/blender_maxwell/utils/bl_cache/signal.py

@@ -39,8 +39,6 @@ class Signal(enum.StrEnum):
 
 		InvalidateCache: The cache should be invalidated.
 		InvalidateCacheNoUpdate: The cache should be invalidated, but no update method should be run.
-		DoUpdate: Any update method that the cache triggers on change should be run.
-			An update is **not guaranteeed** to be run, merely requested.
 
 		ResetEnumItems: Cached dynamic enum items should be recomputed on next use.
 		ResetStrSearch: Cached string-search items should be recomputed on next use.
@@ -53,7 +51,6 @@ class Signal(enum.StrEnum):
 	# Invalidation
 	InvalidateCache: str = str(uuid.uuid4())
 	InvalidateCacheNoUpdate: str = str(uuid.uuid4())
-	DoUpdate: str = str(uuid.uuid4())
 
 	# Reset Signals
 	## -> Invalidates data adjascent to fields.

src/blender_maxwell/utils/bl_instance.py

@@ -220,7 +220,13 @@ class BLInstance:
 		for str_search_prop_name in self.blfields_str_search:
 			setattr(self, str_search_prop_name, bl_cache.Signal.ResetStrSearch)
 
-	def invalidate_blfield_deps(self, prop_name: str) -> None:
+	def trace_blfields_to_clear(
+		self,
+		prop_name: str,
+		prev_blfields_to_clear: list[
+			tuple[str, typ.Literal['invalidate', 'reset_enum', 'reset_strsearch']]
+		] = (),
+	) -> list[str]:
 		"""Invalidates all properties that depend on `prop_name`.
 
 		A property can recursively depend on other properties, including specificity as to whether the cache should be invalidated, the enum items be recomputed, or the string search items be recomputed.
@@ -232,35 +238,110 @@ class BLInstance:
 			The dictionaries governing exactly what invalidates what, and how, are encoded as `self.blfield_deps`, `self.blfield_dynamic_enum_deps`, and `self.blfield_str_search_deps`.
 			All of these are filled when creating the `BLInstance` subclass, using `self.declare_blfield_dep()`, generally via the `BLField` descriptor (which internally uses `BLProp`).
 		"""
+		if prev_blfields_to_clear:
+			blfields_to_clear = prev_blfields_to_clear.copy()
+		else:
+			blfields_to_clear = []
+
 		# Invalidate Dependent Properties (incl. DynEnums and StrSearch)
-		## -> NOTE: Dependent props may also trigger `on_prop_changed`.
-		## -> Don't abuse dependencies :)
-		for deps, invalidate_signal in zip(
+		## -> InvalidateCacheNoUpdate: Exactly what it sounds like.
+		## -> ResetEnumItems: Won't trigger on_prop_changed.
+		## -> -- To get on_prop_changed after, do explicit 'InvalidateCache'.
+		## -> StrSearch: It's a straight computation, no on_prop_changed.
+		for deps, clear_method in zip(
 			[
 				self.blfield_deps,
 				self.blfield_dynamic_enum_deps,
 				self.blfield_str_search_deps,
 			],
-			[
-				bl_cache.Signal.InvalidateCache,
-				bl_cache.Signal.ResetEnumItems,
-				bl_cache.Signal.ResetStrSearch,
-			],
+			['invalidate', 'reset_enum', 'reset_strsearch'],
 			strict=True,
 		):
 			if prop_name in deps:
 				for dst_prop_name in deps[prop_name]:
-					log.debug(
-						'%s: "%s" is invalidating "%s"',
-						self.bl_label,
-						prop_name,
-						dst_prop_name,
-					)
-					setattr(
-						self,
-						dst_prop_name,
-						invalidate_signal,
-					)
+					# Mark Dependency for Clearance
+					## -> Duplicates are OK for now, we'll clear them later.
+					blfields_to_clear.append((dst_prop_name, clear_method))
+
+					# Compute Recursive Dependencies for Clearance
+					## -> As we go deeper, 'previous fields' is set.
+					if dst_prop_name in self.blfields:
+						blfields_to_clear += self.trace_blfields_to_clear(
+							dst_prop_name,
+							prev_blfields_to_clear=blfields_to_clear,
+						)
+
+		match (bool(prev_blfields_to_clear), bool(blfields_to_clear)):
+			# Nothing to Clear
+			## -> This is a recursive base case for no-dependency BLFields.
+			case (False, False):
+				return []
+
+			# Only Old: Return Old
+			## -> This is a recursive base case for the deepest field w/o deps.
+			## -> When there are previous BLFields, this cannot be recursive root
+			## -> Otherwise, we'd need to de-duplicate.
+			case (True, False):
+				return prev_blfields_to_clear  ## Is never recursive root
+
+			# Only New: Deduplicate (from right) w/Order Preservation
+			## -> This is the recursive root.
+			## -> The first time there are new BLFields to clear, we dedupe.
+			## -> This is the ONLY case where we need to dedupe.
+			## -> Deduping deeper would be extraneous (though not damaging).
+			case (False, True):
+				return list(reversed(dict.fromkeys(reversed(blfields_to_clear))))
+
+			# New And Old: Concatenate
+			## -> This is merely a "transport" step, sandwiched btwn base/root.
+			## -> As such, deduplication would not be wrong, just extraneous.
+			## -> Since invalidation is in a hot-loop, don't do such things.
+			case (True, True):
+				return blfields_to_clear
+
+	def clear_blfields_after(self, prop_name: str) -> list[str]:
+		"""Clear (invalidate) all `BLField`s that have become invalid as a result of a change to `prop_name`.
+
+		Uses `self.trace_blfields_to_clear()` to deduce the names and unique ordering of `BLField`s to clear.
+		Then, update-less `bl_cache.Signal`s are written in order to invalidate each `BLField` cache without invoking `self.on_prop_changed()`.
+		Finally, the list of cleared `BLField`s is returned.
+
+		Notes:
+			Generally, this should be called from `on_prop_changed()`.
+			The resulting cleared fields can then be analyzed / used in a domain specific way as needed by the particular `BLInstance`.
+
+		Returns:
+			The topologically ordered right-de-duplicated list of BLFields that were cleared.
+		"""
+		blfields_to_clear = self.trace_blfields_to_clear(prop_name)
+
+		# Invalidate BLFields
+		## -> trace_blfields_to_clear only gave us what/how to invalidate.
+		## -> It's the responsibility of on_prop_changed to actually do so.
+		# log.debug(
+		# '%s (NodeSocket): Clearing BLFields after "%s": "%s"',
+		# self.bl_label,
+		# prop_name,
+		# blfields_to_clear,
+		# )
+		for blfield, clear_method in blfields_to_clear:
+			# log.debug(
+			# '%s (NodeSocket): Clearing BLField: %s (%s)',
+			# self.bl_label,
+			# blfield,
+			# clear_method,
+			# )
+			setattr(
+				self,
+				blfield,
+				{
+					'invalidate': bl_cache.Signal.InvalidateCacheNoUpdate,
+					'reset_enum': bl_cache.Signal.ResetEnumItems,  ## No updates
+					'reset_strsearch': bl_cache.Signal.ResetStrSearch,
+				}[clear_method],
+			)
+
+		return [(prop_name, 'invalidate'), *blfields_to_clear]
 
 	def on_bl_prop_changed(self, bl_prop_name: str, _: bpy.types.Context) -> None:
 		"""Called when a property has been updated via the Blender UI.

src/blender_maxwell/utils/extra_sympy_units.py

@@ -44,6 +44,7 @@ from pydantic_core import core_schema as pyd_core_schema
 from blender_maxwell import contracts as ct
 
 from . import logger
+from .staticproperty import staticproperty
 
 log = logger.get(__name__)
 
@@ -69,7 +70,7 @@ class MathType(enum.StrEnum):
 	Complex = enum.auto()
 
 	@staticmethod
-	def combine(*mathtypes: list[typ.Self]) -> typ.Self:
+	def combine(*mathtypes: list[typ.Self], optional: bool = False) -> typ.Self | None:
 		if MathType.Complex in mathtypes:
 			return MathType.Complex
 		if MathType.Real in mathtypes:
@@ -79,6 +80,9 @@ class MathType(enum.StrEnum):
 		if MathType.Integer in mathtypes:
 			return MathType.Integer
 
+		if optional:
+			return None
+
 		msg = f"Can't combine mathtypes {mathtypes}"
 		raise ValueError(msg)
 
@@ -113,7 +117,7 @@ class MathType(enum.StrEnum):
 				return complex(pyobj, 0)
 
 	@staticmethod
-	def from_expr(sp_obj: SympyType) -> type:
+	def from_expr(sp_obj: SympyType, optional: bool = False) -> type | None:
 		if isinstance(sp_obj, sp.MatrixBase):
 			return MathType.combine(
 				*[MathType.from_expr(v) for v in sp.flatten(sp_obj)]
@@ -134,6 +138,9 @@ class MathType(enum.StrEnum):
 		if sp_obj in [sp.zoo, -sp.zoo]:
 			return MathType.Complex
 
+		if optional:
+			return None
+
 		msg = f"Can't determine MathType from sympy object: {sp_obj}"
 		raise ValueError(msg)
 
@@ -957,6 +964,48 @@ def unit_str_to_unit(unit_str: str) -> Unit | None:
 ####################
 # - "Physical" Type
 ####################
+def unit_dim_to_unit_dim_deps(
+	unit_dims: SympyType,
+) -> dict[spu.dimensions.Dimension, int] | None:
+	dimsys_SI = spu.systems.si.dimsys_SI
+
+	# Retrieve Dimensional Dependencies
+	try:
+		return dimsys_SI.get_dimensional_dependencies(unit_dims)
+
+	# Catch TypeError
+	## -> Happens if `+` or `-` is in `unit`.
+	## -> Generally, it doesn't make sense to add/subtract differing unit dims.
+	## -> Thus, when trying to figure out the unit dimension, there isn't one.
+	except TypeError:
+		return None
+
+
+def unit_to_unit_dim_deps(
+	unit: SympyType,
+) -> dict[spu.dimensions.Dimension, int] | None:
+	# Retrieve Dimensional Dependencies
+	## -> NOTE: .subs() alone seems to produce sp.Symbol atoms.
+	## -> This is extremely problematic; `Dims` arithmetic has key properties.
+	## -> So we have to go all the way to the dimensional dependencies.
+	## -> This isn't really respecting the args, but it seems to work :)
+	return unit_dim_to_unit_dim_deps(
+		unit.subs({arg: arg.dimension for arg in unit.atoms(spu.Quantity)})
+	)
+
+
+def compare_unit_dims(unit_dim_l: SympyType, unit_dim_r: SympyType) -> bool:
+	return unit_dim_to_unit_dim_deps(unit_dim_l) == unit_dim_to_unit_dim_deps(
+		unit_dim_r
+	)
+
+
+def compare_unit_dim_to_unit_dim_deps(
+	unit_dim: SympyType, unit_dim_deps: dict[spu.dimensions.Dimension, int]
+) -> bool:
+	return unit_dim_to_unit_dim_deps(unit_dim) == unit_dim_deps
+
+
 class PhysicalType(enum.StrEnum):
 	"""Type identifiers for expressions with both `MathType` and a unit, aka a "physical" type."""
 
@@ -1005,7 +1054,7 @@ class PhysicalType(enum.StrEnum):
 	Illuminance = enum.auto()
 
 	@functools.cached_property
-	def unit_dim(self):
+	def unit_dim(self) -> SympyType:
 		PT = PhysicalType
 		return {
 			PT.NonPhysical: None,
@@ -1050,6 +1099,95 @@ class PhysicalType(enum.StrEnum):
 			PT.Illuminance: Dims.luminous_intensity / Dims.length**2,
 		}[self]
 
+	@staticproperty
+	def unit_dims() -> dict[typ.Self, SympyType]:
+		return {
+			physical_type: physical_type.unit_dim
+			for physical_type in list(PhysicalType)
+		}
+
+	@functools.cached_property
+	def color(self):
+		"""A color corresponding to the physical type.
+
+		The color selections were initially generated using AI, as this is a rote task that's better adjusted than invented.
+		The LLM provided the following rationale for its choices:
+
+		> Non-Physical: Grey signifies neutrality and non-physical nature.
+		> Global:
+		>    Time: Blue is often associated with calmness and the passage of time.
+		>    Angle and Solid Angle: Different shades of blue and cyan suggest angular dimensions and spatial aspects.
+		>    Frequency and Angular Frequency: Darker shades of blue to maintain the link to time.
+		> Cartesian:
+		>    Length, Area, Volume: Shades of green to represent spatial dimensions, with intensity increasing with dimension.
+		> Mechanical:
+		>    Velocity and Acceleration: Red signifies motion and dynamics, with lighter reds for related quantities.
+		>    Mass: Dark red for the fundamental property.
+		>    Force and Pressure: Shades of red indicating intensity.
+		> Energy:
+		>    Work and Power: Orange signifies energy transformation, with lighter oranges for related quantities.
+		>    Temperature: Yellow for heat.
+		> Electrodynamics:
+		>    Current and related quantities: Cyan shades indicating flow.
+		>    Voltage, Capacitance: Greenish and blueish cyan for electrical potential.
+		>    Impedance, Conductance, Conductivity: Purples and magentas to signify resistance and conductance.
+		>    Magnetic properties: Magenta shades for magnetism.
+		>    Electric Field: Light blue.
+		>    Magnetic Field: Grey, as it can be considered neutral in terms of direction.
+		> Luminal:
+		>    Luminous properties: Yellows to signify light and illumination.
+		>
+		> This color mapping helps maintain intuitive connections for users interacting with these physical types.
+		"""
+		PT = PhysicalType
+		return {
+			PT.NonPhysical: (0.75, 0.75, 0.75, 1.0),  # Light Grey: Non-physical
+			# Global
+			PT.Time: (0.5, 0.5, 1.0, 1.0),  # Light Blue: Time
+			PT.Angle: (0.5, 0.75, 1.0, 1.0),  # Light Blue: Angle
+			PT.SolidAngle: (0.5, 0.75, 0.75, 1.0),  # Light Cyan: Solid Angle
+			PT.Freq: (0.5, 0.5, 0.9, 1.0),  # Light Blue: Frequency
+			PT.AngFreq: (0.5, 0.5, 0.8, 1.0),  # Light Blue: Angular Frequency
+			# Cartesian
+			PT.Length: (0.5, 1.0, 0.5, 1.0),  # Light Green: Length
+			PT.Area: (0.6, 1.0, 0.6, 1.0),  # Light Green: Area
+			PT.Volume: (0.7, 1.0, 0.7, 1.0),  # Light Green: Volume
+			# Mechanical
+			PT.Vel: (1.0, 0.5, 0.5, 1.0),  # Light Red: Velocity
+			PT.Accel: (1.0, 0.6, 0.6, 1.0),  # Light Red: Acceleration
+			PT.Mass: (0.75, 0.5, 0.5, 1.0),  # Light Red: Mass
+			PT.Force: (0.9, 0.5, 0.5, 1.0),  # Light Red: Force
+			PT.Pressure: (1.0, 0.7, 0.7, 1.0),  # Light Red: Pressure
+			# Energy
+			PT.Work: (1.0, 0.75, 0.5, 1.0),  # Light Orange: Work
+			PT.Power: (1.0, 0.85, 0.5, 1.0),  # Light Orange: Power
+			PT.PowerFlux: (1.0, 0.8, 0.6, 1.0),  # Light Orange: Power Flux
+			PT.Temp: (1.0, 1.0, 0.5, 1.0),  # Light Yellow: Temperature
+			# Electrodynamics
+			PT.Current: (0.5, 1.0, 1.0, 1.0),  # Light Cyan: Current
+			PT.CurrentDensity: (0.5, 0.9, 0.9, 1.0),  # Light Cyan: Current Density
+			PT.Charge: (0.5, 0.85, 0.85, 1.0),  # Light Cyan: Charge
+			PT.Voltage: (0.5, 1.0, 0.75, 1.0),  # Light Greenish Cyan: Voltage
+			PT.Capacitance: (0.5, 0.75, 1.0, 1.0),  # Light Blueish Cyan: Capacitance
+			PT.Impedance: (0.6, 0.5, 0.75, 1.0),  # Light Purple: Impedance
+			PT.Conductance: (0.7, 0.5, 0.8, 1.0),  # Light Purple: Conductance
+			PT.Conductivity: (0.8, 0.5, 0.9, 1.0),  # Light Purple: Conductivity
+			PT.MFlux: (0.75, 0.5, 0.75, 1.0),  # Light Magenta: Magnetic Flux
+			PT.MFluxDensity: (
+				0.85,
+				0.5,
+				0.85,
+				1.0,
+			),  # Light Magenta: Magnetic Flux Density
+			PT.Inductance: (0.8, 0.5, 0.8, 1.0),  # Light Magenta: Inductance
+			PT.EField: (0.75, 0.75, 1.0, 1.0),  # Light Blue: Electric Field
+			PT.HField: (0.75, 0.75, 0.75, 1.0),  # Light Grey: Magnetic Field
+			# Luminal
+			PT.LumIntensity: (1.0, 0.95, 0.5, 1.0),  # Light Yellow: Luminous Intensity
+			PT.LumFlux: (1.0, 0.95, 0.6, 1.0),  # Light Yellow: Luminous Flux
+			PT.Illuminance: (1.0, 1.0, 0.75, 1.0),  # Pale Yellow: Illuminance
+		}[self]
+
 	@functools.cached_property
 	def default_unit(self) -> list[Unit]:
 		PT = PhysicalType
@@ -1256,17 +1394,59 @@ class PhysicalType(enum.StrEnum):
 		}[self]
 
 	@staticmethod
-	def from_unit(unit: Unit, optional: bool = False) -> list[Unit] | None:
-		for physical_type in list(PhysicalType):
-			if unit in physical_type.valid_units:
-				return physical_type
-		## TODO: Optimize
+	def from_unit(unit: Unit | None, optional: bool = False) -> typ.Self | None:
+		"""Attempt to determine a matching `PhysicalType` from a unit.
+
+		NOTE: It is not guaranteed that `unit` is within `valid_units`, only that it can be converted to any unit in `valid_units`.
+
+		Returns:
+			The matched `PhysicalType`.
+
+			If none could be matched, then either return `None` (if `optional` is set) or error.
+
+		Raises:
+			ValueError: If no `PhysicalType` could be matched, and `optional` is `False`.
+		"""
+		if unit is None:
+			return ct.PhysicalType.NonPhysical
+
+		unit_dim_deps = unit_to_unit_dim_deps(unit)
+		if unit_dim_deps is not None:
+			for physical_type, candidate_unit_dim in PhysicalType.unit_dims.items():
+				if compare_unit_dim_to_unit_dim_deps(candidate_unit_dim, unit_dim_deps):
+					return physical_type
 
 		if optional:
 			return None
 		msg = f'Could not determine PhysicalType for {unit}'
 		raise ValueError(msg)
 
+	@staticmethod
+	def from_unit_dim(
+		unit_dim: SympyType | None, optional: bool = False
+	) -> typ.Self | None:
+		"""Attempts to match an arbitrary unit dimension expression to a corresponding `PhysicalType`.
+
+		For comparing arbitrary unit dimensions (via expressions of `spu.dimensions.Dimension`), it is critical that equivalent dimensions are also compared as equal (ex. `mass*length/time^2 == force`).
+		To do so, we employ the `SI` unit conventions, for extracting the fundamental dimensional dependencies of unit dimension expressions.
+
+		Returns:
+			The matched `PhysicalType`.
+
+			If none could be matched, then either return `None` (if `optional` is set) or error.
+
+		Raises:
+			ValueError: If no `PhysicalType` could be matched, and `optional` is `False`.
+		"""
+		for physical_type, candidate_unit_dim in PhysicalType.unit_dims.items():
+			if compare_unit_dims(unit_dim, candidate_unit_dim):
+				return physical_type
+
+		if optional:
+			return None
+		msg = f'Could not determine PhysicalType for {unit_dim}'
+		raise ValueError(msg)
+
 	@functools.cached_property
 	def valid_shapes(self) -> list[typ.Literal[(3,), (2,)] | None]:
 		PT = PhysicalType

src/blender_maxwell/utils/image_ops.py

@@ -17,7 +17,6 @@
 """Useful image processing operations for use in the addon."""
 
 import enum
-import functools
 import typing as typ
 
 import jax
@@ -27,13 +26,13 @@ import matplotlib
 import matplotlib.axis as mpl_ax
 import matplotlib.backends.backend_agg
 import matplotlib.figure
-import matplotlib.style as mplstyle
+import numpy as np
 import seaborn as sns
 
 from blender_maxwell import contracts as ct
+from blender_maxwell.utils import extra_sympy_units as spux
 from blender_maxwell.utils import logger
 
-# mplstyle.use('fast')  ## TODO: Does this do anything?
 sns.set_theme()
 
 log = logger.get(__name__)
@@ -139,7 +138,7 @@ def rgba_image_from_2d_map(
 ####################
 # - MPL Helpers
 ####################
-@functools.lru_cache(maxsize=16)
+# @functools.lru_cache(maxsize=16)
 def mpl_fig_canvas_ax(width_inches: float, height_inches: float, dpi: int):
 	fig = matplotlib.figure.Figure(
 		figsize=[width_inches, height_inches], dpi=dpi, layout='tight'
@@ -160,9 +159,9 @@ def plot_box_plot_1d(data, ax: mpl_ax.Axis) -> None:
 	x_sym, y_sym = list(data.keys())
 
 	ax.boxplot([data[y_sym]])
-	ax.set_title(f'{x_sym.name_pretty} -> {y_sym.name_pretty}')
+	ax.set_title(f'{x_sym.name_pretty} → {y_sym.name_pretty}')
 	ax.set_xlabel(x_sym.plot_label)
-	ax.set_xlabel(y_sym.plot_label)
+	ax.set_ylabel(y_sym.plot_label)
 
 
 def plot_bar(data, ax: mpl_ax.Axis) -> None:
@@ -173,26 +172,31 @@ def plot_bar(data, ax: mpl_ax.Axis) -> None:
 
 	ax.set_title(f'{x_sym.name_pretty} -> {heights_sym.name_pretty}')
 	ax.set_xlabel(x_sym.plot_label)
-	ax.set_xlabel(heights_sym.plot_label)
+	ax.set_ylabel(heights_sym.plot_label)
 
 
-# (ℝ) -> ℝ
+# (ℝ) -> ℝ (| sometimes complex)
 def plot_curve_2d(data, ax: mpl_ax.Axis) -> None:
 	x_sym, y_sym = list(data.keys())
 
+	if y_sym.mathtype is spux.MathType.Complex:
+		ax.plot(data[x_sym], data[y_sym].real, label='ℝ')
+		ax.plot(data[x_sym], data[y_sym].imag, label='𝕀')
+		ax.legend()
+
 	ax.plot(data[x_sym], data[y_sym])
-	ax.set_title(f'{x_sym.name_pretty} -> {y_sym.name_pretty}')
+	ax.set_title(f'{x_sym.name_pretty} → {y_sym.name_pretty}')
 	ax.set_xlabel(x_sym.plot_label)
-	ax.set_xlabel(y_sym.plot_label)
+	ax.set_ylabel(y_sym.plot_label)
 
 
 def plot_points_2d(data, ax: mpl_ax.Axis) -> None:
 	x_sym, y_sym = list(data.keys())
 
 	ax.scatter(data[x_sym], data[y_sym])
-	ax.set_title(f'{x_sym.name_pretty} -> {y_sym.name_pretty}')
+	ax.set_title(f'{x_sym.name_pretty} → {y_sym.name_pretty}')
 	ax.set_xlabel(x_sym.plot_label)
-	ax.set_xlabel(y_sym.plot_label)
+	ax.set_ylabel(y_sym.plot_label)
 
 
 # (ℝ, ℤ) -> ℝ
@@ -202,34 +206,30 @@ def plot_curves_2d(data, ax: mpl_ax.Axis) -> None:
 	for i, label in enumerate(data[label_sym]):
 		ax.plot(data[x_sym], data[y_sym][:, i], label=label)
 
-	ax.set_title(f'{x_sym.name_pretty} -> {y_sym.name_pretty}')
+	ax.set_title(f'{x_sym.name_pretty} → {y_sym.name_pretty}')
 	ax.set_xlabel(x_sym.plot_label)
-	ax.set_xlabel(y_sym.plot_label)
+	ax.set_ylabel(y_sym.plot_label)
 	ax.legend()
 
 
-def plot_filled_curves_2d(
-	data: jtyp.Float32[jtyp.Array, 'x_size 2'], info, ax: mpl_ax.Axis
-) -> None:
-	x_sym, _, y_sym = list(data.keys())
+def plot_filled_curves_2d(data, ax: mpl_ax.Axis) -> None:
+	x_sym, _, y_sym = list(data.keys(data))
 
 	ax.fill_between(data[x_sym], data[y_sym][:, 0], data[x_sym], data[y_sym][:, 1])
-	ax.set_title(f'{x_sym.name_pretty} -> {y_sym.name_pretty}')
+	ax.set_title(f'{x_sym.name_pretty} → {y_sym.name_pretty}')
 	ax.set_xlabel(x_sym.plot_label)
-	ax.set_xlabel(y_sym.plot_label)
+	ax.set_ylabel(y_sym.plot_label)
 	ax.legend()
 
 
 # (ℝ, ℝ) -> ℝ
-def plot_heatmap_2d(
-	data: jtyp.Float32[jtyp.Array, 'x_size y_size'], info, ax: mpl_ax.Axis
-) -> None:
+def plot_heatmap_2d(data, ax: mpl_ax.Axis) -> None:
 	x_sym, y_sym, c_sym = list(data.keys())
 
 	heatmap = ax.imshow(data[c_sym], aspect='equal', interpolation='none')
 	ax.figure.colorbar(heatmap, cax=ax)
 
-	ax.set_title(f'({x_sym.name_pretty}, {y_sym.name_pretty}) -> {c_sym.plot_label}')
+	ax.set_title(f'({x_sym.name_pretty}, {y_sym.name_pretty}) → {c_sym.plot_label}')
 	ax.set_xlabel(x_sym.plot_label)
 	ax.set_xlabel(y_sym.plot_label)
 	ax.legend()

src/blender_maxwell/utils/sim_symbols.py

@@ -24,7 +24,6 @@ from fractions import Fraction
 import jaxtyping as jtyp
 import pydantic as pyd
 import sympy as sp
-import sympy.physics.units as spu
 
 from . import extra_sympy_units as spux
 from . import logger, serialize
@@ -88,6 +87,7 @@ class SimSymbolName(enum.StrEnum):
 	Wavelength = enum.auto()
 	Frequency = enum.auto()
 
+	Perm = enum.auto()
 	PermXX = enum.auto()
 	PermYY = enum.auto()
 	PermZZ = enum.auto()
@@ -161,6 +161,7 @@ class SimSymbolName(enum.StrEnum):
 				# Optics
 				SSN.Wavelength: 'wl',
 				SSN.Frequency: 'freq',
+				SSN.Perm: 'eps_r',
 				SSN.PermXX: 'eps_xx',
 				SSN.PermYY: 'eps_yy',
 				SSN.PermZZ: 'eps_zz',
@@ -179,6 +180,7 @@ class SimSymbolName(enum.StrEnum):
 			SSN.LowerTheta: 'θ',
 			SSN.LowerPhi: 'φ',
 			# Fields
+			SSN.Er: 'Er',
 			SSN.Etheta: 'Eθ',
 			SSN.Ephi: 'Eφ',
 			SSN.Hr: 'Hr',
@@ -186,10 +188,11 @@ class SimSymbolName(enum.StrEnum):
 			SSN.Hphi: 'Hφ',
 			# Optics
 			SSN.Wavelength: 'λ',
-			SSN.Frequency: '𝑓',
-			SSN.PermXX: 'ε_xx',
-			SSN.PermYY: 'ε_yy',
-			SSN.PermZZ: 'ε_zz',
+			SSN.Frequency: 'fᵣ',
+			SSN.Perm: 'εᵣ',
+			SSN.PermXX: 'εᵣ[xx]',
+			SSN.PermYY: 'εᵣ[yy]',
+			SSN.PermZZ: 'εᵣ[zz]',
 		}.get(self, self.name)
 
 
@@ -248,6 +251,8 @@ class SimSymbol(pyd.BaseModel):
 	## -> See self.domain.
 	## -> We have to deconstruct symbolic interval semantics a bit for UI.
 	is_constant: bool = False
+	exclude_zero: bool = False
+
 	interval_finite_z: tuple[int, int] = (0, 1)
 	interval_finite_q: tuple[tuple[int, int], tuple[int, int]] = ((0, 1), (1, 1))
 	interval_finite_re: tuple[float, float] = (0.0, 1.0)
@@ -284,20 +289,25 @@ class SimSymbol(pyd.BaseModel):
 	@functools.cached_property
 	def unit_label(self) -> str:
 		"""Pretty unit label, which is an empty string when there is no unit."""
-		return spux.sp_to_str(self.unit) if self.unit is not None else ''
+		return spux.sp_to_str(self.unit.n(4)) if self.unit is not None else ''
+
+	@functools.cached_property
+	def name_unit_label(self) -> str:
+		"""Pretty name | unit label, which is just the name when there is no unit."""
+		if self.unit is None:
+			return self.name_pretty
+		return f'{self.name_pretty} | {self.unit_label}'
 
 	@functools.cached_property
 	def def_label(self) -> str:
 		"""Pretty definition label, exposing the symbol definition."""
-		return f'{self.name_pretty} | {self.unit_label} ∈ {self.mathtype_size_label}'
+		return f'{self.name_unit_label} ∈ {self.mathtype_size_label}'
 		## TODO: Domain of validity from self.domain?
 
 	@functools.cached_property
 	def plot_label(self) -> str:
 		"""Pretty plot-oriented label."""
-		return f'{self.name_pretty}' + (
-			f'({self.unit})' if self.unit is not None else ''
-		)
+		return f'{self.name_pretty} ({self.unit_label})'
 
 	####################
 	# - Computed Properties
@@ -307,6 +317,11 @@ class SimSymbol(pyd.BaseModel):
 		"""Factor corresponding to the tracked unit, which can be multiplied onto exported values without `None`-checking."""
 		return self.unit if self.unit is not None else sp.S(1)
 
+	@functools.cached_property
+	def unit_dim(self) -> spux.SympyExpr:
+		"""Unit dimension factor corresponding to the tracked unit, which can be multiplied onto exported values without `None`-checking."""
+		return self.unit if self.unit is not None else sp.S(1)
+
 	@functools.cached_property
 	def size(self) -> tuple[int, ...] | None:
 		return {
@@ -403,6 +418,29 @@ class SimSymbol(pyd.BaseModel):
 			case (False, False):
 				return sp.S(self.mathtype.coerce_compatible_pyobj(-1))
 
+	@functools.cached_property
+	def is_nonzero(self) -> bool:
+		if self.exclude_zero:
+			return True
+
+		def check_real_domain(real_domain):
+			return (
+				(
+					real_domain.left == 0
+					and real_domain.left_open
+					or real_domain.right == 0
+					and real_domain.right_open
+				)
+				or real_domain.left > 0
+				or real_domain.right < 0
+			)
+
+		if self.mathtype is spux.MathType.Complex:
+			return check_real_domain(self.domain[0]) and check_real_domain(
+				self.domain[1]
+			)
+		return check_real_domain(self.domain)
+
 	####################
 	# - Properties
 	####################
@@ -434,23 +472,15 @@ class SimSymbol(pyd.BaseModel):
 				mathtype_kwargs |= {'complex': True}
 
 		# Non-Zero Assumption
-		if (
-			(
-				self.domain.left == 0
-				and self.domain.left_open
-				or self.domain.right == 0
-				and self.domain.right_open
-			)
-			or self.domain.left > 0
-			or self.domain.right < 0
-		):
+		if self.is_nonzero:
 			mathtype_kwargs |= {'nonzero': True}
 
 		# Positive/Negative Assumption
-		if self.domain.left >= 0:
-			mathtype_kwargs |= {'positive': True}
-		elif self.domain.right <= 0:
-			mathtype_kwargs |= {'negative': True}
+		if self.mathtype is not spux.MathType.Complex:
+			if self.domain.left >= 0:
+				mathtype_kwargs |= {'positive': True}
+			elif self.domain.right <= 0:
+				mathtype_kwargs |= {'negative': True}
 
 		# Scalar: Return Symbol
 		if self.rows == 1 and self.cols == 1:
@@ -521,8 +551,8 @@ class SimSymbol(pyd.BaseModel):
 						self.valid_domain_value, strip_unit=True
 					),
 					# Defaults: FlowKind.Range
-					'default_min': self.domain.start,
-					'default_max': self.domain.end,
+					'default_min': self.conform(self.domain.start, strip_unit=True),
+					'default_max': self.conform(self.domain.end, strip_unit=True),
 				}
 			msg = f'Tried to generate an ExprSocket from a SymSymbol "{self.name}", but its unit ({self.unit}) is not a valid unit of its physical type ({self.physical_type}) (SimSymbol={self})'
 			raise NotImplementedError(msg)
@@ -671,7 +701,9 @@ class SimSymbol(pyd.BaseModel):
 		sym_name: SimSymbolName,
 		expr: spux.SympyExpr,
 		unit_expr: spux.SympyExpr,
-	) -> typ.Self:
+		is_constant: bool = False,
+		optional: bool = False,
+	) -> typ.Self | None:
 		"""Deduce a `SimSymbol` that matches the output of a given expression (and unit expression).
 
 		This is an essential method, allowing for the ded
@@ -697,12 +729,28 @@ class SimSymbol(pyd.BaseModel):
 		# MathType from Expr Assumptions
 		## -> All input symbols have assumptions, because we are very pedantic.
 		## -> Therefore, we should be able to reconstruct the MathType.
-		mathtype = spux.MathType.from_expr(expr)
+		mathtype = spux.MathType.from_expr(expr, optional=optional)
+		if mathtype is None:
+			return None
 
 		# PhysicalType as "NonPhysical"
 		## -> 'unit' still applies - but we can't guarantee a PhysicalType will.
 		## -> Therefore, this is what we gotta do.
-		physical_type = spux.PhysicalType.NonPhysical
+		if spux.uses_units(unit_expr):
+			simplified_unit_expr = sp.simplify(unit_expr)
+			expr_physical_type = spux.PhysicalType.from_unit(
+				simplified_unit_expr, optional=True
+			)
+
+			physical_type = (
+				spux.PhysicalType.NonPhysical
+				if expr_physical_type is None
+				else expr_physical_type
+			)
+			unit = simplified_unit_expr
+		else:
+			physical_type = spux.PhysicalType.NonPhysical
+			unit = None
 
 		# Rows/Cols from Expr (if Matrix)
 		rows, cols = expr.shape if isinstance(expr, sp.MatrixBase) else (1, 1)
@@ -711,9 +759,11 @@ class SimSymbol(pyd.BaseModel):
 			sym_name=sym_name,
 			mathtype=mathtype,
 			physical_type=physical_type,
-			unit=unit_expr if unit_expr != 1 else None,
+			unit=unit,
 			rows=rows,
 			cols=cols,
+			is_constant=is_constant,
+			exclude_zero=expr.is_zero is not None and not expr.is_zero,
 		)
 
 	####################