feat: various sym-flow modifications

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

@@ -14,12 +14,12 @@
 # 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 dataclasses
 import functools
 import typing as typ
 
 import jaxtyping as jtyp
 import numpy as np
+import pydantic as pyd
 import sympy as sp
 
 from blender_maxwell.utils import extra_sympy_units as spux
@@ -29,8 +29,7 @@ log = logger.get(__name__)
 
 
 # TODO: Our handling of 'is_sorted' is sloppy and probably wrong.
-@dataclasses.dataclass(frozen=True, kw_only=True)
+class ArrayFlow(pyd.BaseModel):
-class ArrayFlow:
 	"""A homogeneous, realized array of numerical values with an optionally-attached unit and sort-tracking.
 
 	While the principle is simple, arrays-with-units ends up being a powerful basis for derived and computed features/methods/processing.
@@ -41,7 +40,9 @@ class ArrayFlow:
 			None if unitless.
 	"""
 
-	values: jtyp.Shaped[jtyp.Array, '...']
+	model_config = pyd.ConfigDict(frozen=True, arbitrary_types_allowed=True)
+
+	values: jtyp.Inexact[jtyp.Array, '...']  ## TODO: Custom field type
 	unit: spux.Unit | None = None
 
 	is_sorted: bool = False

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

@@ -18,6 +18,7 @@ import enum
 import functools
 import typing as typ
 
+from blender_maxwell.contracts import BLEnumElement
 from blender_maxwell.utils import extra_sympy_units as spux
 from blender_maxwell.utils import logger
 from blender_maxwell.utils.staticproperty import staticproperty
@@ -99,6 +100,17 @@ class FlowKind(enum.StrEnum):
 	def to_icon(_: typ.Self) -> str:
 		return ''
 
+	@property
+	def name(self) -> str:
+		return FlowKind.to_name(self)
+
+	@property
+	def icon(self) -> str:
+		return FlowKind.to_icon(self)
+
+	def bl_enum_element(self, i) -> BLEnumElement:
+		return (str(self), self.name, self.name, self.icon, i)
+
 	####################
 	# - Static Properties
 	####################
@@ -162,7 +174,7 @@ class FlowKind(enum.StrEnum):
 	def socket_shape(self) -> str:
 		"""Return the socket shape associated with this `FlowKind`.
 
-		**ONLY** valid for `FlowKind`s that can be considered "active".
+		Should generally only be used with `active_kinds`.
 
 		Raises:
 			ValueError: If this `FlowKind` cannot ever be considered "active".
@@ -172,7 +184,7 @@ class FlowKind(enum.StrEnum):
 			FlowKind.Array: 'SQUARE',
 			FlowKind.Range: 'SQUARE',
 			FlowKind.Func: 'DIAMOND',
-		}[self]
+		}.get(self, 'CIRCLE')
 
 	####################
 	# - Class Methods

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

@@ -14,40 +14,17 @@
 # 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 dataclasses
+r"""Implements the core of the math system via `FuncFlow`, which allows high-performance, fully-expressive workflows with data that can be "very large", and/or whose input parameters are not yet fully known.
-import functools
-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__)
-
-LazyFunction: typ.TypeAlias = typ.Callable[[typ.Any, ...], typ.Any]
-
-
-@dataclasses.dataclass(frozen=True, kw_only=True)
-class FuncFlow:
-	r"""Defines a flow of data as incremental function composition.
-
-	For specific math system usage instructions, please consult the documentation of relevant nodes.
 
 # Introduction
 When using nodes to do math, it becomes immediately obvious to express **flows of data as composed function chains**.
 Doing so has several advantages:
 
-	- **Interactive**: Since no large-array math is being done, the UI can be designed to feel fast and snappy.
+- **Interactive**: Since no large-array math is being done, the UI can be designed to feel fast and snappy, greatly boosting the will to experiment and ultimate productivity.
-	- **Symbolic**: Since no numerical math is being done yet, we can choose to keep our input parameters as symbolic variables with no performance impact.
+- **Symbolic**: Since no numerical math is being done yet, we can inject symbolic variables at-will, enabling effortless ex. parameter sweeping, band-structure generation, differentiable can choose to keep our input parameters as symbolic variables with no performance impact.
-	- **Performant**: Since no operations are happening, the UI feels fast and snappy.
+- **Performant**: Since the data pipeline is built as a single function w/o side effects, that function can be often be JIT-optimized for highly-optimized execution on the instruction sets used by modern massively-parallel devices, like modern CPUs (SSE/AVX), GPUs (ex. PTX), and HPC clusters (network-sharding to ARM/x86).
+
+The result is a math system optimized for the analysis typically needed in electrodynamic contexts, prioritizing clarity and flexibility at soft-real-time, even with gigabytes of data on relatively weak hardware.
 
 ## Strongly Related FlowKinds
 For doing math, `Func` relies on two other `FlowKind`s, which must run in parallel:
@@ -238,6 +215,35 @@ class FuncFlow:
 	This enables our humble interface to implement fully functional **inverse design** of parameterized structures, using only nodes.
 
 But above all, we hope that this math system is fun, practical, and maybe even interesting.
+"""
+
+import functools
+import typing as typ
+from types import MappingProxyType
+
+import jax
+import jaxtyping as jtyp
+import pydantic as pyd
+import sympy as sp
+
+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__)
+
+LazyFunction: typ.TypeAlias = typ.Callable[[typ.Any, ...], typ.Any]
+
+
+class FuncFlow(pyd.BaseModel):
+	r"""Defines a flow of data as incremental function composition.
+
+	For theoretical information, please see the documentation of this module.
+	For specific math system usage instructions, please consult the documentation of relevant nodes.
 
 	Attributes:
 		func: The function that generates the represented value.
@@ -247,14 +253,16 @@ class FuncFlow:
 			See the documentation of `self.func_jax()`.
 	"""
 
+	model_config = pyd.ConfigDict(frozen=True)
+
 	func: LazyFunction
-	func_args: list[sim_symbols.SimSymbol] = dataclasses.field(default_factory=list)
+	func_args: list[sim_symbols.SimSymbol] = pyd.Field(default_factory=list)
-	func_kwargs: dict[str, sim_symbols.SimSymbol] = dataclasses.field(
+	func_kwargs: dict[str, sim_symbols.SimSymbol] = pyd.Field(default_factory=dict)
-		default_factory=dict
+	func_output: sim_symbols.SimSymbol | None = None
-	)
+
 	supports_jax: bool = False
 
-	concatenated: bool = False
+	is_concatenated: bool = False
 
 	####################
 	# - Functions
@@ -318,6 +326,7 @@ class FuncFlow:
 			{}
 		),
 	) -> typ.Self:
+		"""Run the represented function with the best optimization available, given particular choices for all function arguments and for all unrealized symbols."""
 		if self.supports_jax:
 			return self.func_jax(
 				*params.scaled_func_args(symbol_values),
@@ -371,14 +380,55 @@ class FuncFlow:
 
 		return data | {info.output: self.realize(params, symbol_values=symbol_values)}
 
+	def realize_partial(
+		self, params: ParamsFlow
+	) -> typ.Callable[
+		[int | float | complex | jtyp.Inexact[jtyp.Array, '...'], ...],
+		jtyp.Inexact[jtyp.Array, '...'],
+	]:
+		"""Create a purely-numerical function, which takes only numerical.
+
+		The units/types/shape/etc. of the returned numerical type conforms to the `SimSymbol` specification of relevant `self.func_args` entries and `self.func_output`.
+
+		This function should be used whenever the unrealized result of a `FuncFlow` needs to be used as the argument to another `FuncFlow`.
+		By using `realize_partial()`, two things are ensured:
+
+		- Since the function defined in `.compose_within()` must be purely numerical, the usual `.realize()` mechanism can't be used to sweep away the pre-realized symbol values.
+		- Since this `FuncFlow` is completely consumed, with no symbols / arguments / etc. explicitly surviving, its impact on the data flow can be considered to have been effectively terminated after using this function.
+
+		Notes:
+			Be **very careful about units**.
+			Ideally, the bottom function should use `.scale_to_unit()` before invoking `.compose_within()` with the output of this function.
+		"""
+		pre_realized_syms = list(
+			params.realize_symbols(params.realized_symbols, allow_partial=True).values()
+		)
+
+		def realizer(
+			*sym_args: int | float | complex | jtyp.Inexact[jtyp.Array, '...'],
+		) -> jtyp.Inexact[jtyp.Array, '...']:
+			return self.func(
+				*[
+					func_arg_n(*sym_args, *pre_realized_syms)
+					for func_arg_n in params.func_args_n
+				],
+				**{
+					func_arg_name: func_kwarg_n(*sym_args, *pre_realized_syms)
+					for func_arg_name, func_kwarg_n in params.func_kwargs_n.items()
+				},
+			)
+
+		return realizer
+
 	####################
-	# - Composition Operations
+	# - Operations
 	####################
 	def compose_within(
 		self,
 		enclosing_func: LazyFunction,
-		enclosing_func_args: list[type] = (),
+		enclosing_func_args: list[sim_symbols.SimSymbol] = (),
-		enclosing_func_kwargs: dict[str, type] = MappingProxyType({}),
+		enclosing_func_kwargs: dict[str, sim_symbols.SimSymbol] = MappingProxyType({}),
+		enclosing_func_output: sim_symbols.SimSymbol | None = None,
 		supports_jax: bool = False,
 	) -> typ.Self:
 		"""Compose `self.func` within the given enclosing function, which itself takes arguments, and create a new `FuncFlow` to contain it.
@@ -415,6 +465,10 @@ class FuncFlow:
 		Returns:
 			A lazy function that takes both the enclosed and enclosing arguments, and returns the value of the enclosing function (whose first argument is the output value of the enclosed function).
 		"""
+		## TODO: Support unit system conversion at the point of composition.
+		## -- This may require us to track the units of the function output.
+		## TODO: Support JAX-evaluation when jax support changes from True to False.
+		## -- This would allow big data flows to compose performantly as arguments into non-JAX functions.
 		return FuncFlow(
 			func=lambda *args, **kwargs: enclosing_func(
 				self.func(
@@ -426,6 +480,7 @@ class FuncFlow:
 			),
 			func_args=self.func_args + list(enclosing_func_args),
 			func_kwargs=self.func_kwargs | dict(enclosing_func_kwargs),
+			func_output=enclosing_func_output,
 			supports_jax=self.supports_jax and supports_jax,
 		)
 
@@ -472,7 +527,7 @@ class FuncFlow:
 				*list(args[: len(self.func_args)]),
 				**{k: v for k, v in kwargs.items() if k in self.func_kwargs},
 			)
-			if not self.concatenated:
+			if not self.is_concatenated:
 				return (ret,)
 			return ret
 
@@ -487,5 +542,83 @@ class FuncFlow:
 			func_args=self.func_args + other.func_args,
 			func_kwargs=self.func_kwargs | other.func_kwargs,
 			supports_jax=self.supports_jax and other.supports_jax,
-			concatenated=True,
+			is_concatenated=True,
 		)
+
+	def scale_to_unit(self, unit: spux.Unit | None = None) -> typ.Self:
+		"""Encloses this function in a unit-converting function, whose output is a converted, unitless scalar.
+
+		`unit` must be manually guaranteed to be compatible with `self.unit`.
+		"""
+		if self.func_output is not None:
+			# Retrieve Output Unit
+			output_unit = self.func_output.unit
+
+			# Compile Efficient Unit-Conversion Function
+			a = self.func_output.mathtype.sp_symbol_a
+			unit_convert_expr = (
+				spux.scale_to_unit(a * output_unit, unit)
+				if self.func_output.unit is not None
+				else a
+			)
+			unit_convert_func = sp.lambdify(a, unit_convert_expr.n(), 'jax')
+
+			# Compose Unit-Converted FuncFlow
+			return self.compose_within(
+				enclosing_func=unit_convert_func,
+				supports_jax=True,
+				enclosing_func_output=self.func_output.update(unit=unit),
+			)
+
+		msg = f'Tried to scale a FuncFlow to a unit system, but it has no tracked output SimSymbol. ({self})'
+		raise ValueError(msg)
+
+	def scale_to_unit_system(
+		self, unit_system: spux.UnitSystem | None = None
+	) -> typ.Self:
+		"""Encloses this function in a unit-converting function, whose output is a converted, unitless scalar.
+
+		Using `self.output_symbol`, which tracks the units of the output, we can determine a scaling factor to multiply the (numerical) function output by in order to conform it to the given unit system.
+
+		In general, **don't use this**.
+		Any superfluous numerical operations in a data pipeline can enhance instabilities and interfere with JIT-optimization (floating-point arithmetic isn't commutative, for example).
+		However, occasionally, we need to "intercept" a lazy data flow, for example when realizing a `FlowKind.Value` that doesn't understand symbols or units - but which only accepts a float/complex scalar/array with pre-determined unit convention.
+
+		For this purpose alone, this method is provided to pre-scale a `FuncFlow`, just before using `realize()` / `__or__` and then `realize()`.
+		**To encourage proper usage** (and ease implementation), the output unit in `self.func_output` of the output will be reset to `None` - indicating that the output can only be handled as a unitless scalar w/semantic meaning tracked elsewhere.
+
+		Notes:
+			**ONLY** use with output types that support meaningful arbitrary multiplication.
+
+			A scale-only sympy expression will be used to produce an optimized JAX function of a single variable, which will then be composed onto the existing `FuncFlow`.
+
+		Parameters:
+			unit_system: The unit system to conform the function output to.
+
+		Returns:
+			A new `FuncFlow` that conforms to the new unit, but is itself now considered unitless.
+		"""
+		if self.func_output is not None:
+			# Retrieve Output Unit
+			output_unit = self.func_output.unit
+
+			# Compile Efficient Unit-Conversion Function
+			a = self.func_output.mathtype.sp_symbol_a
+			unit_convert_expr = (
+				spux.strip_unit_system(
+					spux.convert_to_unit_system(a * output_unit, unit_system)
+				)
+				if self.func_output.unit is not None
+				else a
+			)
+			unit_convert_func = sp.lambdify(a, unit_convert_expr.n(), 'jax')
+
+			# Compose Unit-Converted FuncFlow
+			return self.compose_within(
+				enclosing_func=unit_convert_func,
+				supports_jax=True,
+				enclosing_func_output=self.func_output.update(unit=None),
+			)
+
+		msg = f'Tried to scale a FuncFlow to a unit system, but it has no tracked output SimSymbol. ({self})'
+		raise ValueError(msg)

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

@@ -14,17 +14,15 @@
 # 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 dataclasses
 import enum
 import functools
 import typing as typ
-from fractions import Fraction
 from types import MappingProxyType
 
 import jax.numpy as jnp
 import jaxtyping as jtyp
+import pydantic as pyd
 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, sim_symbols
@@ -61,8 +59,7 @@ class ScalingMode(enum.StrEnum):
 		return ''
 
 
-@dataclasses.dataclass(frozen=True, kw_only=True)
+class RangeFlow(pyd.BaseModel):
-class RangeFlow:
 	r"""Represents a finite spaced array using symbolic boundary expressions.
 
 	Whenever an array can be represented like this, the advantages over an `ArrayFlow` are numerous.
@@ -92,8 +89,10 @@ class RangeFlow:
 		symbols: Set of variables from which `start` and/or `stop` are determined.
 	"""
 
-	start: spux.ScalarUnitlessComplexExpr
+	model_config = pyd.ConfigDict(frozen=True)
-	stop: spux.ScalarUnitlessComplexExpr
+
+	start: spux.ScalarUnitlessRealExpr
+	stop: spux.ScalarUnitlessRealExpr
 	steps: int = 0
 	scaling: ScalingMode = ScalingMode.Lin
 
@@ -102,7 +101,7 @@ class RangeFlow:
 	symbols: frozenset[sim_symbols.SimSymbol] = frozenset()
 
 	# Helper Attributes
-	pre_fourier_ideal_midpoint: spux.ScalarUnitlessComplexExpr | None = None
+	pre_fourier_ideal_midpoint: spux.ScalarUnitlessRealExpr | None = None
 
 	####################
 	# - SimSymbol Interop
@@ -218,14 +217,26 @@ class RangeFlow:
 		)
 		return combined_mathtype
 
-	@property
+	@functools.cached_property
 	def ideal_midpoint(self) -> spux.SympyExpr:
 		return (self.stop + self.start) / 2
 
-	@property
+	@functools.cached_property
 	def ideal_range(self) -> spux.SympyExpr:
 		return self.stop - self.start
 
+	@functools.cached_property
+	def ideal_step_size(self) -> spux.SympyExpr:
+		return self.ideal_range / (self.steps - 1)
+
+	@functools.cached_property
+	def is_always_nonzero(self) -> spux.SympyExpr:
+		if self.start > 0 or self.stop < 0:
+			return True
+
+		is_zero = (self.start % self.ideal_step_size).is_zero
+		return is_zero if is_zero is not None else False
+
 	####################
 	# - Methods
 	####################
@@ -452,7 +463,7 @@ class RangeFlow:
 		symbol_values: dict[sim_symbols.SimSymbol, spux.SympyExpr] = MappingProxyType(
 			{}
 		),
-	) -> dict[sp.Symbol, spux.ScalarUnitlessComplexExpr]:
+	) -> dict[sp.Symbol, spux.ScalarUnitlessRealExpr]:
 		"""Realize **all** input symbols to the `RangeFlow`.
 
 		Parameters:
@@ -480,7 +491,7 @@ class RangeFlow:
 					raise NotImplementedError(msg)
 
 				realized_syms |= {sym: v}
-
+			return realized_syms
 		msg = f'RangeFlow: Not all symbols were given a value during realization (symbols={self.symbols}, symbol_values={symbol_values})'
 		raise ValueError(msg)
 

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

@@ -14,13 +14,13 @@
 # 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 dataclasses
 import functools
 import typing as typ
 from fractions import Fraction
 from types import MappingProxyType
 
 import jaxtyping as jtyp
+import pydantic as pyd
 import sympy as sp
 
 from blender_maxwell.utils import extra_sympy_units as spux
@@ -28,31 +28,35 @@ from blender_maxwell.utils import logger, sim_symbols
 
 from .array import ArrayFlow
 from .expr_info import ExprInfo
-from .flow_kinds import FlowKind
 from .lazy_range import RangeFlow
 
 log = logger.get(__name__)
 
 
-@dataclasses.dataclass(frozen=True, kw_only=True)
+class ParamsFlow(pyd.BaseModel):
-class ParamsFlow:
 	"""Retrieves all symbols by concatenating int, real, and complex symbols, and sorting them by name.
 
 	Returns:
 		All symbols valid for use in the expression.
 	"""
 
-	arg_targets: list[sim_symbols.SimSymbol] = dataclasses.field(default_factory=list)
+	model_config = pyd.ConfigDict(frozen=True)
-	kwarg_targets: list[str, sim_symbols.SimSymbol] = dataclasses.field(
-		default_factory=dict
-	)
 
-	func_args: list[spux.SympyExpr] = dataclasses.field(default_factory=list)
+	arg_targets: list[sim_symbols.SimSymbol] = pyd.Field(default_factory=list)
-	func_kwargs: dict[str, spux.SympyExpr] = dataclasses.field(default_factory=dict)
+	kwarg_targets: dict[str, sim_symbols.SimSymbol] = pyd.Field(default_factory=dict)
+
+	func_args: list[spux.SympyExpr] = pyd.Field(default_factory=list)
+	func_kwargs: dict[str, spux.SympyExpr] = pyd.Field(default_factory=dict)
 
 	symbols: frozenset[sim_symbols.SimSymbol] = frozenset()
+	realized_symbols: dict[
+		sim_symbols.SimSymbol, spux.SympyExpr | RangeFlow | ArrayFlow
+	] = pyd.Field(default_factory=dict)
 
-	is_differentiable: bool = False
+	@functools.cached_property
+	def diff_symbols(self) -> set[sim_symbols.SimSymbol]:
+		"""Set of all unrealized `SimSymbol`s that can act as inputs when differentiating the function for which this `ParamsFlow` tracks arguments."""
+		return {sym for sym in self.symbols if sym.can_diff}
 
 	####################
 	# - Symbols
@@ -78,6 +82,27 @@ class ParamsFlow:
 		"""
 		return [sym.sp_symbol_matsym for sym in self.sorted_symbols]
 
+	@functools.cached_property
+	def all_sorted_symbols(self) -> list[sim_symbols.SimSymbol]:
+		"""Retrieves all symbols by concatenating int, real, and complex symbols, and sorting them by name.
+
+		Returns:
+			All symbols valid for use in the expression.
+		"""
+		key_func = lambda sym: sym.name  # noqa: E731
+		return sorted(self.symbols, key=key_func) + sorted(
+			self.realized_symbols.keys(), key=key_func
+		)
+
+	@functools.cached_property
+	def all_sorted_sp_symbols(self) -> list[sim_symbols.SimSymbol]:
+		"""Retrieves all symbols by concatenating int, real, and complex symbols, and sorting them by name.
+
+		Returns:
+			All symbols valid for use in the expression.
+		"""
+		return [sym.sp_symbol_matsym for sym in self.all_sorted_symbols]
+
 	####################
 	# - JIT'ed Callables for Numerical Function Arguments
 	####################
@@ -101,7 +126,7 @@ class ParamsFlow:
 		"""
 		return [
 			sp.lambdify(
-				self.sorted_sp_symbols,
+				self.all_sorted_sp_symbols,
 				target_sym.conform(func_arg, strip_unit=True),
 				'jax',
 			)
@@ -127,7 +152,7 @@ class ParamsFlow:
 		"""
 		return {
 			key: sp.lambdify(
-				self.sorted_sp_symbols,
+				self.all_sorted_sp_symbols,
 				self.kwarg_targets[key].conform(func_arg, strip_unit=True),
 				'jax',
 			)
@@ -142,8 +167,9 @@ class ParamsFlow:
 		symbol_values: dict[
 			sim_symbols.SimSymbol, spux.SympyExpr | RangeFlow | ArrayFlow
 		] = MappingProxyType({}),
+		allow_partial: bool = False,
 	) -> dict[
-		sp.Symbol,
+		sim_symbols.SimSymbol,
 		int | float | Fraction | float | complex | jtyp.Shaped[jtyp.Array, '...'] :,
 	]:
 		"""Fully realize all symbols by assigning them a value.
@@ -160,10 +186,12 @@ class ParamsFlow:
 		Returns:
 			A dictionary almost with `.subs()`, other than `jax` arrays.
 		"""
-		if set(self.symbols) == set(symbol_values.keys()):
+		if allow_partial or set(self.all_sorted_symbols) == set(symbol_values.keys()):
 			realized_syms = {}
-			for sym in self.sorted_symbols:
+			for sym in self.all_sorted_symbols:
-				sym_value = symbol_values[sym]
+				sym_value = symbol_values.get(sym)
+				if sym_value is None and allow_partial:
+					continue
 
 				if isinstance(sym_value, spux.SympyType):
 					v = sym.scale(sym_value)
@@ -214,7 +242,9 @@ class ParamsFlow:
 		Parameters:
 			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())
+		realized_symbols = list(
+			self.realize_symbols(symbol_values | self.realized_symbols).values()
+		)
 		return [func_arg_n(*realized_symbols) for func_arg_n in self.func_args_n]
 
 	def scaled_func_kwargs(
@@ -227,10 +257,11 @@ class ParamsFlow:
 
 		Other than the `dict[str, ...]` key, the semantics are identical to `self.scaled_func_args()`.
 		"""
-		realized_symbols = self.realize_symbols(symbol_values)
+		realized_symbols = self.realize_symbols(symbol_values | self.realized_symbols)
+
 		return {
-			func_arg_name: func_arg_n(**realized_symbols)
+			func_arg_name: func_kwarg_n(**realized_symbols)
-			for func_arg_name, func_arg_n in self.func_kwargs_n.items()
+			for func_arg_name, func_kwarg_n in self.func_kwargs_n.items()
 		}
 
 	####################
@@ -251,7 +282,7 @@ class ParamsFlow:
 			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 and other.is_differentiable,
+			realized_symbols=self.realized_symbols | other.realized_symbols,
 		)
 
 	def compose_within(
@@ -261,7 +292,6 @@ class ParamsFlow:
 		enclosing_func_args: list[spux.SympyExpr] = (),
 		enclosing_func_kwargs: dict[str, spux.SympyExpr] = MappingProxyType({}),
 		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),
@@ -269,13 +299,41 @@ class ParamsFlow:
 			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=(
+			realized_symbols=self.realized_symbols,
-				self.is_differentiable
-				if not enclosing_symbols
-				else (self.is_differentiable & enclosing_is_differentiable)
-			),
 		)
 
+	def realize_partial(
+		self,
+		symbol_values: dict[
+			sim_symbols.SimSymbol, spux.SympyExpr | RangeFlow | ArrayFlow
+		],
+	) -> typ.Self:
+		"""Provide a particular expression/range/array to realize some symbols.
+
+		Essentially removes symbols from `self.symbols`, and adds the symbol w/value to `self.realized_symbols`.
+		As a result, only the still-unrealized symbols need to be passed at the time of realization (using ex. `self.scaled_func_args()`).
+
+		Parameters:
+			symbol_values: The value to realize for each `SimSymbol`.
+				**All keys** must be identically matched to a single element of `self.symbol`.
+				Can be empty, in which case an identical new `ParamsFlow` will be returned.
+
+		Raises:
+			ValueError: If any symbol in `symbol_values`
+		"""
+		syms = set(symbol_values.keys())
+		if syms.issubset(self.symbols) or not syms:
+			return ParamsFlow(
+				arg_targets=self.arg_targets,
+				kwarg_targets=self.kwarg_targets,
+				func_args=self.func_args,
+				func_kwargs=self.func_kwargs,
+				symbols=self.symbols - syms,
+				realized_symbols=self.realized_symbols | symbol_values,
+			)
+		msg = f'ParamsFlow: Not all partially realized symbols are defined on the ParamsFlow (symbols={self.symbols}, symbol_values={symbol_values})'
+		raise ValueError(msg)
+
 	####################
 	# - Generate ExprSocketDef
 	####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/managed_objs/managed_bl_image.py

@@ -16,7 +16,7 @@
 
 """Declares `ManagedBLImage`."""
 
-# import time
+import time
 import typing as typ
 
 import bpy
@@ -261,7 +261,7 @@ class ManagedBLImage(base.ManagedObj):
 		dpi: int | None = None,
 		bl_select: bool = False,
 	):
-		# times = [time.perf_counter()]
+		times = ['START', time.perf_counter()]
 
 		# Compute Plot Dimensions
 		# aspect_ratio, _dpi, _width_inches, _height_inches, width_px, height_px = (
@@ -277,22 +277,22 @@ class ManagedBLImage(base.ManagedObj):
 		# _width_inches, _height_inches, _dpi
 		# )
 		fig, canvas, ax = image_ops.mpl_fig_canvas_ax(width_inches, height_inches, dpi)
-		# times.append(['MPL Fig Canvas Axis', time.perf_counter() - times[0]])
+		times.append(['MPL Fig Canvas Axis', time.perf_counter() - times[0]])
 
 		# fig.clear()
 		ax.clear()
-		# times.append(['Clear Axis', time.perf_counter() - times[0]])
+		times.append(['Clear Axis', time.perf_counter() - times[0]])
 
 		# Plot w/User Parameter
 		func_plotter(ax)
-		# times.append(['Plot!', time.perf_counter() - times[0]])
+		times.append(['Plot!', time.perf_counter() - times[0]])
 
 		# Save Figure to BytesIO
 		canvas.draw()
-		# times.append(['Draw Pixels', time.perf_counter() - times[0]])
+		times.append(['Draw Pixels', time.perf_counter() - times[0]])
 
 		canvas_width_px, canvas_height_px = fig.canvas.get_width_height()
-		# times.append(['Get Canvas Dims', time.perf_counter() - times[0]])
+		times.append(['Get Canvas Dims', time.perf_counter() - times[0]])
 		image_data = (
 			np.float32(
 				np.flipud(
@@ -303,7 +303,7 @@ class ManagedBLImage(base.ManagedObj):
 			)
 			/ 255
 		)
-		# times.append(['Load Data from Canvas', time.perf_counter() - times[0]])
+		times.append(['Load Data from Canvas', time.perf_counter() - times[0]])
 
 		# Optimized Write to Blender Image
 		bl_image = self.bl_image(canvas_width_px, canvas_height_px, 'RGBA', 'uint8')

src/blender_maxwell/node_trees/maxwell_sim_nodes/node_tree.py

@@ -15,6 +15,8 @@
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
 import contextlib
+import functools
+import queue
 import typing as typ
 
 import bpy
@@ -26,6 +28,14 @@ from .managed_objs.managed_bl_image import ManagedBLImage
 
 log = logger.get(__name__)
 
+link_action_queue = queue.Queue()
+
+
+def set_link_validity(link: bpy.types.NodeLink, validity: bool) -> None:
+	log.critical('Set %s validity to %s', str(link), str(validity))
+	link.is_valid = validity
+
+
 ####################
 # - Cache Management
 ####################
@@ -45,58 +55,93 @@ class DeltaNodeLinkCache(typ.TypedDict):
 
 
 class NodeLinkCache:
-	"""A pointer-based cache of node links in a node tree.
+	"""A volatile pointer-based cache of node links in a node tree.
+
+	Warnings:
+		Everything here is **extremely** unsafe.
+		Even a single mistake **will** cause a use-after-free crash of Blender.
+
+		Used perfectly, it allows for powerful features; anything less, and it's an epic liability.
 
 	Attributes:
-		_node_tree: Reference to the owning node tree.
+		_node_tree: Reference to the node tree for which this cache is valid.
-		link_ptrs_as_links:
+		link_ptrs: Memory-address identifiers for all node links that currently exist in `_node_tree`.
-		link_ptrs: Pointers (as in integer memory adresses) to `NodeLink`s.
+		link_ptrs_as_links: Mapping from pointers (integers) to actual `NodeLink` objects.
-		link_ptrs_as_links: Map from pointers to actual `NodeLink`s.
+			**WARNING**: If the pointer-referenced object no longer exists, then Blender **will crash immediately** upon attempting to use it. There is no way to mitigate this.
-		link_ptrs_from_sockets: Map from pointers to `NodeSocket`s, representing the source of each `NodeLink`.
+		socket_ptrs: Memory-address identifiers for all sockets that currently exist in `_node_tree`.
-		link_ptrs_from_sockets: Map from pointers to `NodeSocket`s, representing the destination of each `NodeLink`.
+		socket_ptrs_as_sockets: Mapping from pointers (integers) to actual `NodeSocket` objects.
+			**WARNING**: If the pointer-referenced object no longer exists, then Blender **will crash immediately** upon attempting to use it. There is no way to mitigate this.
+		socket_ptr_refcount: The amount of links currently connected to a given socket pointer.
+			Used to drive the deletion of socket pointers using only knowledge about `link_ptr` removal.
+		link_ptrs_as_from_socket_ptrs: The pointer of the source socket, defined for every node link pointer.
+		link_ptrs_as_to_socket_ptrs: The pointer of the destination socket, defined for every node link pointer.
 	"""
 
 	def __init__(self, node_tree: bpy.types.NodeTree):
-		"""Initialize the cache from a node tree.
+		"""Defines and fills the cache from a live node tree."""
-
-		Parameters:
-			node_tree: The Blender node tree whose `NodeLink`s will be cached.
-		"""
 		self._node_tree = node_tree
 
-		# Link PTR and PTR->REF
 		self.link_ptrs: set[MemAddr] = set()
 		self.link_ptrs_as_links: dict[MemAddr, bpy.types.NodeLink] = {}
 
-		# Socket PTR and PTR->REF
 		self.socket_ptrs: set[MemAddr] = set()
 		self.socket_ptrs_as_sockets: dict[MemAddr, bpy.types.NodeSocket] = {}
 		self.socket_ptr_refcount: dict[MemAddr, int] = {}
 
-		# Link PTR -> Socket PTR
 		self.link_ptrs_as_from_socket_ptrs: dict[MemAddr, MemAddr] = {}
 		self.link_ptrs_as_to_socket_ptrs: dict[MemAddr, MemAddr] = {}
 
+		self.link_ptrs_invalid: set[MemAddr] = set()
+
 		# Fill Cache
 		self.regenerate()
 
 	def remove_link(self, link_ptr: MemAddr) -> None:
-		"""Removes a link pointer from the cache, indicating that the link doesn't exist anymore.
+		"""Reports a link as removed, causing it to be removed from the cache.
+
+		This **must** be run whenever a node link is deleted.
+		**Failure to to so WILL result in segmentation fault** at an unknown future time.
+
+		In particular, the following actions are taken:
+		- The entry in `self.link_ptrs_as_links` is deleted.
+		- Any entry in `self.link_ptrs_invalid` is deleted (if exists).
 
 		Notes:
-			- **DOES NOT** remove PTR->REF dictionary entries
+			Invoking this method directly causes the removed node links to not be reported as "removed" by `NodeLinkCache.regenerate()`.
-			- Invoking this method directly causes the removed node links to not be reported as "removed" by `NodeLinkCache.regenerate()`.
+			In some cases, this may be desirable, ex. for internal methods that shouldn't trip a `DataChanged` flow event.
-			- This **must** be done whenever a node link is deleted.
-			- Failure to do so may result in a segmentation fault at arbitrary future time.
 
 		Parameters:
-			link_ptr: Pointer to remove from the cache.
+			link_ptr: The pointer (integer) to remove from the cache.
+
+		Raises:
+			KeyError: If `link_ptr` is not a member of either `self.link_ptrs`, or of `self.link_ptrs_as_links`.
 		"""
 		self.link_ptrs.remove(link_ptr)
 		self.link_ptrs_as_links.pop(link_ptr)
 
+		if link_ptr in self.link_ptrs_invalid:
+			self.link_ptrs_invalid.remove(link_ptr)
+
 	def remove_sockets_by_link_ptr(self, link_ptr: MemAddr) -> None:
-		"""Removes a single pointer's reference to its from/to sockets."""
+		"""Deassociate from all sockets referenced by a link, respecting the socket pointer reference-count.
+
+		The `NodeLinkCache` stores references to all socket pointers referenced by any link.
+		Since several links can be associated with each socket, we must keep a "reference count" per-socket.
+		When the "reference count" drops to zero, then there are no longer any `NodeLink`s that refer to it, and therefore it should be removed from the `NodeLinkCache`.
+
+		This method facilitates that process by:
+		- Extracting (with removal) the from / to socket pointers associated with `link_ptr`.
+		- If the socket pointer has a reference count of `1`, then it is **completely removed**.
+		- If the socket pointer has a reference count of `>1`, then the reference count is decremented by `1`.
+
+		Notes:
+			In general, this should be called together with `remove_link`.
+			However, in certain cases, this process also needs to happen by itself.
+
+		Parameters:
+			link_ptr: The pointer (integer) to remove from the cache.
+		"""
+		# Remove Socket Pointers
 		from_socket_ptr = self.link_ptrs_as_from_socket_ptrs.pop(link_ptr, None)
 		to_socket_ptr = self.link_ptrs_as_to_socket_ptrs.pop(link_ptr, None)
 
@@ -113,31 +158,40 @@ class NodeLinkCache:
 				self.socket_ptr_refcount[socket_ptr] -= 1
 
 	def regenerate(self) -> DeltaNodeLinkCache:
-		"""Regenerates the cache from the internally-linked node tree.
+		"""Efficiently scans the internally referenced node tree to thoroughly update all attributes of this `NodeLinkCache`.
 
 		Notes:
-			- This is designed to run within the `update()` invocation of the node tree.
+			This runs in a **very** hot loop, within the `update()` function of the node tree.
-			- This should be a very fast function, since it is called so much.
+			Anytime anything happens in the node tree, `update()` (and therefore this method) is called.
+
+			Thus, performance is of the utmost importance.
+			Just a few microseconds too much may be amplified dozens of times over in practice, causing big stutters.
 		"""
 		# Compute All NodeLink Pointers
+		## -> It can be very inefficient to do any full-scan of the node tree.
+		## -> However, simply extracting the pointer: link ends up being fast.
+		## -> This pattern seems to be the best we can do, efficiency-wise.
 		all_link_ptrs_as_links = {
 			link.as_pointer(): link for link in self._node_tree.links
 		}
 		all_link_ptrs = set(all_link_ptrs_as_links.keys())
 
 		# Compute Added/Removed Links
+		## -> In essence, we've created a 'diff' here.
+		## -> Set operations are fast, and expressive!
 		added_link_ptrs = all_link_ptrs - self.link_ptrs
 		removed_link_ptrs = self.link_ptrs - all_link_ptrs
 
 		# Edge Case: 'from_socket' Reassignment
-		## (Reverse engineered) When all:
+		## (Reverse Engineered) When all are true:
-		##     - Created a new link between the same two nodes.
+		##     - Created a new link between the same nodes as previous link.
-		##     - Matching 'to_socket'.
+		##     - Matching 'to_socket' as the previous link.
-		##     - Non-matching 'from_socket' on the same node.
+		##     - Non-matching 'from_socket', but on the same node.
-		## -> THEN the link_ptr will not change, but the from_socket ptr should.
+		## -> THEN the link_ptr will not change, but the from_socket ptr does.
-		if len(added_link_ptrs) == 0 and len(removed_link_ptrs) == 0:
+		if not added_link_ptrs and not removed_link_ptrs:
 			# Find the Link w/Reassigned 'from_socket' PTR
-			## A bit of a performance hit from the search, but it's an edge case.
+			## -> This isn't very fast, but the edge case isn't so common.
+			## -> Comprehensions are still quite optimized.
 			_link_ptr_as_from_socket_ptrs = {
 				link_ptr: (
 					from_socket_ptr,
@@ -149,9 +203,9 @@ class NodeLinkCache:
 			}
 
 			# Completely Remove the Old Link (w/Reassigned 'from_socket')
-			## This effectively reclassifies the edge case as a normal 're-add'.
+			## -> Casts the edge case to look like a typical 're-add'.
 			for link_ptr in _link_ptr_as_from_socket_ptrs:
-				log.info(
+				log.debug(
 					'Edge-Case - "from_socket" Reassigned in NodeLink w/o New NodeLink Pointer: %s',
 					link_ptr,
 				)
@@ -159,21 +213,25 @@ class NodeLinkCache:
 				self.remove_sockets_by_link_ptr(link_ptr)
 
 			# Recompute Added/Removed Links
-			## The algorithm will now detect an "added link".
+			## -> Guide the usual algorithm to detect an "added link".
 			added_link_ptrs = all_link_ptrs - self.link_ptrs
 			removed_link_ptrs = self.link_ptrs - all_link_ptrs
 
-		# Shuffle Cache based on Change in Links
+		# Delete Removed Links
-		## Remove Entries for Removed Pointers
+		## -> NOTE: We leave dangling socket information on purpose.
+		## -> This information will be used to ask for 'removal consent'.
+		## -> To truly remove, must call 'remove_socket_by_link_ptr' later.
 		for removed_link_ptr in removed_link_ptrs:
 			self.remove_link(removed_link_ptr)
-			## User must manually call 'remove_socket_by_link_ptr' later.
-			## For now, leave dangling socket information by-link.
 
-		# Add New Link Pointers
+		# Create Added Links
+		## -> First, simply concatenate the added link pointers.
 		self.link_ptrs |= added_link_ptrs
 		for link_ptr in added_link_ptrs:
-			# Add Link PTR->REF
+			# Create Pointer -> Reference Entry
+			## -> This allows us to efficiently access the link by-pointer.
+			## -> Doing so otherwise requires a full search.
+			## -> **If link is deleted w/o report, access will cause crash**.
 			new_link = all_link_ptrs_as_links[link_ptr]
 			self.link_ptrs_as_links[link_ptr] = new_link
 
@@ -183,34 +241,69 @@ class NodeLinkCache:
 			to_socket = new_link.to_socket
 			to_socket_ptr = to_socket.as_pointer()
 
-			# Add Socket PTR, PTR -> REF
+			# Add Socket Information
 			for socket_ptr, bl_socket in zip(  # noqa: B905
 				[from_socket_ptr, to_socket_ptr],
 				[from_socket, to_socket],
 			):
-				# Increment RefCount of Socket PTR
+				# RefCount > 0: Increment RefCount of Socket PTR
 				## This happens if another link also uses the same socket.
 				## 1. An output socket links to several inputs.
 				## 2. A multi-input socket links from several inputs.
 				if socket_ptr in self.socket_ptr_refcount:
 					self.socket_ptr_refcount[socket_ptr] += 1
+
+				# RefCount == 0: Create Socket Pointer w/Reference
+				## -> Also initialize the refcount for the socket pointer.
 				else:
-					## RefCount == 0: Add PTR, PTR -> REF
 					self.socket_ptrs.add(socket_ptr)
 					self.socket_ptrs_as_sockets[socket_ptr] = bl_socket
 					self.socket_ptr_refcount[socket_ptr] = 1
 
-			# Add Link PTR -> Socket PTR
+			# Add Entry from Link Pointer -> Socket Pointer
 			self.link_ptrs_as_from_socket_ptrs[link_ptr] = from_socket_ptr
 			self.link_ptrs_as_to_socket_ptrs[link_ptr] = to_socket_ptr
 
 		return {'added': added_link_ptrs, 'removed': removed_link_ptrs}
 
+	def update_validity(self) -> DeltaNodeLinkCache:
+		"""Query all cached links to determine whether they are valid."""
+		self.link_ptrs_invalid = {
+			link_ptr for link_ptr, link in self.link_ptrs_as_links if not link.is_valid
+		}
+
+	def report_validity(self, link_ptr: MemAddr, validity: bool) -> None:
+		"""Report a link as invalid."""
+		if validity and link_ptr in self.link_ptrs_invalid:
+			self.link_ptrs_invalid.remove(link_ptr)
+		elif not validity and link_ptr not in self.link_ptrs_invalid:
+			self.link_ptrs_invalid.add(link_ptr)
+
+	def set_validities(self) -> None:
+		"""Set the validity of links in the node tree according to the internal cache.
+
+		Validity doesn't need to be removed, as update() automatically cleans up by default.
+		"""
+		for link in [
+			link
+			for link_ptr, link in self.link_ptrs_as_links.items()
+			if link_ptr in self.link_ptrs_invalid
+		]:
+			if link.is_valid:
+				link.is_valid = False
+
 
 ####################
 # - Node Tree Definition
 ####################
 class MaxwellSimTree(bpy.types.NodeTree):
+	"""Node tree containing a node-based program for design and analysis of Maxwell PDE simulations.
+
+	Attributes:
+		is_active: Whether the node tree should be considered to be in a usable state, capable of updating Blender data.
+			In general, only one `MaxwellSimTree` should be active at a time.
+	"""
+
 	bl_idname = ct.TreeType.MaxwellSim.value
 	bl_label = 'Maxwell Sim Editor'
 	bl_icon = ct.Icon.SimNodeEditor
@@ -219,63 +312,6 @@ class MaxwellSimTree(bpy.types.NodeTree):
 		default=True,
 	)
 
-	####################
-	# - Lock Methods
-	####################
-	def unlock_all(self) -> None:
-		"""Unlock all nodes in the node tree, making them editable."""
-		log.info('Unlocking All Nodes in NodeTree "%s"', self.bl_label)
-		for node in self.nodes:
-			if node.type in ['REROUTE', 'FRAME']:
-				continue
-			node.locked = False
-			for bl_socket in [*node.inputs, *node.outputs]:
-				bl_socket.locked = False
-
-	@contextlib.contextmanager
-	def replot(self) -> None:
-		self.is_currently_replotting = True
-		self.something_plotted = False
-
-		try:
-			yield
-		finally:
-			self.is_currently_replotting = False
-			if not self.something_plotted:
-				ManagedBLImage.hide_preview()
-
-	def report_show_plot(self, node: bpy.types.Node) -> None:
-		if hasattr(self, 'is_currently_replotting') and self.is_currently_replotting:
-			self.something_plotted = True
-
-	@contextlib.contextmanager
-	def repreview_all(self) -> None:
-		all_nodes_with_preview_active = {
-			node.instance_id: node
-			for node in self.nodes
-			if node.type not in ['REROUTE', 'FRAME'] and node.preview_active
-		}
-		self.is_currently_repreviewing = True
-		self.newly_previewed_nodes = {}
-
-		try:
-			yield
-		finally:
-			self.is_currently_repreviewing = False
-			for dangling_previewed_node in [
-				node
-				for node_instance_id, node in all_nodes_with_preview_active.items()
-				if node_instance_id not in self.newly_previewed_nodes
-			]:
-				dangling_previewed_node.preview_active = False
-
-	def report_show_preview(self, node: bpy.types.Node) -> None:
-		if (
-			hasattr(self, 'is_currently_repreviewing')
-			and self.is_currently_repreviewing
-		):
-			self.newly_previewed_nodes[node.instance_id] = node
-
 	####################
 	# - Init Methods
 	####################
@@ -290,7 +326,54 @@ class MaxwellSimTree(bpy.types.NodeTree):
 			self.node_link_cache = NodeLinkCache(self)
 
 	####################
-	# - Update Methods
+	# - Lock Methods
+	####################
+	def unlock_all(self) -> None:
+		"""Unlock all nodes in the node tree, making them editable.
+
+		Notes:
+			All `MaxwellSimNode`s have a `.locked` attribute, which prevents the entire UI from being modified.
+
+			This method simply sets the `locked` attribute to `False` on all nodes.
+		"""
+		log.info('Unlocking All Nodes in NodeTree "%s"', self.bl_label)
+		for node in self.nodes:
+			if node.type in ['REROUTE', 'FRAME']:
+				continue
+
+			# Unlock Node
+			if node.locked:
+				node.locked = False
+
+			# Unlock Node Sockets
+			for bl_socket in [*node.inputs, *node.outputs]:
+				if bl_socket.locked:
+					bl_socket.locked = False
+
+	####################
+	# - Link Update Methods
+	####################
+	def report_link_validity(self, link: bpy.types.NodeLink, validity: bool) -> None:
+		"""Report that a particular `NodeLink` should be considered to be either valid or invalid.
+
+		The `NodeLink.is_valid` attribute is generally (and automatically) used to indicate the detection of cycles in the node tree.
+		However, visually, it causes a very clear "error red" highlight to appear on the node link, which can extremely useful when determining the reasons behind unexpected outout.
+
+		Notes:
+			Run by `MaxwellSimSocket` when a link should be shown to be "invalid".
+		"""
+		## TODO: Doesn't quite work.
+		# log.debug(
+		# 'Reported Link Validity %s (is_valid=%s, from_socket=%s, to_socket=%s)',
+		# validity,
+		# link.is_valid,
+		# link.from_socket,
+		# link.to_socket,
+		# )
+		# self.node_link_cache.report_validity(link.as_pointer(), validity)
+
+	####################
+	# - Node Update Methods
 	####################
 	def on_node_removed(self, node: bpy.types.Node):
 		"""Run by `MaxwellSimNode.free()` when a node is being removed.
@@ -327,32 +410,36 @@ class MaxwellSimTree(bpy.types.NodeTree):
 				self.node_link_cache.remove_link(link_ptr)
 				self.node_link_cache.remove_sockets_by_link_ptr(link_ptr)
 
-	def update(self) -> None:
+	def update(self) -> None:  # noqa: PLR0912, C901
 		"""Monitors all changes to the node tree, potentially responding with appropriate callbacks.
 
 		Notes:
 			- Run by Blender when "anything" changes in the node tree.
 			- Responds to node link changes with callbacks, with the help of a performant node link cache.
 		"""
+		# Perform Initial Load
+		## -> Presume update() is run before the first link is altered.
+		## -> Else, the first link of the session will not update caches.
+		## -> We still remain slightly unsure of the exact semantics.
+		## -> Therefore, self.on_load() is also called as a load_post handler.
+		if not hasattr(self, 'node_link_cache'):
+			self.on_load()
+			return
+
+		# Register Validity Updater
+		## -> They will be run after the update() method.
+		## -> Between update() and set_validities, all is_valid=True are cleared.
+		## -> Therefore, 'set_validities' only needs to set all is_valid=False.
+		bpy.app.timers.register(self.node_link_cache.set_validities)
+
+		# Ignore Updates
+		## -> Certain corrective processes require suppressing the next update.
+		## -> Otherwise, link corrections may trigger some nasty recursions.
 		if not hasattr(self, 'ignore_update'):
 			self.ignore_update = False
 
-		if not hasattr(self, 'node_link_cache'):
+		# Regenerate NodeLinkCache
-			self.on_load()
-			## We presume update() is run before the first link is altered.
-			## - Else, the first link of the session will not update caches.
-			## - We remain slightly unsure of the semantics.
-			## - Therefore, self.on_load() is also called as a load_post handler.
-			return
-
-		# Ignore Update
-		## Manually set to implement link corrections w/o recursion.
-		if self.ignore_update:
-			return
-
-		# Compute Changes to Node Links
 		delta_links = self.node_link_cache.regenerate()
-
 		link_corrections = {
 			'to_remove': [],
 			'to_add': [],

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

@@ -358,6 +358,11 @@ class ExtractDataNode(base.MaxwellSimNode):
 				## -> Those string labels explain the integer as ex. Ex, Ey, Hy.
 				idx_labels = valid_monitor_attrs(sim_data, monitor_name)
 
+				# Extract Info
+				## -> We only need the output symbol.
+				## -> All labelled outputs have the same output SimSymbol.
+				info = extract_info(monitor_data, idx_labels[0])
+
 				# Generate FuncFlow Per Index Label
 				## -> We extract each XArray as an attribute of monitor_data.
 				## -> We then bind its values into a unique func_flow.
@@ -377,7 +382,8 @@ class ExtractDataNode(base.MaxwellSimNode):
 				## -> Then, 'compose_within' lets us stack them along axis=0.
 				## -> The "new" axis=0 is int-indexed axis w/idx_labels labels!
 				return functools.reduce(lambda a, b: a | b, func_flows).compose_within(
-					enclosing_func=lambda data: jnp.stack(data, axis=0)
+					lambda data: jnp.stack(data, axis=0),
+					func_output=info.output,
 				)
 			return ct.FlowSignal.FlowPending
 		return ct.FlowSignal.FlowPending

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

@@ -65,12 +65,12 @@ class FilterOperation(enum.StrEnum):
 		FO = FilterOperation
 		return {
 			# Slice
-			FO.Slice: '=a[i:j]',
+			FO.Slice: '≈a[v₁:v₂]',
-			FO.SliceIdx: '≈a[v₁:v₂]',
+			FO.SliceIdx: '=a[i:j]',
 			# Pin
-			FO.PinLen1: 'pinₐ',
+			FO.PinLen1: 'a[0] → a',
-			FO.Pin: 'pinₐ ≈v',
+			FO.Pin: 'a[v] ⇝ a',
-			FO.PinIdx: 'pinₐ =i',
+			FO.PinIdx: 'a[i] → a',
 			# Reinterpret
 			FO.Swap: 'a₁ ↔ a₂',
 		}[value]
@@ -517,6 +517,7 @@ class FilterMathNode(base.MaxwellSimNode):
 			return lazy_func.compose_within(
 				operation.jax_func(axis_0, axis_1, slice_tuple=slice_tuple),
 				enclosing_func_args=operation.func_args,
+				enclosing_func_output=info.output,
 				supports_jax=True,
 			)
 		return ct.FlowSignal.FlowPending

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

@@ -547,22 +547,30 @@ class MapMathNode(base.MaxwellSimNode):
 	####################
 	@events.computes_output_socket(
 		'Expr',
+		# Loaded
 		kind=ct.FlowKind.Func,
 		props={'operation'},
 		input_sockets={'Expr'},
 		input_socket_kinds={
 			'Expr': ct.FlowKind.Func,
 		},
+		output_sockets={'Expr'},
+		output_socket_kinds={'Expr': ct.FlowKind.Info},
 	)
-	def compute_func(self, props, input_sockets) -> ct.FuncFlow | ct.FlowSignal:
+	def compute_func(
-		operation = props['operation']
+		self, props, input_sockets, output_sockets
+	) -> ct.FuncFlow | ct.FlowSignal:
 		expr = input_sockets['Expr']
+		output_info = output_sockets['Expr']
 
 		has_expr = not ct.FlowSignal.check(expr)
+		has_output_info = not ct.FlowSignal.check(output_info)
 
+		operation = props['operation']
 		if has_expr and operation is not None:
 			return expr.compose_within(
 				operation.jax_func,
+				enclosing_func_output=output_info.output,
 				supports_jax=True,
 			)
 		return ct.FlowSignal.FlowPending

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

@@ -146,7 +146,6 @@ class BinaryOperation(enum.StrEnum):
 		outl = info_l.output
 		outr = info_r.output
 		match (outl.shape_len, outr.shape_len):
-			# match (ol.shape_len, info_r.output.shape_len):
 			# Number | *
 			## Number | Number
 			case (0, 0):
@@ -154,15 +153,25 @@ class BinaryOperation(enum.StrEnum):
 					BO.Add,
 					BO.Sub,
 					BO.Mul,
-					BO.Div,
-					BO.Pow,
 				]
+
+				# Check Non-Zero Right Hand Side
+				## -> Obviously, we can't ever divide by zero.
+				## -> Sympy's assumptions system must always guarantee rhs != 0.
+				## -> If it can't, then we simply don't expose division.
+				## -> The is_zero assumption must be provided elsewhere.
+				## -> NOTE: This may prevent some valid uses of division.
+				## -> Watch out for "division is missing" bugs.
+				if info_r.output.is_nonzero:
+					ops.append(BO.Div)
+
 				if (
 					info_l.output.physical_type == spux.PhysicalType.Length
 					and info_l.output.unit == info_r.output.unit
 				):
 					ops += [BO.Atan2]
-				return ops
+
+				return [*ops, BO.Pow]
 
 			## Number | Vector
 			case (0, 1):
@@ -336,7 +345,13 @@ class BinaryOperation(enum.StrEnum):
 	# - InfoFlow Transform
 	####################
 	def transform_infos(self, info_l: ct.InfoFlow, info_r: ct.InfoFlow):
-		"""Deduce the output information by using `self.sp_func` to operate on the two output `SimSymbol`s, then capturing the information associated with the resulting expression."""
+		"""Deduce the output information by using `self.sp_func` to operate on the two output `SimSymbol`s, then capturing the information associated with the resulting expression.
+
+		Warnings:
+			`self` MUST be an element of `BinaryOperation.by_infos(info_l, info_r).
+
+			If not, bad things will happen.
+		"""
 		return info_l.operate_output(
 			info_r,
 			lambda a, b: self.sp_func([a, b]),
@@ -479,29 +494,35 @@ class OperateMathNode(base.MaxwellSimNode):
 	@events.computes_output_socket(
 		'Expr',
 		kind=ct.FlowKind.Func,
+		# Loaded
 		props={'operation'},
 		input_sockets={'Expr L', 'Expr R'},
 		input_socket_kinds={
 			'Expr L': ct.FlowKind.Func,
 			'Expr R': ct.FlowKind.Func,
 		},
+		output_sockets={'Expr'},
+		output_socket_kinds={'Expr': ct.FlowKind.Info},
 	)
-	def compose_func(self, props: dict, input_sockets: dict):
+	def compute_func(self, props, input_sockets, output_sockets):
 		operation = props['operation']
 		if operation is None:
 			return ct.FlowSignal.FlowPending
 
 		expr_l = input_sockets['Expr L']
 		expr_r = input_sockets['Expr R']
+		output_info = output_sockets['Expr']
 
 		has_expr_l = not ct.FlowSignal.check(expr_l)
 		has_expr_r = not ct.FlowSignal.check(expr_r)
+		has_output_info = not ct.FlowSignal.check(output_info)
 
 		# Compute Jax Function
 		## -> The operation enum directly provides the appropriate function.
-		if has_expr_l and has_expr_r:
+		if has_expr_l and has_expr_r and has_output_info:
 			return (expr_l | expr_r).compose_within(
-				enclosing_func=operation.jax_func,
+				operation.jax_func,
+				enclosing_func_output=output_info.output,
 				supports_jax=True,
 			)
 		return ct.FlowSignal.FlowPending
@@ -520,6 +541,8 @@ class OperateMathNode(base.MaxwellSimNode):
 		},
 	)
 	def compute_info(self, props, input_sockets) -> ct.InfoFlow:
+		BO = BinaryOperation
+
 		operation = props['operation']
 		info_l = input_sockets['Expr L']
 		info_r = input_sockets['Expr R']
@@ -533,7 +556,7 @@ class OperateMathNode(base.MaxwellSimNode):
 			has_info_l
 			and has_info_r
 			and operation is not None
-			and operation in BinaryOperation.by_infos(info_l, info_r)
+			and operation in BO.by_infos(info_l, info_r)
 		):
 			return operation.transform_infos(info_l, info_r)
 

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

@@ -606,27 +606,32 @@ class TransformMathNode(base.MaxwellSimNode):
 		input_socket_kinds={
 			'Expr': {ct.FlowKind.Func, ct.FlowKind.Info},
 		},
+		output_sockets={'Expr'},
+		output_socket_kinds={'Expr': ct.FlowKind.Info},
 	)
-	def compute_func(self, props, input_sockets) -> ct.FuncFlow | ct.FlowSignal:
+	def compute_func(
+		self, props, input_sockets, output_sockets
+	) -> ct.FuncFlow | ct.FlowSignal:
 		"""Transform the input `InfoFlow` depending on the transform operation."""
 		TO = TransformOperation
-		operation = props['operation']
+
 		lazy_func = input_sockets['Expr'][ct.FlowKind.Func]
 		info = input_sockets['Expr'][ct.FlowKind.Info]
+		output_info = output_sockets['Expr']
 
 		has_info = not ct.FlowSignal.check(info)
 		has_lazy_func = not ct.FlowSignal.check(lazy_func)
+		has_output_info = not ct.FlowSignal.check(output_info)
 
-		if operation is not None and has_lazy_func and has_info:
+		operation = props['operation']
-			# Retrieve Properties
+		if operation is not None and has_lazy_func and has_info and has_output_info:
 			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)),
+							enclosing_func_output=output_info.output,
 							supports_jax=True,
 						)
 					return ct.FlowSignal.FlowPending
@@ -634,6 +639,7 @@ class TransformMathNode(base.MaxwellSimNode):
 				case _:
 					return lazy_func.compose_within(
 						operation.jax_func(),
+						enclosing_func_output=output_info.output,
 						supports_jax=True,
 					)
 

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

@@ -406,7 +406,7 @@ class VizNode(base.MaxwellSimNode):
 		},
 		all_loose_input_sockets=True,
 	)
-	def compute_dummy_value(self, props, input_sockets, loose_input_sockets):
+	def compute_previews(self, props, input_sockets, loose_input_sockets):
 		"""Needed for the plot to regenerate in the viewer."""
 		return ct.PreviewsFlow(bl_image_name=props['sim_node_name'])
 
@@ -433,7 +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)')
+		log.debug('Show Plot')
 		lazy_func = input_sockets['Expr'][ct.FlowKind.Func]
 		info = input_sockets['Expr'][ct.FlowKind.Info]
 		params = input_sockets['Expr'][ct.FlowKind.Params]
@@ -456,6 +456,7 @@ class VizNode(base.MaxwellSimNode):
 					sym: loose_input_sockets[sym.name] for sym in params.sorted_symbols
 				},
 			)
+			## TODO: CACHE entries that don't change, PLEASEEE
 
 			# Match Viz Type & Perform Visualization
 			## -> Viz Target determines how to plot.

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

@@ -207,12 +207,12 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 		stop_propagation=True,
 	)
 	def _on_sim_node_name_changed(self, props):
-		log.debug(
+		# log.debug(
-			'Changed Sim Node Name of a "%s" to "%s" (self=%s)',
+		# 'Changed Sim Node Name of a "%s" to "%s" (self=%s)',
-			self.bl_idname,
+		# self.bl_idname,
-			props['sim_node_name'],
+		# props['sim_node_name'],
-			str(self),
+		# str(self),
-		)
+		# )
 
 		# (Re)Construct Managed Objects
 		## -> Due to 'prev_name', the new MObjs will be renamed on construction
@@ -360,27 +360,48 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 	####################
 	# - Socket Management
 	####################
-	## TODO: Check for namespace collisions in sockets to prevent silent errors
 	def _prune_inactive_sockets(self):
-		"""Remove all "inactive" sockets from the node.
+		"""Remove all inactive sockets from the node, while only updating sockets that can be non-destructively updated.
 
-		A socket is considered "inactive" when it shouldn't be defined (per `self.active_socket_defs), but is present nonetheless.
+		The first step is easy: We determine, by-name, which sockets should no longer be defined, then remove them correctly.
+
+		The second step is harder: When new sockets have overlapping names, should they be removed, or should they merely have some properties updated?
+		Removing and re-adding the same socket is an accurate, generally robust approach, but it comes with a big caveat: **Existing node links will be cut**, even when it might semantically make sense to simply alter the socket's properties, keeping the links.
+
+		Different `bl_socket.socket_type`s can never be updated - they must be removed.
+		Otherwise, `SocketDef.compare(bl_socket)` allows us to granularly determine whether a particular `bl_socket` has changed with respect to the desired specification.
+		When the comparison is `False`, we can carefully utilize `SocketDef.init()` to re-initialize the socket, guaranteeing that the altered socket is up to the new specification.
 		"""
 		node_tree = self.id_data
 		for direc in ['input', 'output']:
-			all_bl_sockets = self._bl_sockets(direc)
+			bl_sockets = self._bl_sockets(direc)
-			active_bl_socket_defs = self.active_socket_defs(direc)
+			active_socket_defs = self.active_socket_defs(direc)
 
 			# Determine Sockets to Remove
+			## -> Name: If the existing socket name isn't "active".
+			## -> Type: If the existing socket_type != "active" SocketDef.
 			bl_sockets_to_remove = [
 				bl_socket
-				for socket_name, bl_socket in all_bl_sockets.items()
+				for socket_name, bl_socket in bl_sockets.items()
-				if socket_name not in active_bl_socket_defs
+				if (
-				or socket_name
+					socket_name not in active_socket_defs
-				in (
+					or bl_socket.socket_type
-					self.loose_input_sockets
+					is not active_socket_defs[socket_name].socket_type
-					if direc == 'input'
+				)
-					else self.loose_output_sockets
+			]
+
+			# Determine Sockets to Update
+			## -> Name: If the existing socket name is "active".
+			## -> Type: If the existing socket_type == "active" SocketDef.
+			## -> Compare: If the existing socket differs from the SocketDef.
+			bl_sockets_to_update = [
+				bl_socket
+				for socket_name, bl_socket in bl_sockets.items()
+				if (
+					socket_name in active_socket_defs
+					and bl_socket.socket_type
+					is active_socket_defs[socket_name].socket_type
+					and not active_socket_defs[socket_name].compare(bl_socket)
 				)
 			]
 
@@ -392,24 +413,25 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 				## -> The NodeLinkCache needs to be adjusted manually.
 				node_tree.on_node_socket_removed(bl_socket)
 
-				# 2. Invalidate the input socket cache across all kinds.
+				# 2. Perform the removal using Blender's API.
+				## -> Actually removes the socket.
+				bl_sockets.remove(bl_socket)
+
+				# 3. Invalidate the input socket cache across all kinds.
 				## -> Prevents phantom values from remaining available.
+				## -> Done after socket removal to protect from race condition.
 				self._compute_input.invalidate(
 					input_socket_name=bl_socket_name,
 					kind=...,
 					unit_system=...,
 				)
 
-				# 3. Perform the removal using Blender's API.
-				## -> Actually removes the socket.
-				all_bl_sockets.remove(bl_socket)
-
 				if direc == 'input':
 					# 4. Run all trigger-only `on_value_changed` callbacks.
 					## -> Runs any event methods that relied on the socket.
 					## -> Only methods that don't **require** the socket.
-					## Trigger-Only: If method loads no socket data, it runs.
+					## Only Trigger: If method loads no socket data, it runs.
-					## `optional`: If method optional-loads socket, it runs.
+					## Optional: If method optional-loads socket, it runs.
 					triggered_event_methods = [
 						event_method
 						for event_method in self.filtered_event_methods_by_event(
@@ -419,32 +441,52 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 						not in event_method.callback_info.must_load_sockets
 					]
 					for event_method in triggered_event_methods:
-						log.critical(
-							'%s: Running %s',
-							self.sim_node_name,
-							str(event_method),
-						)
 						event_method(self)
 
+			# Update Sockets
+			for bl_socket in bl_sockets_to_update:
+				bl_socket_name = bl_socket.name
+				socket_def = active_socket_defs[bl_socket_name]
+
+				# 1. Pretend to Initialize for the First Time
+				## -> NOTE: The socket's caches will be completely regenerated.
+				## -> NOTE: A full FlowKind update will occur, but only one.
+				bl_socket.is_initializing = True
+				socket_def.preinit(bl_socket)
+				socket_def.init(bl_socket)
+				socket_def.postinit(bl_socket)
+
+				# 2. Re-Test Socket Capabilities
+				## -> Factors influencing CapabilitiesFlow may have changed.
+				## -> Therefore, we must re-test all link capabilities.
+				bl_socket.remove_invalidated_links()
+
+				# 3. Invalidate the input socket cache across all kinds.
+				## -> Prevents phantom values from remaining available.
+				self._compute_input.invalidate(
+					input_socket_name=bl_socket_name,
+					kind=...,
+					unit_system=...,
+				)
+
 	def _add_new_active_sockets(self):
 		"""Add and initialize all "active" sockets that aren't on the node.
 
 		Existing sockets within the given direction are not re-created.
 		"""
 		for direc in ['input', 'output']:
-			all_bl_sockets = self._bl_sockets(direc)
+			bl_sockets = self._bl_sockets(direc)
-			active_bl_socket_defs = self.active_socket_defs(direc)
+			active_socket_defs = self.active_socket_defs(direc)
 
 			# Define BL Sockets
 			created_sockets = {}
-			for socket_name, socket_def in active_bl_socket_defs.items():
+			for socket_name, socket_def in active_socket_defs.items():
 				# Skip Existing Sockets
-				if socket_name in all_bl_sockets:
+				if socket_name in bl_sockets:
 					continue
 
 				# Create BL Socket from Socket
-				## Set 'display_shape' from 'socket_shape'
+				bl_sockets.new(
-				all_bl_sockets.new(
 					str(socket_def.socket_type.value),
 					socket_name,
 				)
@@ -454,9 +496,9 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 
 			# Initialize Just-Created BL Sockets
 			for bl_socket_name, socket_def in created_sockets.items():
-				socket_def.preinit(all_bl_sockets[bl_socket_name])
+				socket_def.preinit(bl_sockets[bl_socket_name])
-				socket_def.init(all_bl_sockets[bl_socket_name])
+				socket_def.init(bl_sockets[bl_socket_name])
-				socket_def.postinit(all_bl_sockets[bl_socket_name])
+				socket_def.postinit(bl_sockets[bl_socket_name])
 
 				# Invalidate Cached NoFlows
 				self._compute_input.invalidate(
@@ -637,9 +679,10 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 				lambda a, b: a | b,
 				[
 					self._compute_input(
-						socket, kind=ct.FlowKind.Previews, unit_system=None
+						socket_name,
+						kind=ct.FlowKind.Previews,
 					)
-					for socket in [bl_socket.name for bl_socket in self.inputs]
+					for socket_name in [bl_socket.name for bl_socket in self.inputs]
 				],
 				ct.PreviewsFlow(),
 			)
@@ -897,9 +940,19 @@ class MaxwellSimNode(bpy.types.Node, bl_instance.BLInstance):
 							)
 							altered_socket_kinds[dep_out_sckname].add(dep_out_kind)
 
+			# Clear Output Socket Cache(s)
+			## -> We aggregate it manually, so it needs a special invl.
+			## -> See self.compute_output()
+			if socket_kinds is not None and ct.FlowKind.Previews in socket_kinds:
+				for out_sckname in self.outputs.keys():  # noqa: SIM118
+					self.compute_output.invalidate(
+						output_socket_name=out_sckname,
+						kind=ct.FlowKind.Previews,
+					)
+					altered_socket_kinds[out_sckname].add(ct.FlowKind.Previews)
+
 		# 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_names, None)

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

@@ -266,7 +266,7 @@ def event_decorator(  # noqa: PLR0913
 			)
 
 			# Loose Sockets
-			## Compute All Loose Input Sockets
+			## -> Determined by the active_kind of each loose input socket.
 			method_kw_args |= (
 				{
 					'loose_input_sockets': {

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

@@ -29,6 +29,8 @@ from ... import base, events
 
 
 class ScientificConstantNode(base.MaxwellSimNode):
+	"""A well-known constant usable as itself, or as a symbol."""
+
 	node_type = ct.NodeType.ScientificConstant
 	bl_label = 'Scientific Constant'
 
@@ -88,6 +90,11 @@ class ScientificConstantNode(base.MaxwellSimNode):
 	####################
 	# - UI
 	####################
+	def draw_label(self):
+		if self.sci_constant_str:
+			return f'Const: {self.sci_constant_str}'
+		return self.bl_label
+
 	def draw_props(self, _: bpy.types.Context, col: bpy.types.UILayout) -> None:
 		col.prop(self, self.blfields['sci_constant_str'], text='')
 
@@ -156,6 +163,7 @@ class ScientificConstantNode(base.MaxwellSimNode):
 		props={'sci_constant', 'sci_constant_sym'},
 	)
 	def compute_lazy_func(self, props) -> typ.Any:
+		"""Simple `FuncFlow` that computes the symbol value, with output units tracked correctly."""
 		sci_constant = props['sci_constant']
 		sci_constant_sym = props['sci_constant_sym']
 
@@ -165,6 +173,7 @@ class ScientificConstantNode(base.MaxwellSimNode):
 					[sci_constant_sym.sp_symbol], sci_constant_sym.sp_symbol, 'jax'
 				),
 				func_args=[sci_constant_sym],
+				func_output=sci_constant_sym,
 				supports_jax=True,
 			)
 		return ct.FlowSignal.FlowPending
@@ -175,6 +184,7 @@ class ScientificConstantNode(base.MaxwellSimNode):
 		props={'sci_constant_sym'},
 	)
 	def compute_info(self, props: dict) -> typ.Any:
+		"""Simple `FuncFlow` that computes the symbol value, with output units tracked correctly."""
 		sci_constant_sym = props['sci_constant_sym']
 
 		if sci_constant_sym is not None:
@@ -193,8 +203,12 @@ class ScientificConstantNode(base.MaxwellSimNode):
 		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],
+				func_args=[sci_constant_sym.sp_symbol],
-				is_differentiable=True,
+				symbols={sci_constant_sym},
+			).realize_partial(
+				{
+					sci_constant_sym: sci_constant,
+				}
 			)
 		return ct.FlowSignal.FlowPending
 

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

@@ -216,10 +216,11 @@ class SymbolConstantNode(base.MaxwellSimNode):
 		props={'symbol'},
 	)
 	def compute_lazy_func(self, props) -> typ.Any:
-		sp_sym = props['symbol'].sp_symbol
+		sym = props['symbol']
 		return ct.FuncFlow(
-			func=sp.lambdify(sp_sym, sp_sym, 'jax'),
+			func=sp.lambdify(sym.sp_symbol_matsym, sym.sp_symbol_matsym, 'jax'),
-			func_args=[sp_sym],
+			func_args=[sym],
+			func_output=sym,
 			supports_jax=True,
 		)
 
@@ -235,6 +236,7 @@ class SymbolConstantNode(base.MaxwellSimNode):
 	)
 	def compute_info(self, props) -> typ.Any:
 		return ct.InfoFlow(
+			dims={props['symbol']: None},
 			output=props['symbol'],
 		)
 
@@ -251,9 +253,6 @@ class SymbolConstantNode(base.MaxwellSimNode):
 			arg_targets=[sym],
 			func_args=[sym.sp_symbol],
 			symbols={sym},
-			is_differentiable=(
-				sym.mathtype in [spux.MathType.Real, spux.MathType.Complex]
-			),
 		)
 
 

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

@@ -198,9 +198,10 @@ class DataFileImporterNode(base.MaxwellSimNode):
 		'Expr',
 		kind=ct.FlowKind.Func,
 		# Loaded
+		props={'output_name', 'output_mathtype', 'output_physical_type', 'output_unit'},
 		input_sockets={'File Path'},
 	)
-	def compute_func(self, input_sockets) -> td.Simulation:
+	def compute_func(self, props, input_sockets) -> td.Simulation:
 		"""Declare a lazy, composable function that returns the loaded data.
 
 		Returns:
@@ -209,6 +210,12 @@ class DataFileImporterNode(base.MaxwellSimNode):
 		file_path = input_sockets['File Path']
 		has_file_path = not ct.FlowSignal.check(file_path)
 
+		func_output = sim_symbols.SimSymbol(
+			sym_name=props['output_name'],
+			mathtype=props['output_mathtype'],
+			physical_type=props['output_physical_type'],
+			unit=props['output_unit'],
+		)
 		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:
@@ -217,13 +224,18 @@ class DataFileImporterNode(base.MaxwellSimNode):
 				if data_file_format.loader_is_jax_compatible:
 					return ct.FuncFlow(
 						func=lambda: data_file_format.loader(file_path),
+						func_output=func_output,
 						supports_jax=True,
 					)
 
 				# No Jax Compatibility: Eager Data Loading
 				## -> Load the data now and bind it.
 				data = data_file_format.loader(file_path)
-				return ct.FuncFlow(func=lambda: data, supports_jax=True)
+				return ct.FuncFlow(
+					func=lambda: data,
+					func_output=func_output,
+					supports_jax=True,
+				)
 			return ct.FlowSignal.FlowPending
 		return ct.FlowSignal.FlowPending
 

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

@@ -86,22 +86,45 @@ class ViewerNode(base.MaxwellSimNode):
 	# - Properties: Computed FlowKinds
 	####################
 	@events.on_value_changed(
-		socket_name='Any',
+		# Trigger
+		prop_name='console_print_kind',
+		# Loaded
+		props={'auto_expr', 'console_print_kind'},
 	)
-	def on_input_changed(self) -> None:
+	def on_print_kind_changed(self, props) -> None:
+		self.inputs['Any'].active_kind = props['console_print_kind']
+
+		if props['auto_expr']:
+			setattr(
+				self,
+				'input_' + props['console_print_kind'].property_name,
+				bl_cache.Signal.InvalidateCache,
+			)
+
+	@events.on_value_changed(
+		# Trugger
+		socket_name='Any',
+		# Loaded
+		props={'auto_expr', 'console_print_kind'},
+	)
+	def on_input_changed(self, props) -> None:
 		"""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):
+		# Invalidate PreviewsFlow
-			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,
+			'input_' + ct.FlowKind.Previews.property_name,
+			bl_cache.Signal.InvalidateCache,
+		)
+
+		# Invalidate PreviewsFlow
+		if props['auto_expr']:
+			setattr(
+				self,
+				'input_' + props['console_print_kind'].property_name,
 				bl_cache.Signal.InvalidateCache,
 			)
 

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

@@ -14,8 +14,10 @@
 # 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 functools
 import typing as typ
 
+import bpy
 import sympy as sp
 
 from blender_maxwell.utils import bl_cache
@@ -26,6 +28,8 @@ from .. import base, events
 
 
 class CombineNode(base.MaxwellSimNode):
+	"""Combine single objects (ex. Source, Monitor, Structure) into a list."""
+
 	node_type = ct.NodeType.Combine
 	bl_label = 'Combine'
 
@@ -33,112 +37,222 @@ class CombineNode(base.MaxwellSimNode):
 	# - Sockets
 	####################
 	input_socket_sets: typ.ClassVar = {
-		'Maxwell Sources': {},
+		'Sources': {},
-		'Maxwell Structures': {},
+		'Structures': {},
-		'Maxwell Monitors': {},
+		'Monitors': {},
 	}
 	output_socket_sets: typ.ClassVar = {
-		'Maxwell Sources': {
+		'Sources': {
 			'Sources': sockets.MaxwellSourceSocketDef(
-				is_list=True,
+				active_kind=ct.FlowKind.Array,
 			),
 		},
-		'Maxwell Structures': {
+		'Structures': {
 			'Structures': sockets.MaxwellStructureSocketDef(
-				is_list=True,
+				active_kind=ct.FlowKind.Array,
 			),
 		},
-		'Maxwell Monitors': {
+		'Monitors': {
 			'Monitors': sockets.MaxwellMonitorSocketDef(
-				is_list=True,
+				active_kind=ct.FlowKind.Array,
 			),
 		},
 	}
 
 	####################
-	# - Draw
+	# - Properties
 	####################
-	amount: int = bl_cache.BLField(2, abs_min=1, prop_ui=True)
+	concatenate_first: bool = bl_cache.BLField(False)
+	value_or_func: ct.FlowKind = bl_cache.BLField(
+		enum_cb=lambda self, _: self._value_or_func(),
+	)
+
+	def _value_or_func(self):
+		return [
+			flow_kind.bl_enum_element(i)
+			for i, flow_kind in enumerate([ct.FlowKind.Value, ct.FlowKind.Func])
+		]
 
 	####################
 	# - Draw
 	####################
-	def draw_props(self, context, layout):
+	def draw_props(self, _, layout: bpy.types.UILayout):
-		layout.prop(self, self.blfields['amount'], text='')
+		layout.prop(self, self.blfields['value_or_func'], text='')
+
+		if self.value_or_func is ct.FlowKind.Value:
+			layout.prop(
+				self,
+				self.blfields['concatenate_first'],
+				text='Concatenate',
+				toggle=True,
+			)
 
 	####################
 	# - Events
 	####################
 	@events.on_value_changed(
-		# Trigger
+		any_loose_input_socket=True,
-		prop_name={'active_socket_set', 'amount'},
+		prop_name={'active_socket_set', 'concatenate_first', 'value_or_func'},
-		props={'active_socket_set', 'amount'},
 		run_on_init=True,
+		# Loaded
+		props={'active_socket_set', 'concatenate_first', 'value_or_func'},
 	)
-	def on_inputs_changed(self, props):
+	def on_inputs_changed(self, props) -> None:
-		if props['active_socket_set'] == 'Maxwell Sources':
+		"""Always create one extra loose input socket."""
-			if (
+		active_socket_set = props['active_socket_set']
-				not self.loose_input_sockets
+
-				or not next(iter(self.loose_input_sockets)).startswith('Source')
+		# Deduce SocketDef
-				or len(self.loose_input_sockets) != props['amount']
+		## -> Cheat by retrieving the class from the output sockets.
-			):
+		SocketDef = self.output_socket_sets[active_socket_set][
-				self.loose_input_sockets = {
+			active_socket_set
-					f'Source #{i}': sockets.MaxwellSourceSocketDef()
+		].__class__
-					for i in range(props['amount'])
+
-				}
+		# Deduce Current "Filled"
+		## -> The first linked socket from the end bounds the "filled" region.
+		## -> The length of that region, plus one, will be the new amount.
+		reverse_linked_idxs = [
+			i
+			for i, bl_socket in enumerate(reversed(self.inputs.values()))
+			if bl_socket.is_linked
+		]
+		current_filled = len(self.inputs) - (
+			reverse_linked_idxs[0] if reverse_linked_idxs else len(self.inputs)
+		)
+		new_amount = current_filled + 1
+
+		# Deduce SocketDef | Current Amount
+		concatenate_first = props['concatenate_first']
+		flow_kind = props['value_or_func']
 
-		elif props['active_socket_set'] == 'Maxwell Structures':
-			if (
-				not self.loose_input_sockets
-				or not next(iter(self.loose_input_sockets)).startswith('Structure')
-				or len(self.loose_input_sockets) != props['amount']
-			):
 		self.loose_input_sockets = {
-					f'Structure #{i}': sockets.MaxwellStructureSocketDef()
+			'#0': SocketDef(
-					for i in range(props['amount'])
+				active_kind=flow_kind
-				}
+				if flow_kind is ct.FlowKind.Func or not concatenate_first
-		elif props['active_socket_set'] == 'Maxwell Monitors':
+				else ct.FlowKind.Array
-			if (
+			)
-				not self.loose_input_sockets
+		} | {f'#{i}': SocketDef(active_kind=flow_kind) for i in range(1, new_amount)}
-				or not next(iter(self.loose_input_sockets)).startswith('Monitor')
-				or len(self.loose_input_sockets) != props['amount']
-			):
-				self.loose_input_sockets = {
-					f'Monitor #{i}': sockets.MaxwellMonitorSocketDef()
-					for i in range(props['amount'])
-				}
-		elif self.loose_input_sockets:
-			self.loose_input_sockets = {}
 
 	####################
-	# - Output Socket Computation
+	# - FlowKind.Array|Func
+	####################
+	def compute_combined(
+		self,
+		loose_input_sockets,
+		input_flow_kind: typ.Literal[ct.FlowKind.Value, ct.FlowKind.Func],
+		output_flow_kind: typ.Literal[ct.FlowKind.Array, ct.FlowKind.Func],
+	) -> list[typ.Any] | ct.FuncFlow | ct.FlowSignal:
+		"""Correctly compute the combined loose input sockets, given a valid combination of input and output `FlowKind`s.
+
+		If there is no output, or the flows aren't compatible, return `FlowPending`.
+		"""
+		match (input_flow_kind, output_flow_kind):
+			case (ct.FlowKind.Value, ct.FlowKind.Array):
+				value_flows = [
+					inp
+					for inp in loose_input_sockets.values()
+					if not ct.FlowSignal.check(inp)
+				]
+				if value_flows:
+					return value_flows
+				return ct.FlowSignal.FlowPending
+
+			case (ct.FlowKind.Func, ct.FlowKind.Func):
+				func_flows = [
+					inp
+					for inp in loose_input_sockets.values()
+					if not ct.FlowSignal.check(inp)
+				]
+				if func_flows:
+					return functools.reduce(
+						lambda a, b: a | b,
+						func_flows,
+					)
+				return ct.FlowSignal.FlowPending
+
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - Output: Sources
 	####################
 	@events.computes_output_socket(
 		'Sources',
 		kind=ct.FlowKind.Array,
 		all_loose_input_sockets=True,
-		props={'amount'},
+		props={'value_or_func'},
+	)
+	def compute_sources_array(
+		self, props, loose_input_sockets
+	) -> list[typ.Any] | ct.FlowSignal:
+		"""Compute sources."""
+		return self.compute_combined(
+			loose_input_sockets, props['value_or_func'], ct.FlowKind.Array
 		)
-	def compute_sources(self, loose_input_sockets, props) -> sp.Expr:
-		return [loose_input_sockets[f'Source #{i}'] for i in range(props['amount'])]
 
+	@events.computes_output_socket(
+		'Sources',
+		kind=ct.FlowKind.Func,
+		all_loose_input_sockets=True,
+		props={'value_or_func'},
+	)
+	def compute_sources_func(self, props, loose_input_sockets) -> list[typ.Any]:
+		"""Compute (lazy) sources."""
+		return self.compute_combined(
+			loose_input_sockets, props['value_or_func'], ct.FlowKind.Func
+		)
+
+	####################
+	# - Output: Structures
+	####################
 	@events.computes_output_socket(
 		'Structures',
 		kind=ct.FlowKind.Array,
 		all_loose_input_sockets=True,
-		props={'amount'},
+		props={'value_or_func'},
+	)
+	def compute_structures_array(self, props, loose_input_sockets) -> sp.Expr:
+		"""Compute structures."""
+		return self.compute_combined(
+			loose_input_sockets, props['value_or_func'], ct.FlowKind.Array
 		)
-	def compute_structures(self, loose_input_sockets, props) -> sp.Expr:
-		return [loose_input_sockets[f'Structure #{i}'] for i in range(props['amount'])]
 
+	@events.computes_output_socket(
+		'Structures',
+		kind=ct.FlowKind.Func,
+		all_loose_input_sockets=True,
+		props={'value_or_func'},
+	)
+	def compute_structures_func(self, props, loose_input_sockets) -> list[typ.Any]:
+		"""Compute (lazy) structures."""
+		return self.compute_combined(
+			loose_input_sockets, props['value_or_func'], ct.FlowKind.Func
+		)
+
+	####################
+	# - Output: Monitors
+	####################
 	@events.computes_output_socket(
 		'Monitors',
 		kind=ct.FlowKind.Array,
 		all_loose_input_sockets=True,
-		props={'amount'},
+		props={'value_or_func'},
+	)
+	def compute_monitors_array(self, props, loose_input_sockets) -> sp.Expr:
+		"""Compute monitors."""
+		return self.compute_combined(
+			loose_input_sockets, props['value_or_func'], ct.FlowKind.Array
+		)
+
+	@events.computes_output_socket(
+		'Monitors',
+		kind=ct.FlowKind.Func,
+		all_loose_input_sockets=True,
+		props={'value_or_func'},
+	)
+	def compute_monitors_func(self, props, loose_input_sockets) -> list[typ.Any]:
+		"""Compute (lazy) monitors."""
+		return self.compute_combined(
+			loose_input_sockets, props['value_or_func'], ct.FlowKind.Func
 		)
-	def compute_monitors(self, loose_input_sockets, props) -> sp.Expr:
-		return [loose_input_sockets[f'Monitor #{i}'] for i in range(props['amount'])]
 
 
 ####################

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

@@ -14,17 +14,26 @@
 # 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/>.
 
+"""Implements `FDTDSimNode`."""
+
 import typing as typ
 
-import sympy as sp
+import bpy
 import tidy3d as td
+import tidy3d.plugins.adjoint as tdadj
+
+from blender_maxwell.utils import bl_cache, logger
 
 from ... import contracts as ct
 from ... import sockets
 from .. import base, events
 
+log = logger.get(__name__)
+
 
 class FDTDSimNode(base.MaxwellSimNode):
+	"""Definition of a complete FDTD simulation, including boundary conditions, domain, sources, structures, monitors, and other configuration."""
+
 	node_type = ct.NodeType.FDTDSim
 	bl_label = 'FDTD Simulation'
 
@@ -35,51 +44,255 @@ class FDTDSimNode(base.MaxwellSimNode):
 		'BCs': sockets.MaxwellBoundCondsSocketDef(),
 		'Domain': sockets.MaxwellSimDomainSocketDef(),
 		'Sources': sockets.MaxwellSourceSocketDef(
-			is_list=True,
+			active_kind=ct.FlowKind.Array,
 		),
 		'Structures': sockets.MaxwellStructureSocketDef(
-			is_list=True,
+			active_kind=ct.FlowKind.Array,
 		),
 		'Monitors': sockets.MaxwellMonitorSocketDef(
-			is_list=True,
+			active_kind=ct.FlowKind.Array,
 		),
 	}
-	output_sockets: typ.ClassVar = {
+	output_socket_sets: typ.ClassVar = {
-		'Sim': sockets.MaxwellFDTDSimSocketDef(),
+		'Single': {
+			'Sim': sockets.MaxwellFDTDSimSocketDef(active_kind=ct.FlowKind.Value),
+		},
+		'Batch': {
+			'Sim': sockets.MaxwellFDTDSimSocketDef(active_kind=ct.FlowKind.Array),
+		},
+		'Lazy': {
+			'Sim': sockets.MaxwellFDTDSimSocketDef(active_kind=ct.FlowKind.Func),
+		},
 	}
 
 	####################
-	# - Output Socket Computation
+	# - 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,
+		)
+
+	####################
+	# - Events
+	####################
+	@events.on_value_changed(
+		# Trigger
+		socket_name={'Sources', 'Structures', 'Domain', 'BCs', 'Monitors'},
+		run_on_init=True,
+		# Loaded
+		props={'active_socket_set'},
+		output_sockets={'Sim'},
+		output_socket_kinds={'Sim': ct.FlowKind.Params},
+	)
+	def on_any_changed(self, props, output_sockets) -> None:
+		"""Create loose input sockets."""
+		params = output_sockets['Sim']
+		has_params = not ct.FlowSignal.check(params)
+
+		# Declare Loose Sockets that Realize Symbols
+		## -> This happens if Params contains not-yet-realized symbols.
+		active_socket_set = props['active_socket_set']
+		if active_socket_set in ['Value', 'Batch'] and has_params and params.symbols:
+			if set(self.loose_input_sockets) != {sym.name for sym in params.symbols}:
+				self.loose_input_sockets = {
+					sym.name: sockets.ExprSocketDef(
+						**(
+							expr_info
+							| {
+								'active_kind': ct.FlowKind.Value,
+								'use_value_range_swapper': (
+									active_socket_set == 'Value'
+								),
+							}
+						)
+					)
+					for sym, expr_info in params.sym_expr_infos.items()
+				}
+
+		elif self.loose_input_sockets:
+			self.loose_input_sockets = {}
+
+	####################
+	# - FlowKind.Value
 	####################
 	@events.computes_output_socket(
 		'Sim',
 		kind=ct.FlowKind.Value,
+		# Loaded
+		props={'differentiable'},
 		input_sockets={'Sources', 'Structures', 'Domain', 'BCs', 'Monitors'},
 		input_socket_kinds={
 			'Sources': ct.FlowKind.Array,
 			'Structures': ct.FlowKind.Array,
-			'Domain': ct.FlowKind.Value,
-			'BCs': ct.FlowKind.Value,
 			'Monitors': ct.FlowKind.Array,
 		},
+		output_sockets={'Sim'},
+		output_socket_kinds={'Sim': ct.FlowKind.Params},
 	)
-	def compute_fdtd_sim(self, input_sockets: dict) -> sp.Expr:
+	def compute_fdtd_sim_value(
-		if any(ct.FlowSignal.check(inp) for inp in input_sockets):
+		self, props, input_sockets, output_sockets
-			return ct.FlowSignal.FlowPending
+	) -> td.Simulation | tdadj.JaxSimulation | ct.FlowSignal:
-
+		"""Compute a single FDTD simulation definition, so long as the inputs are neither symbolic or differentiable."""
 		sim_domain = input_sockets['Domain']
 		sources = input_sockets['Sources']
 		structures = input_sockets['Structures']
 		bounds = input_sockets['BCs']
 		monitors = input_sockets['Monitors']
+		output_params = output_sockets['Sim']
+
+		has_sim_domain = not ct.FlowSignal.check(sim_domain)
+		has_sources = not ct.FlowSignal.check(sources)
+		has_structures = not ct.FlowSignal.check(structures)
+		has_bounds = not ct.FlowSignal.check(bounds)
+		has_monitors = not ct.FlowSignal.check(monitors)
+		has_output_params = not ct.FlowSignal.check(output_params)
+
+		differentiable = props['differentiable']
+		if (
+			has_sim_domain
+			and has_sources
+			and has_structures
+			and has_bounds
+			and has_monitors
+			and has_output_params
+			and not differentiable
+		):
 			return td.Simulation(
 				**sim_domain,
-			structures=structures,
 				sources=sources,
-			monitors=monitors,
+				structures=structures,
 				boundary_spec=bounds,
+				monitors=monitors,
 			)
-		## TODO: Visualize the boundary conditions on top of the sim domain
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind.Func
+	####################
+	@events.computes_output_socket(
+		'Sim',
+		kind=ct.FlowKind.Func,
+		# Loaded
+		props={'differentiable'},
+		input_sockets={'Sources', 'Structures', 'Domain', 'BCs', 'Monitors'},
+		input_socket_kinds={
+			'Sources': ct.FlowKind.Func,
+			'Structures': ct.FlowKind.Func,
+			'Monitors': ct.FlowKind.Func,
+		},
+		output_sockets={'Sim'},
+		output_socket_kinds={'Sim': ct.FlowKind.Params},
+	)
+	def compute_fdtd_sim_func(
+		self, props, input_sockets, output_sockets
+	) -> td.Simulation | tdadj.JaxSimulation | ct.FlowSignal:
+		"""Compute a single simulation, given that all inputs are non-symbolic."""
+		sim_domain = input_sockets['Domain']
+		sources = input_sockets['Sources']
+		structures = input_sockets['Structures']
+		bounds = input_sockets['BCs']
+		monitors = input_sockets['Monitors']
+		output_params = output_sockets['Sim']
+
+		has_sim_domain = not ct.FlowSignal.check(sim_domain)
+		has_sources = not ct.FlowSignal.check(sources)
+		has_structures = not ct.FlowSignal.check(structures)
+		has_bounds = not ct.FlowSignal.check(bounds)
+		has_monitors = not ct.FlowSignal.check(monitors)
+		has_output_params = not ct.FlowSignal.check(output_params)
+
+		if (
+			has_sim_domain
+			and has_sources
+			and has_structures
+			and has_bounds
+			and has_monitors
+			and has_output_params
+		):
+			differentiable = props['differentiable']
+			if differentiable:
+				return (
+					sim_domain | sources | structures | bounds | monitors
+				).compose_within(
+					enclosing_func=lambda els: tdadj.JaxSimulation(
+						**els[0],
+						sources=els[1],
+						structures=els[2]['static'],
+						input_structures=els[2]['differentiable'],
+						boundary_spec=els[3],
+						monitors=els[4]['static'],
+						output_monitors=els[4]['differentiable'],
+					),
+					supports_jax=True,
+				)
+			return (
+				sim_domain | sources | structures | bounds | monitors
+			).compose_within(
+				enclosing_func=lambda els: td.Simulation(
+					**els[0],
+					sources=els[1],
+					structures=els[2],
+					boundary_spec=els[3],
+					monitors=els[4],
+				),
+				supports_jax=False,
+			)
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind.Params
+	####################
+	@events.computes_output_socket(
+		'Sim',
+		kind=ct.FlowKind.Params,
+		# Loaded
+		props={'differentiable'},
+		input_sockets={'Sources', 'Structures', 'Domain', 'BCs', 'Monitors'},
+		input_socket_kinds={
+			'Sources': ct.FlowKind.Params,
+			'Structures': ct.FlowKind.Params,
+			'Monitors': ct.FlowKind.Params,
+		},
+	)
+	def compute_fdtd_sim_params(
+		self, props, input_sockets
+	) -> td.Simulation | tdadj.JaxSimulation | ct.FlowSignal:
+		"""Compute a single simulation, given that all inputs are non-symbolic."""
+		sim_domain = input_sockets['Domain']
+		sources = input_sockets['Sources']
+		structures = input_sockets['Structures']
+		bounds = input_sockets['BCs']
+		monitors = input_sockets['Monitors']
+
+		has_sim_domain = not ct.FlowSignal.check(sim_domain)
+		has_sources = not ct.FlowSignal.check(sources)
+		has_structures = not ct.FlowSignal.check(structures)
+		has_bounds = not ct.FlowSignal.check(bounds)
+		has_monitors = not ct.FlowSignal.check(monitors)
+
+		if (
+			has_sim_domain
+			and has_sources
+			and has_structures
+			and has_bounds
+			and has_monitors
+		):
+			# Determine Differentiable Match
+			## -> 'structures' is diff when **any** are diff.
+			## -> 'monitors' is also diff when **any** are diff.
+			## -> Only parameters through diff structs can be diff'ed by.
+			## -> Similarly, only diff monitors will have gradients computed.
+			return sim_domain | sources | structures | bounds | monitors
+		return ct.FlowSignal.FlowPending
 
 
 ####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/simulations/sim_domain.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/>.
 
+"""Implements `SimDomainNode`."""
+
 import typing as typ
 
 import sympy as sp
@@ -31,6 +33,8 @@ log = logger.get(__name__)
 
 
 class SimDomainNode(base.MaxwellSimNode):
+	"""The domain of a simulation in space and time, including bounds, discretization strategy, and the ambient medium."""
+
 	node_type = ct.NodeType.SimDomain
 	bl_label = 'Sim Domain'
 	use_sim_node_name = True
@@ -69,26 +73,109 @@ class SimDomainNode(base.MaxwellSimNode):
 	}
 
 	####################
-	# - Outputs
+	# - FlowKind.Value
 	####################
 	@events.computes_output_socket(
 		'Domain',
+		kind=ct.FlowKind.Value,
+		# Loaded
+		output_sockets={'Domain'},
+		output_socket_kinds={'Domain': {ct.FlowKind.Func, ct.FlowKind.Params}},
+	)
+	def compute_domain_value(self, output_sockets) -> ct.ParamsFlow | ct.FlowSignal:
+		"""Compute the particular value of the simulation domain from strictly non-symbolic inputs."""
+		output_func = output_sockets['Domain'][ct.FlowKind.Func]
+		output_params = output_sockets['Domain'][ct.FlowKind.Params]
+
+		has_output_func = not ct.FlowSignal.check(output_func)
+		has_output_params = not ct.FlowSignal.check(output_params)
+
+		if has_output_func and has_output_params and not output_params.symbols:
+			return output_func.realize(output_params)
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind.Func
+	####################
+	@events.computes_output_socket(
+		'Domain',
+		kind=ct.FlowKind.Func,
+		# Loaded
 		input_sockets={'Duration', 'Center', 'Size', 'Grid', 'Ambient Medium'},
-		unit_systems={'Tidy3DUnits': ct.UNITS_TIDY3D},
+		input_socket_kinds={
-		scale_input_sockets={
+			'Duration': ct.FlowKind.Func,
-			'Duration': 'Tidy3DUnits',
+			'Center': ct.FlowKind.Func,
-			'Center': 'Tidy3DUnits',
+			'Size': ct.FlowKind.Func,
-			'Size': 'Tidy3DUnits',
+			'Grid': ct.FlowKind.Func,
+			'Ambient Medium': ct.FlowKind.Func,
 		},
 	)
-	def compute_domain(self, input_sockets, unit_systems) -> sp.Expr:
+	def compute_domain_func(self, input_sockets) -> ct.ParamsFlow | ct.FlowSignal:
-		return {
+		"""Compute the particular value of the simulation domain from strictly non-symbolic inputs."""
-			'run_time': input_sockets['Duration'],
+		duration = input_sockets['Duration']
-			'center': input_sockets['Center'],
+		center = input_sockets['Center']
-			'size': input_sockets['Size'],
+		size = input_sockets['Size']
-			'grid_spec': input_sockets['Grid'],
+		grid = input_sockets['Grid']
-			'medium': input_sockets['Ambient Medium'],
+		medium = input_sockets['Ambient Medium']
-		}
+
+		has_duration = not ct.FlowSignal.check(duration)
+		has_center = not ct.FlowSignal.check(center)
+		has_size = not ct.FlowSignal.check(size)
+		has_grid = not ct.FlowSignal.check(grid)
+		has_medium = not ct.FlowSignal.check(medium)
+
+		if has_duration and has_center and has_size and has_grid and has_medium:
+			return (
+				duration.scale_to_unit_system(ct.UNITS_TIDY3D)
+				| center.scale_to_unit_system(ct.UNITS_TIDY3D)
+				| size.scale_to_unit_system(ct.UNITS_TIDY3D)
+				| grid
+				| medium
+			).compose_within(
+				enclosing_func=lambda els: {
+					'run_time': els[0],
+					'center': tuple(els[1].flatten()),
+					'size': tuple(els[2].flatten()),
+					'grid_spec': els[3],
+					'medium': els[4],
+				},
+				supports_jax=False,
+			)
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind.Params
+	####################
+	@events.computes_output_socket(
+		'Domain',
+		kind=ct.FlowKind.Params,
+		# Loaded
+		input_sockets={'Duration', 'Center', 'Size', 'Grid', 'Ambient Medium'},
+		input_socket_kinds={
+			'Duration': ct.FlowKind.Params,
+			'Center': ct.FlowKind.Params,
+			'Size': ct.FlowKind.Params,
+			'Grid': ct.FlowKind.Params,
+			'Ambient Medium': ct.FlowKind.Params,
+		},
+	)
+	def compute_domain_params(self, input_sockets) -> ct.ParamsFlow | ct.FlowSignal:
+		"""Compute the output `ParamsFlow` of the simulation domain from strictly non-symbolic inputs."""
+		duration = input_sockets['Duration']
+		center = input_sockets['Center']
+		size = input_sockets['Size']
+		grid = input_sockets['Grid']
+		medium = input_sockets['Ambient Medium']
+
+		has_duration = not ct.FlowSignal.check(duration)
+		has_center = not ct.FlowSignal.check(center)
+		has_size = not ct.FlowSignal.check(size)
+		has_grid = not ct.FlowSignal.check(grid)
+		has_medium = not ct.FlowSignal.check(medium)
+
+		if has_duration and has_center and has_size and has_grid and has_medium:
+			return duration | center | size | grid | medium
+		return ct.FlowSignal.FlowPending
 
 	####################
 	# - Preview
@@ -100,37 +187,39 @@ class SimDomainNode(base.MaxwellSimNode):
 		props={'sim_node_name'},
 	)
 	def compute_previews(self, props):
+		"""Mark the managed preview object for preview when `Domain` is linked to a viewer."""
 		return ct.PreviewsFlow(bl_object_names={props['sim_node_name']})
 
 	@events.on_value_changed(
-		## Trigger
+		# Trigger
 		socket_name={'Center', 'Size'},
 		run_on_init=True,
 		# Loaded
 		input_sockets={'Center', 'Size'},
 		managed_objs={'modifier'},
-		unit_systems={'BlenderUnits': ct.UNITS_BLENDER},
+		output_sockets={'Domain'},
-		scale_input_sockets={
+		output_socket_kinds={'Domain': ct.FlowKind.Params},
-			'Center': 'BlenderUnits',
-		},
 	)
-	def on_input_changed(
+	def on_input_changed(self, managed_objs, input_sockets, output_sockets) -> None:
-		self,
+		"""Preview the simulation domain based on input parameters, so long as they are not dependent on unrealized symbols."""
-		managed_objs,
+		output_params = output_sockets['Domain']
-		input_sockets,
+		center = input_sockets['Center']
-		unit_systems,
+
-	):
+		has_output_params = not ct.FlowSignal.check(output_params)
+		has_center = not ct.FlowSignal.check(center)
+
+		if has_center and has_output_params and not output_params.symbols:
 			# Push Loose Input Values to GeoNodes Modifier
 			managed_objs['modifier'].bl_modifier(
 				'NODES',
 				{
 					'node_group': import_geonodes(GeoNodes.SimulationSimDomain),
-				'unit_system': unit_systems['BlenderUnits'],
+					'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/sources/point_dipole_source.py

@@ -71,35 +71,129 @@ class PointDipoleSourceNode(base.MaxwellSimNode):
 		layout.prop(self, self.blfields['pol_axis'], expand=True)
 
 	####################
-	# - Outputs
+	# - FlowKind.Value
 	####################
 	@events.computes_output_socket(
 		'Source',
-		input_sockets={'Temporal Shape', 'Center', 'Interpolate'},
+		# Loaded
 		props={'pol_axis'},
-		unit_systems={'Tidy3DUnits': ct.UNITS_TIDY3D},
+		input_sockets={'Temporal Shape', 'Center', 'Interpolate'},
-		scale_input_sockets={
+		output_sockets={'Source'},
-			'Center': 'Tidy3DUnits',
+		output_socket_kinds={'Source': ct.FlowKind.Params},
-		},
 	)
-	def compute_source(
+	def compute_source_value(
-		self,
+		self, input_sockets, props, output_sockets
-		input_sockets: dict[str, typ.Any],
+	) -> td.PointDipole | ct.FlowSignal:
-		props: dict[str, typ.Any],
+		"""Compute the point dipole source, given that all inputs are non-symbolic."""
-		unit_systems: dict,
+		temporal_shape = input_sockets['Temporal Shape']
-	) -> td.PointDipole:
+		center = input_sockets['Center']
+		interpolate = input_sockets['Interpolate']
+		output_params = output_sockets['Source']
+
+		has_temporal_shape = not ct.FlowSignal.check(temporal_shape)
+		has_center = not ct.FlowSignal.check(center)
+		has_interpolate = not ct.FlowSignal.check(interpolate)
+		has_output_params = not ct.FlowSignal.check(output_params)
+
+		if (
+			has_temporal_shape
+			and has_center
+			and has_interpolate
+			and has_output_params
+			and not output_params.symbols
+		):
 			pol_axis = {
 				ct.SimSpaceAxis.X: 'Ex',
 				ct.SimSpaceAxis.Y: 'Ey',
 				ct.SimSpaceAxis.Z: 'Ez',
 			}[props['pol_axis']]
+			## TODO: Need Hx, Hy, Hz too?
 
 			return td.PointDipole(
-			center=input_sockets['Center'],
+				center=spux.convert_to_unit_system(center, ct.UNITS_TIDY3D),
-			source_time=input_sockets['Temporal Shape'],
+				source_time=temporal_shape,
-			interpolate=input_sockets['Interpolate'],
+				interpolate=interpolate,
 				polarization=pol_axis,
 			)
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind.Func
+	####################
+	@events.computes_output_socket(
+		'Source',
+		kind=ct.FlowKind.Func,
+		# Loaded
+		props={'pol_axis'},
+		input_sockets={'Temporal Shape', 'Center', 'Interpolate'},
+		input_socket_kinds={
+			'Temporal Shape': ct.FlowKind.Func,
+			'Center': ct.FlowKind.Func,
+			'Interpolate': ct.FlowKind.Func,
+		},
+		output_sockets={'Source'},
+		output_socket_kinds={'Source': ct.FlowKind.Params},
+	)
+	def compute_source_func(self, props, input_sockets, output_sockets) -> td.Box:
+		"""Compute a lazy function for the point dipole source."""
+		center = input_sockets['Center']
+		temporal_shape = input_sockets['Temporal Shape']
+		interpolate = input_sockets['Interpolate']
+		output_params = output_sockets['Source']
+
+		has_center = not ct.FlowSignal.check(center)
+		has_temporal_shape = not ct.FlowSignal.check(temporal_shape)
+		has_interpolate = not ct.FlowSignal.check(interpolate)
+		has_output_params = not ct.FlowSignal.check(output_params)
+
+		if has_temporal_shape and has_center and has_interpolate and has_output_params:
+			pol_axis = {
+				ct.SimSpaceAxis.X: 'Ex',
+				ct.SimSpaceAxis.Y: 'Ey',
+				ct.SimSpaceAxis.Z: 'Ez',
+			}[props['pol_axis']]
+			## TODO: Need Hx, Hy, Hz too?
+
+			return (center | temporal_shape | interpolate).compose_within(
+				enclosing_func=lambda els: td.PointDipole(
+					center=els[0],
+					source_time=els[1],
+					interpolate=els[2],
+					polarization=pol_axis,
+				)
+			)
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind.Params
+	####################
+	@events.computes_output_socket(
+		'Source',
+		kind=ct.FlowKind.Params,
+		# Loaded
+		input_sockets={'Temporal Shape', 'Center', 'Interpolate'},
+		input_socket_kinds={
+			'Temporal Shape': ct.FlowKind.Params,
+			'Center': ct.FlowKind.Params,
+			'Interpolate': ct.FlowKind.Params,
+		},
+	)
+	def compute_params(
+		self,
+		input_sockets,
+	) -> td.PointDipole | ct.FlowSignal:
+		"""Compute the point dipole source, given that all inputs are non-symbolic."""
+		temporal_shape = input_sockets['Temporal Shape']
+		center = input_sockets['Center']
+		interpolate = input_sockets['Interpolate']
+
+		has_temporal_shape = not ct.FlowSignal.check(temporal_shape)
+		has_center = not ct.FlowSignal.check(center)
+		has_interpolate = not ct.FlowSignal.check(interpolate)
+
+		if has_temporal_shape and has_center and has_interpolate:
+			return temporal_shape | center | interpolate
+		return ct.FlowSignal.FlowPending
 
 	####################
 	# - Preview

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

@@ -16,15 +16,19 @@
 
 """Implements the `TemporalShapeNode`."""
 
+import enum
 import typing as typ
 
 import bpy
+import numpy as np
 import sympy as sp
 import sympy.physics.units as spu
 import tidy3d as td
+from tidy3d.components.data.data_array import TimeDataArray as td_TimeDataArray
+from tidy3d.components.data.dataset import TimeDataset as td_TimeDataset
 
+from blender_maxwell.utils import bl_cache, logger, sim_symbols
 from blender_maxwell.utils import extra_sympy_units as spux
-from blender_maxwell.utils import logger, sim_symbols
 
 from ... import contracts as ct
 from ... import managed_objs, sockets
@@ -33,14 +37,10 @@ from .. import base, events
 log = logger.get(__name__)
 
 
-_max_e_socket_def = sockets.ExprSocketDef(
+# Select Default Time Unit for Envelope
-	mathtype=spux.MathType.Complex,
+## -> Chosen to align with the default envelope_time_unit.
-	physical_type=spux.PhysicalType.EField,
+## -> This causes it to be correct from the start.
-	default_value=1 + 0j,
+t_def = sim_symbols.t(spux.PhysicalType.Time.valid_units[0])
-)
-_offset_socket_def = sockets.ExprSocketDef(default_value=5, abs_min=2.5)
-
-t_ps = sim_symbols.t(spu.picosecond)
 
 
 class TemporalShapeNode(base.MaxwellSimNode):
@@ -63,17 +63,18 @@ class TemporalShapeNode(base.MaxwellSimNode):
 			default_unit=spux.THz,
 			default_value=200,
 		),
+		'max E': sockets.ExprSocketDef(
+			mathtype=spux.MathType.Complex,
+			physical_type=spux.PhysicalType.EField,
+			default_value=1 + 0j,
+		),
+		'Offset Time': sockets.ExprSocketDef(default_value=5, abs_min=2.5),
 	}
 	input_socket_sets: typ.ClassVar = {
 		'Pulse': {
-			'max E': _max_e_socket_def,
-			'Offset Time': _offset_socket_def,
 			'Remove DC': sockets.BoolSocketDef(default_value=True),
 		},
-		'Constant': {
+		'Constant': {},
-			'max E': _max_e_socket_def,
-			'Offset Time': _offset_socket_def,
-		},
 		'Symbolic': {
 			't Range': sockets.ExprSocketDef(
 				active_kind=ct.FlowKind.Range,
@@ -84,8 +85,8 @@ class TemporalShapeNode(base.MaxwellSimNode):
 				default_steps=100,
 			),
 			'Envelope': sockets.ExprSocketDef(
-				default_symbols=[t_ps],
+				default_symbols=[t_def],
-				default_value=10 * t_ps.sp_symbol,
+				default_value=10 * t_def.sp_symbol,
 			),
 		},
 	}
@@ -98,6 +99,55 @@ class TemporalShapeNode(base.MaxwellSimNode):
 		'plot': managed_objs.ManagedBLImage,
 	}
 
+	####################
+	# - Properties
+	####################
+	active_envelope_time_unit: enum.StrEnum = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_time_units(),
+	)
+
+	def search_time_units(self) -> list[ct.BLEnumElement]:
+		"""Compute all valid time units."""
+		return [
+			(sp.sstr(unit), spux.sp_to_str(unit), sp.sstr(unit), '', i)
+			for i, unit in enumerate(spux.PhysicalType.Time.valid_units)
+		]
+
+	@bl_cache.cached_bl_property(depends_on={'active_envelope_time_unit'})
+	def envelope_time_unit(self) -> spux.Unit | None:
+		"""Gets the current active unit for the envelope time symbol.
+
+		Returns:
+			The current active `sympy` unit.
+
+			If the socket expression is unitless, this returns `None`.
+		"""
+		if self.active_envelope_time_unit is not None:
+			return spux.unit_str_to_unit(self.active_envelope_time_unit)
+
+		return None
+
+	####################
+	# - UI
+	####################
+	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout):
+		if (
+			self.active_socket_set == 'Symbolic'
+			and self.inputs.get('Envelope')
+			and not self.inputs['Envelope'].is_linked
+		):
+			row = layout.row()
+			row.alignment = 'CENTER'
+			row.label(text='Envelope Time Unit')
+
+			row = layout.row()
+			row.prop(
+				self,
+				self.blfields['active_envelope_time_unit'],
+				text='',
+				toggle=True,
+			)
+
 	def draw_info(self, _: bpy.types.Context, layout: bpy.types.UILayout) -> None:
 		if self.active_socket_set != 'Symbolic':
 			box = layout.box()
@@ -118,10 +168,53 @@ class TemporalShapeNode(base.MaxwellSimNode):
 			col.label(text='1 / 2π·σ(𝑓)')
 
 	####################
-	# - FlowKind: Value
+	# - Events
+	####################
+	@events.on_value_changed(
+		# Trigger
+		prop_name={'active_socket_set', 'envelope_time_unit'},
+		# Loaded
+		props={'active_socket_set', 'envelope_time_unit'},
+	)
+	def on_envelope_time_unit_changed(self, props) -> None:
+		"""Ensure the envelope expression's time symbol has the time unit defined by the node."""
+		active_socket_set = props['active_socket_set']
+		envelope_time_unit = props['envelope_time_unit']
+		if active_socket_set == 'Symbolic':
+			bl_socket = self.inputs['Envelope']
+			wanted_t_sym = sim_symbols.t(envelope_time_unit)
+
+			if not bl_socket.symbols or bl_socket.symbols[0] != wanted_t_sym:
+				bl_socket.symbols = [wanted_t_sym]
+
+	####################
+	# - FlowKind.Value
 	####################
 	@events.computes_output_socket(
 		'Temporal Shape',
+		kind=ct.FlowKind.Value,
+		# Loaded
+		output_sockets={'Temporal Shape'},
+		output_socket_kinds={'Temporal Shape': {ct.FlowKind.Func, ct.FlowKind.Params}},
+	)
+	def compute_domain_value(self, output_sockets) -> ct.ParamsFlow | ct.FlowSignal:
+		"""Compute a single temporal shape."""
+		output_func = output_sockets['Temporal Shape'][ct.FlowKind.Func]
+		output_params = output_sockets['Temporal Shape'][ct.FlowKind.Params]
+
+		has_output_func = not ct.FlowSignal.check(output_func)
+		has_output_params = not ct.FlowSignal.check(output_params)
+
+		if has_output_func and has_output_params and not output_params.symbols:
+			return output_func.realize(output_params)
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind: Func
+	####################
+	@events.computes_output_socket(
+		'Temporal Shape',
+		kind=ct.FlowKind.Func,
 		# Loaded
 		props={'active_socket_set'},
 		input_sockets={
@@ -134,60 +227,178 @@ class TemporalShapeNode(base.MaxwellSimNode):
 			'Envelope',
 		},
 		input_socket_kinds={
-			't Range': ct.FlowKind.Range,
+			'max E': ct.FlowKind.Func,
-			'Envelope': ct.FlowKind.Func,
+			'μ Freq': ct.FlowKind.Func,
-		},
+			'σ Freq': ct.FlowKind.Func,
-		input_sockets_optional={
+			'Offset Time': ct.FlowKind.Func,
-			'max E': True,
+			'Remove DC': ct.FlowKind.Value,
-			'Offset Time': True,
+			't Range': ct.FlowKind.Func,
-			'Remove DC': True,
+			'Envelope': {ct.FlowKind.Func, ct.FlowKind.Params},
-			't Range': True,
-			'Envelope': True,
-		},
-		unit_systems={'Tidy3DUnits': ct.UNITS_TIDY3D},
-		scale_input_sockets={
-			'max E': 'Tidy3DUnits',
-			'μ Freq': 'Tidy3DUnits',
-			'σ Freq': 'Tidy3DUnits',
-			't Range': 'Tidy3DUnits',
-			'Offset Time': 'Tidy3DUnits',
 		},
 	)
-	def compute_temporal_shape(
+	def compute_temporal_shape_func(
-		self, props, input_sockets, unit_systems
+		self,
+		props,
+		input_sockets,
 	) -> td.GaussianPulse:
+		"""Compute a single temporal shape from non-parameterized inputs."""
+		mean_freq = input_sockets['μ Freq']
+		std_freq = input_sockets['σ Freq']
+		max_e = input_sockets['max E']
+		offset = input_sockets['Offset Time']
+
+		has_mean_freq = not ct.FlowSignal.check(mean_freq)
+		has_std_freq = not ct.FlowSignal.check(std_freq)
+		has_max_e = not ct.FlowSignal.check(max_e)
+		has_offset = not ct.FlowSignal.check(offset)
+
+		if has_mean_freq and has_std_freq and has_max_e and has_offset:
+			common_func = (
+				max_e.scale_to_unit_system(ct.UNITS_TIDY3D)
+				| mean_freq.scale_to_unit_system(ct.UNITS_TIDY3D)
+				| std_freq.scale_to_unit_system(ct.UNITS_TIDY3D)
+				| offset  ## Already unitless
+			)
 			match props['active_socket_set']:
 				case 'Pulse':
-				return td.GaussianPulse(
+					remove_dc = input_sockets['Remove DC']
-					amplitude=sp.re(input_sockets['max E']),
+
-					phase=sp.im(input_sockets['max E']),
+					has_remove_dc = not ct.FlowSignal.check(remove_dc)
-					freq0=input_sockets['μ Freq'],
+
-					fwidth=input_sockets['σ Freq'],
+					if has_remove_dc:
-					offset=input_sockets['Offset Time'],
+						return common_func.compose_within(
-					remove_dc_component=input_sockets['Remove DC'],
+							lambda els: td.GaussianPulse(
+								amplitude=complex(els[0]).real,
+								phase=complex(els[0]).imag,
+								freq0=els[1],
+								fwidth=els[2],
+								offset=els[3],
+								remove_dc_component=remove_dc,
+							),
 						)
 
 				case 'Constant':
-				return td.ContinuousWave(
+					return common_func.compose_within(
-					amplitude=sp.re(input_sockets['max E']),
+						lambda els: td.GaussianPulse(
-					phase=sp.im(input_sockets['max E']),
+							amplitude=complex(els[0]).real,
-					freq0=input_sockets['μ Freq'],
+							phase=complex(els[0]).imag,
-					fwidth=input_sockets['σ Freq'],
+							freq0=els[1],
-					offset=input_sockets['Offset Time'],
+							fwidth=els[2],
+							offset=els[3],
+						),
 					)
 
 				case 'Symbolic':
-				lzrange = input_sockets['t Range']
+					t_range = input_sockets['t Range']
-				envelope_ps = input_sockets['Envelope'].func_jax
+					envelope = input_sockets['Envelope'][ct.FlowKind.Func]
+					envelope_params = input_sockets['Envelope'][ct.FlowKind.Params]
 
-				return td.CustomSourceTime.from_values(
+					has_t_range = not ct.FlowSignal.check(t_range)
-					freq0=input_sockets['μ Freq'],
+					has_envelope = not ct.FlowSignal.check(envelope)
-					fwidth=input_sockets['σ Freq'],
+					has_envelope_params = not ct.FlowSignal.check(envelope_params)
-					values=envelope_ps(
+
-						lzrange.rescale_to_unit(spu.ps).realize_array.values
+					if (
-					),
+						has_t_range
-					dt=input_sockets['t Range'].realize_step_size(),
+						and has_envelope
+						and has_envelope_params
+						and len(envelope_params.symbols) == 1
+						## TODO: Allow unrealized envelope symbols
+						and any(
+							sym.physical_type is spux.PhysicalType.Time
+							for sym in envelope_params.symbols
 						)
+					):
+						envelope_time_unit = next(
+							sym.unit
+							for sym in envelope_params.symbols
+							if sym.physical_type is spux.PhysicalType.Time
+						)
+
+						# Deduce Partially Realized Envelope Function
+						## -> We need a pure-numerical function w/pre-realized stuff baked in.
+						## -> 'realize_partial' does this for us.
+						envelope_realizer = envelope.realize_partial(envelope_params)
+
+						# Compose w/Envelope Function
+						## -> First, the numerical time values must be converted.
+						## -> This ensures that the raw array is compatible w/the envelope.
+						## -> Then, we can compose w/the purely numerical 'envelope_realizer'.
+						## -> Because of the checks, we've guaranteed that all this is correct.
+						return (
+							common_func  ## 1 | freq0, 2 | fwidth, 3 | offset
+							| t_range.scale_to_unit_system(ct.UNITS_TIDY3D)  ## 4
+							| t_range.scale_to_unit(envelope_time_unit).compose_within(
+								lambda t: envelope_realizer(t)
+							)  ## 5
+						).compose_within(
+							lambda els: td.CustomSourceTime(
+								amplitude=complex(els[0]).real,
+								phase=complex(els[0]).imag,
+								freq0=els[1],
+								fwidth=els[2],
+								offset=els[3],
+								source_time_dataset=td_TimeDataset(
+									values=td_TimeDataArray(
+										els[5], coords={'t': np.array(els[4])}
+									)
+								),
+							)
+						)
+
+		return ct.FlowSignal.FlowPending
+
+	####################
+	# - FlowKind: Params
+	####################
+	@events.computes_output_socket(
+		'Temporal Shape',
+		kind=ct.FlowKind.Params,
+		# Loaded
+		props={'active_socket_set', 'envelope_time_unit'},
+		input_sockets={
+			'max E',
+			'μ Freq',
+			'σ Freq',
+			'Offset Time',
+			't Range',
+		},
+		input_socket_kinds={
+			'max E': ct.FlowKind.Params,
+			'μ Freq': ct.FlowKind.Params,
+			'σ Freq': ct.FlowKind.Params,
+			'Offset Time': ct.FlowKind.Params,
+			't Range': ct.FlowKind.Params,
+		},
+	)
+	def compute_temporal_shape_params(
+		self,
+		props,
+		input_sockets,
+	) -> td.GaussianPulse:
+		"""Compute a single temporal shape from non-parameterized inputs."""
+		mean_freq = input_sockets['μ Freq']
+		std_freq = input_sockets['σ Freq']
+		max_e = input_sockets['max E']
+		offset = input_sockets['Offset Time']
+
+		has_mean_freq = not ct.FlowSignal.check(mean_freq)
+		has_std_freq = not ct.FlowSignal.check(std_freq)
+		has_max_e = not ct.FlowSignal.check(max_e)
+		has_offset = not ct.FlowSignal.check(offset)
+
+		if has_mean_freq and has_std_freq and has_max_e and has_offset:
+			common_params = max_e | mean_freq | std_freq | offset
+			match props['active_socket_set']:
+				case 'Pulse' | 'Constant':
+					return common_params
+
+				case 'Symbolic':
+					t_range = input_sockets['t Range']
+					has_t_range = not ct.FlowSignal.check(t_range)
+
+					if has_t_range:
+						return common_params | t_range | t_range
+		return ct.FlowSignal.FlowPending
 
 
 ####################

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

@@ -88,28 +88,27 @@ class BoxStructureNode(base.MaxwellSimNode):
 		'Structure',
 		kind=ct.FlowKind.Value,
 		# Loaded
-		props={'differentiable'},
 		input_sockets={'Medium', 'Center', 'Size'},
 		output_sockets={'Structure'},
 		output_socket_kinds={'Structure': ct.FlowKind.Params},
 	)
-	def compute_value(self, props, input_sockets, output_sockets) -> td.Box:
+	def compute_value(self, input_sockets, output_sockets) -> td.Box:
-		output_params = output_sockets['Structure']
+		"""Compute a single box structure object, given that all inputs are non-symbolic."""
 		center = input_sockets['Center']
 		size = input_sockets['Size']
 		medium = input_sockets['Medium']
+		output_params = output_sockets['Structure']
 
-		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)
+		has_output_params = not ct.FlowSignal.check(output_params)
 
 		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(
@@ -138,7 +137,8 @@ class BoxStructureNode(base.MaxwellSimNode):
 		output_sockets={'Structure'},
 		output_socket_kinds={'Structure': ct.FlowKind.Params},
 	)
-	def compute_lazy_structure(self, props, input_sockets, output_sockets) -> td.Box:
+	def compute_structure_func(self, props, input_sockets, output_sockets) -> td.Box:
+		"""Compute a possibly-differentiable function, producing a box structure from the input parameters."""
 		output_params = output_sockets['Structure']
 		center = input_sockets['Center']
 		size = input_sockets['Size']
@@ -149,14 +149,8 @@ class BoxStructureNode(base.MaxwellSimNode):
 		has_size = not ct.FlowSignal.check(size)
 		has_medium = not ct.FlowSignal.check(medium)
 
+		if has_output_params and has_center and has_size and has_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(
@@ -169,6 +163,12 @@ class BoxStructureNode(base.MaxwellSimNode):
 					supports_jax=True,
 				)
 			return (center | size | medium).compose_within(
+				## TODO: Unit conversion within the composed function??
+				## -- We do need Tidy3D to be given ex. micrometers in particular.
+				## -- But the previous numerical output might not be micrometers.
+				## -- There must be a way to add a conversion in, without strangeness.
+				## -- Ex. can compose_within() take a unit system?
+				## -- This would require
 				enclosing_func=lambda els: td.Structure(
 					geometry=td.Box(
 						center=tuple(els[0].flatten()),
@@ -205,14 +205,8 @@ class BoxStructureNode(base.MaxwellSimNode):
 		has_medium = not ct.FlowSignal.check(medium)
 
 		if has_center and has_size and has_medium:
-			if props['differentiable'] == (
-				center.is_differentiable
-				and size.is_differentiable
-				and medium.is_differentiable
-			):
 			return center | size | medium
 		return ct.FlowSignal.FlowPending
-		return ct.FlowSignal.FlowPending
 
 	####################
 	# - Events: Preview
@@ -226,6 +220,7 @@ class BoxStructureNode(base.MaxwellSimNode):
 		output_socket_kinds={'Structure': ct.FlowKind.Params},
 	)
 	def compute_previews(self, props, output_sockets):
+		"""Mark the managed preview object when recursively linked to a viewer."""
 		output_params = output_sockets['Structure']
 		has_output_params = not ct.FlowSignal.check(output_params)
 
@@ -245,10 +240,14 @@ class BoxStructureNode(base.MaxwellSimNode):
 	)
 	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']
+
+		has_output_params = not ct.FlowSignal.check(output_params)
+		has_center = not ct.FlowSignal.check(center)
+		if has_center and has_output_params and not output_params.symbols:
+			## TODO: There are strategies for handling examples of symbol values.
+
+			# Push Loose Input Values to GeoNodes Modifier
 			managed_objs['modifier'].bl_modifier(
 				'NODES',
 				{

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

@@ -43,17 +43,28 @@ class SocketDef(pyd.BaseModel, abc.ABC):
 	"""
 
 	socket_type: ct.SocketType
+	active_kind: typ.Literal[
+		ct.FlowKind.Value,
+		ct.FlowKind.Array,
+		ct.FlowKind.Range,
+		ct.FlowKind.Func,
+	] = ct.FlowKind.Value
 
+	####################
+	# - Socket Interaction
+	####################
 	def preinit(self, bl_socket: bpy.types.NodeSocket) -> None:
 		"""Pre-initialize a real Blender node socket from this socket definition.
 
 		Parameters:
 			bl_socket: The Blender node socket to alter using data from this SocketDef.
 		"""
-		log.debug('%s: Start Socket Preinit', bl_socket.bl_label)
+		# 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)
+
+		bl_socket.active_kind = self.active_kind
+		# 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.
@@ -61,12 +72,12 @@ 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)
+		# 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)
+		# log.debug('%s: End Socket Postinit', bl_socket.bl_label)
 
 	@abc.abstractmethod
 	def init(self, bl_socket: bpy.types.NodeSocket) -> None:
@@ -76,6 +87,43 @@ class SocketDef(pyd.BaseModel, abc.ABC):
 			bl_socket: The Blender node socket to alter using data from this SocketDef.
 		"""
 
+	####################
+	# - Comparison
+	####################
+	def compare(self, bl_socket: bpy.types.NodeSocket) -> bool:
+		"""Whether this `SocketDef` can be considered to uniquely define the given `bl_socket`.
+
+		The general criteria for "uniquely defines" is whether **the same `bl_socket`** could be created using this `SocketDef`.
+		The extent to which user-altered properties are considered in this regard is a matter of taste, encapsulated entirely within `self.local_compare()`.
+
+		Notes:
+			Used when determining whether to replace sockets with newer variants when synchronizing changes.
+
+			**NOTE**: Removing/replacing loose input sockets
+
+		Parameters:
+			bl_socket: The Blender node socket to alter using data from this SocketDef.
+		"""
+		return (
+			bl_socket.socket_type is self.socket_type
+			and bl_socket.active_kind is self.active_kind
+			and self.local_compare(bl_socket)
+		)
+
+	def local_compare(self, bl_socket: bpy.types.NodeSocket) -> None:
+		"""Compare this `SocketDef` to an established `bl_socket` in a manner specific to the node.
+
+		Notes:
+			Run by `self.compare()`.
+			Optionally overriden by individual sockets.
+
+			When not overridden, it will always return `False`, indicating that the socket is _never_ uniquely defined by this `SocketDef`.
+
+		Parameters:
+			bl_socket: The Blender node socket to alter using data from this SocketDef.
+		"""
+		return False
+
 	####################
 	# - Serialization
 	####################
@@ -426,8 +474,34 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 		Parameters:
 			socket_kinds: The altered `ct.FlowKind`s flowing through.
 		"""
+		# Run Socket Callbacks
 		self.on_socket_data_changed(socket_kinds)
 
+		# Mark Active FlowKind Links as Invalid
+		## -> Mark link as invalid (very red) if a FlowSignal is traveling.
+		## -> This helps explain why whatever isn't working isn't working.
+		## -> TODO: We need a different approach.
+		# log.debug(
+		# '[%s] Checking FlowKind Validity (socket_kinds=%s)',
+		# self.name,
+		# str(socket_kinds),
+		# )
+		# if self.is_linked and not self.is_output:
+		# link = self.links[0]
+		# linked_flow = self.compute_data(kind=self.active_kind)
+
+		# if (
+		# link.is_valid
+		# and self.active_kind in socket_kinds
+		# and ct.FlowSignal.check_single(linked_flow, ct.FlowSignal.FlowPending)
+		# ):
+		# node_tree = self.id_data
+		# node_tree.report_link_validity(link, False)
+
+		# elif not link.is_valid:
+		# node_tree = self.id_data
+		# node_tree.report_link_validity(link, True)
+
 	def on_socket_data_changed(self, socket_kinds: set[ct.FlowKind]) -> None:
 		"""Called when `ct.FlowEvent.DataChanged` flows through this socket.
 
@@ -479,7 +553,7 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 				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)',
+		# '[%s] [%s] Socket Triggered (socket_kinds=%s)',
 		# self.name,
 		# event,
 		# str(socket_kinds),
@@ -757,7 +831,7 @@ 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
-		## -> Multi-input sockets are not yet supported.
+		## -> Multi-input sockets are not (yet) supported.
 		if linked_values:
 			return linked_values[0]
 
@@ -891,10 +965,14 @@ class MaxwellSimSocket(bpy.types.NodeSocket, bl_instance.BLInstance):
 			# FlowKind Draw Row
 			col = row.column(align=True)
 			{
+				ct.FlowKind.Capabilities: lambda *_: None,
+				ct.FlowKind.Previews: lambda *_: None,
 				ct.FlowKind.Value: self.draw_value,
 				ct.FlowKind.Array: self.draw_array,
 				ct.FlowKind.Range: self.draw_lazy_range,
 				ct.FlowKind.Func: self.draw_lazy_func,
+				ct.FlowKind.Params: lambda *_: None,
+				ct.FlowKind.Info: lambda *_: None,
 			}[self.active_kind](col)
 
 		# Info Drawing

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

@@ -51,6 +51,16 @@ class BoolBLSocket(base.MaxwellSimSocket):
 	def value(self, value: bool) -> None:
 		self.raw_value = value
 
+	@bl_cache.cached_bl_property(depends_on={'value'})
+	def lazy_func(self) -> ct.FuncFlow:
+		return ct.FuncFlow(
+			func=lambda: self.value,
+		)
+
+	@bl_cache.cached_bl_property()
+	def params(self) -> ct.FuncFlow:
+		return ct.ParamsFlow()
+
 
 ####################
 # - Socket Configuration

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

@@ -130,6 +130,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			'physical_type',
 			'unit',
 			'size',
+			'value',
 		}
 	)
 	def output_sym(self) -> sim_symbols.SimSymbol | None:
@@ -140,13 +141,29 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		Raises:
 			NotImplementedError: When `active_kind` is neither `Value`, `Func`, or `Range`.
 		"""
-		if self.symbols:
+		match self.active_kind:
-			if self.active_kind in [ct.FlowKind.Value, ct.FlowKind.Func]:
+			case ct.FlowKind.Value | ct.FlowKind.Func if self.symbols:
 				return self._parse_expr_symbol(
 					self._parse_expr_str(self.raw_value_spstr)
 				)
 
-			if self.active_kind is ct.FlowKind.Range:
+			case ct.FlowKind.Value | ct.FlowKind.Func if not self.symbols:
+				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,
+					exclude_zero=(
+						not self.value.is_zero
+						if self.value.is_zero is not None
+						else False
+					),
+					## TODO: Does this work for matrix elements?
+				)
+
+			case ct.FlowKind.Range if self.symbols:
 				## TODO: Support RangeFlow
 				## -- It's hard; we need a min-span set over bound domains.
 				## -- We... Don't use this anywhere. Yet?
@@ -159,20 +176,37 @@ class ExprBLSocket(base.MaxwellSimSocket):
 				msg = 'RangeFlow support not yet implemented for when self.symbols is not empty'
 				raise NotImplementedError(msg)
 
-			raise NotImplementedError
+			case ct.FlowKind.Range if not self.symbols:
-
 				return sim_symbols.SimSymbol(
 					sym_name=self.output_name,
 					mathtype=self.mathtype,
 					physical_type=self.physical_type,
 					unit=self.unit,
-			rows=self.size.rows,
+					rows=self.lazy_range.steps,
-			cols=self.size.cols,
+					cols=1,
+					exclude_zero=not self.lazy_range.is_always_nonzero,
 				)
 
+	####################
+	# - Value|Range Swapper
+	####################
+	use_value_range_swapper: bool = bl_cache.BLField(False)
+	selected_value_range: ct.FlowKind = bl_cache.BLField(
+		enum_cb=lambda self, _: self._value_or_range(),
+	)
+
+	def _value_or_range(self):
+		return [
+			flow_kind.bl_enum_element(i)
+			for i, flow_kind in enumerate([ct.FlowKind.Value, ct.FlowKind.Range])
+		]
+
 	####################
 	# - Symbols
 	####################
+	lazy_range_name: sim_symbols.SimSymbolName = bl_cache.BLField(
+		sim_symbols.SimSymbolName.Expr
+	)
 	output_name: sim_symbols.SimSymbolName = bl_cache.BLField(
 		sim_symbols.SimSymbolName.Expr
 	)
@@ -343,7 +377,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 
 			See `MaxwellSimTree` for more detail on the link callbacks.
 		"""
-		## NODE: Depends on suppressed on_prop_changed
+		## NOTE: Depends on suppressed on_prop_changed
 
 		if ct.FlowKind.Info in socket_kinds:
 			info = self.compute_data(kind=ct.FlowKind.Info)
@@ -371,7 +405,10 @@ class ExprBLSocket(base.MaxwellSimSocket):
 
 			See `MaxwellSimTree` for more detail on the link callbacks.
 		"""
-		## NODE: Depends on suppressed on_prop_changed
+		## NOTE: Depends on suppressed on_prop_changed
+		if ('selected_value_range', 'invalidate') in cleared_blfields:
+			self.active_kind = self.selected_value_range
+			self.on_active_kind_changed()
 
 		# Conditional Unit-Conversion
 		## -> This is niche functionality, but the only way to convert units.
@@ -757,7 +794,6 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	@bl_cache.cached_bl_property(
 		depends_on={
 			'value',
-			'symbols',
 			'sorted_sp_symbols',
 			'sorted_symbols',
 			'output_sym',
@@ -769,83 +805,88 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		If `self.value` has unknown symbols (as indicated by `self.symbols`), then these will be the arguments of the `FuncFlow`.
 		Otherwise, the returned lazy value function will be a simple excuse for `self.params` to pass the verbatim `self.value`.
 		"""
-		# Symbolic
+		if self.output_sym is not None:
-		## -> `self.value` is guaranteed to be an expression with unknowns.
+			match self.active_kind:
-		## -> The function computes `self.value` with unknowns as arguments.
+				case ct.FlowKind.Value | ct.FlowKind.Func if (
-		if self.symbols:
+					self.sorted_symbols and not ct.FlowSignal.check(self.value)
-			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),
+							self.output_sym.conform(self.value, strip_unit=True),
 							'jax',
 						),
 						func_args=list(self.sorted_symbols),
+						func_output=self.output_sym,
 						supports_jax=True,
 					)
-			return ct.FlowSignal.FlowPending
 
-		# Constant
+				case ct.FlowKind.Value | ct.FlowKind.Func if not self.sorted_symbols:
-		## -> When a `self.value` has no unknowns, use a dummy function.
-		## -> ("Dummy" as in returns the same argument that it takes).
-		## -> This is an excuse to let `ParamsFlow` pass `self.value` verbatim.
-		## -> Generally only useful for operations with other expressions.
 					return ct.FuncFlow(
 						func=lambda v: v,
 						func_args=[self.output_sym],
+						func_output=self.output_sym,
 						supports_jax=True,
 					)
 
-	@bl_cache.cached_bl_property(depends_on={'sorted_symbols'})
+				case ct.FlowKind.Range if self.sorted_symbols:
-	def is_differentiable(self) -> bool:
+					msg = 'RangeFlow support not yet implemented for when self.sorted_symbols is not empty'
-		"""Whether all symbols are differentiable.
+					raise NotImplementedError(msg)
 
-		If there are no symbols, then there is nothing to differentiate, and thus the expression is differentiable.
+				case ct.FlowKind.Range if (
-		"""
+					not self.sorted_symbols and not ct.FlowSignal.check(self.lazy_range)
-		if not self.sorted_symbols:
+				):
-			return True
+					return ct.FuncFlow(
-
+						func=lambda v: v,
-		return all(
+						func_args=[self.output_sym],
-			sym.mathtype in [spux.MathType.Real, spux.MathType.Complex]
+						func_output=self.output_sym,
-			for sym in self.sorted_symbols
+						supports_jax=True,
 					)
 
-	@bl_cache.cached_bl_property(depends_on={'sorted_symbols', 'output_sym', 'value'})
+		return ct.FlowSignal.FlowPending
+
+	@bl_cache.cached_bl_property(
+		depends_on={'sorted_symbols', 'output_sym', 'value', 'lazy_range'}
+	)
 	def params(self) -> ct.ParamsFlow:
 		"""Returns parameter symbols/values to accompany `self.lazy_func`.
 
 		If `self.value` has unknown symbols (as indicated by `self.symbols`), then these will be passed into `ParamsFlow`, which will thus be parameterized (and require realization before use).
 		Otherwise, `self.value` is passed verbatim as the only `ParamsFlow.func_arg`.
 		"""
-		# Symbolic
-		## -> The Expr socket does not declare actual values for the symbols.
-		## -> 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.sorted_symbols:
 		output_sym = self.output_sym
 		if output_sym is not None:
+			match self.active_kind:
+				case ct.FlowKind.Value | ct.FlowKind.Func if self.sorted_symbols:
 					return ct.ParamsFlow(
 						arg_targets=list(self.sorted_symbols),
 						func_args=[sym.sp_symbol for sym in self.sorted_symbols],
-					symbols=self.sorted_symbols,
+						symbols=set(self.sorted_symbols),
-					is_differentiable=self.is_differentiable,
 					)
-			return ct.FlowSignal.FlowPending
 
-		# Constant
+				case ct.FlowKind.Value | ct.FlowKind.Func if (
-		## -> Simply pass self.value verbatim as a function argument.
+					not self.sorted_symbols and not ct.FlowSignal.check(self.value)
-		## -> Easy dice, easy life!
+				):
 					return ct.ParamsFlow(
 						arg_targets=[self.output_sym],
 						func_args=[self.value],
-			is_differentiable=self.is_differentiable,
 					)
 
+				case ct.FlowKind.Range if self.sorted_symbols:
+					msg = 'RangeFlow support not yet implemented for when self.sorted_symbols is not empty'
+					raise NotImplementedError(msg)
+
+				case ct.FlowKind.Range if (
+					not self.sorted_symbols and not ct.FlowSignal.check(self.lazy_range)
+				):
+					return ct.ParamsFlow(
+						arg_targets=[self.output_sym],
+						func_args=[self.output_sym.sp_symbol_matsym],
+						symbols={self.output_sym},
+					).realize_partial({self.output_sym: self.lazy_range})
+
+		return ct.FlowSignal.FlowPending
+
 	@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`.
@@ -858,22 +899,34 @@ class ExprBLSocket(base.MaxwellSimSocket):
 
 		Otherwise, only the output name/size/mathtype/unit corresponding to the socket is passed along.
 		"""
-		# Constant
-		## -> The input SimSymbols become continuous dimensional indices.
-		## -> All domain validity information is defined on the SimSymbol keys.
-		if self.sorted_symbols:
 		output_sym = self.output_sym
 		if output_sym is not None:
+			match self.active_kind:
+				case ct.FlowKind.Value | ct.FlowKind.Func if self.sorted_symbols:
 					return ct.InfoFlow(
 						dims={sym: None for sym in self.sorted_symbols},
 						output=self.output_sym,
 					)
-			return ct.FlowSignal.FlowPending
 
-		# Constant
+				case ct.FlowKind.Value | ct.FlowKind.Func if (
-		## -> We only need the output symbol to describe the raw data.
+					not self.sorted_symbols and not ct.FlowSignal.check(self.lazy_range)
+				):
 					return ct.InfoFlow(output=self.output_sym)
 
+				case ct.FlowKind.Range if self.sorted_symbols:
+					msg = 'InfoFlow support not yet implemented for when self.sorted_symbols is not empty'
+					raise NotImplementedError(msg)
+
+				case ct.FlowKind.Range if (
+					not self.sorted_symbols and not ct.FlowSignal.check(self.lazy_range)
+				):
+					return ct.InfoFlow(
+						dims={self.output_sym: self.lazy_range},
+						output=self.output_sym.update(rows=1),
+					)
+
+		return ct.FlowSignal.FlowPending
+
 	####################
 	# - FlowKind: Capabilities
 	####################
@@ -1039,6 +1092,9 @@ class ExprBLSocket(base.MaxwellSimSocket):
 
 			However, `draw_value` may also be called by the `draw_*` methods of other `FlowKinds`, who may choose to layer more flexibility around this base UI.
 		"""
+		if self.use_value_range_swapper:
+			col.prop(self, self.blfields['selected_value_range'], text='')
+
 		if self.symbols:
 			col.prop(self, self.blfields['raw_value_spstr'], text='')
 
@@ -1097,6 +1153,9 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			If `self.steps == 0`, then the `Range` is considered to have a to-be-determined number of steps.
 			As such, `self.steps` won't be exposed in the UI.
 		"""
+		if self.use_value_range_swapper:
+			col.prop(self, self.blfields['selected_value_range'], text='')
+
 		if self.symbols:
 			col.prop(self, self.blfields['raw_min_spstr'], text='')
 			col.prop(self, self.blfields['raw_max_spstr'], text='')
@@ -1198,13 +1257,11 @@ class ExprBLSocket(base.MaxwellSimSocket):
 # - Socket Configuration
 ####################
 class ExprSocketDef(base.SocketDef):
+	"""Interface for defining an `ExprSocket`."""
+
 	socket_type: ct.SocketType = ct.SocketType.Expr
-	active_kind: typ.Literal[
-		ct.FlowKind.Value,
-		ct.FlowKind.Range,
-		ct.FlowKind.Func,
-	] = ct.FlowKind.Value
 	output_name: sim_symbols.SimSymbolName = sim_symbols.SimSymbolName.Expr
+	use_value_range_swapper: bool = False
 
 	# Socket Interface
 	size: spux.NumberSize1D = spux.NumberSize1D.Scalar
@@ -1458,7 +1515,7 @@ class ExprSocketDef(base.SocketDef):
 		# Check ActiveKind and Size
 		## -> NOTE: This doesn't protect against dynamic changes to either.
 		if (
-			self.active_kind == ct.FlowKind.Range
+			self.active_kind is ct.FlowKind.Range
 			and self.size is not spux.NumberSize1D.Scalar
 		):
 			msg = "Can't have a non-Scalar size when Range is set as the active kind."
@@ -1504,9 +1561,9 @@ class ExprSocketDef(base.SocketDef):
 	# - Initialization
 	####################
 	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
+		bl_socket.use_value_range_swapper = self.use_value_range_swapper
 
 		# Socket Interface
 		## -> Recall that auto-updates are turned off during init()
@@ -1543,6 +1600,25 @@ class ExprSocketDef(base.SocketDef):
 		# Info Draw
 		bl_socket.use_info_draw = True
 
+	def local_compare(self, bl_socket: ExprBLSocket) -> None:
+		"""Determine whether an updateable socket should be re-initialized from this `SocketDef`."""
+
+		def cmp(attr: str):
+			return getattr(bl_socket, attr) == getattr(self, attr)
+
+		return (
+			bl_socket.use_linked_capabilities
+			and cmp('output_name')
+			and cmp('use_value_range_swapper')
+			and cmp('size')
+			and cmp('mathtype')
+			and cmp('physical_type')
+			and cmp('show_func_ui')
+			and cmp('show_info_columns')
+			and cmp('show_name_selector')
+			and bl_socket.use_info_draw
+		)
+
 
 ####################
 # - Blender Registration

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

@@ -117,6 +117,16 @@ class MaxwellBoundCondsBLSocket(base.MaxwellSimSocket):
 			),
 		)
 
+	@bl_cache.cached_bl_property(depends_on={'value'})
+	def lazy_func(self) -> ct.FuncFlow:
+		return ct.FuncFlow(
+			func=lambda: self.value,
+		)
+
+	@bl_cache.cached_bl_property()
+	def params(self) -> ct.FuncFlow:
+		return ct.ParamsFlow()
+
 
 ####################
 # - Socket Configuration

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/maxwell/fdtd_sim.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/>.
 
+import typing as typ
+
 from ... import contracts as ct
 from .. import base
 
@@ -32,6 +34,9 @@ class MaxwellFDTDSimSocketDef(base.SocketDef):
 	def init(self, bl_socket: MaxwellFDTDSimBLSocket) -> None:
 		pass
 
+	def local_compare(self, _: MaxwellFDTDSimBLSocket) -> None:
+		return True
+
 
 ####################
 # - Blender Registration

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

@@ -73,7 +73,7 @@ class MaxwellMediumBLSocket(base.MaxwellSimSocket):
 	def value(self, eps_rel: tuple[float, float]) -> None:
 		self.eps_rel = eps_rel
 
-	@bl_cache.cached_bl_property(depends_on={'value', 'differentiable'})
+	@bl_cache.cached_bl_property(depends_on={'value'})
 	def lazy_func(self) -> ct.FuncFlow:
 		return ct.FuncFlow(
 			func=lambda: self.value,
@@ -82,7 +82,7 @@ class MaxwellMediumBLSocket(base.MaxwellSimSocket):
 
 	@bl_cache.cached_bl_property(depends_on={'differentiable'})
 	def params(self) -> ct.FuncFlow:
-		return ct.ParamsFlow(is_differentiable=self.differentiable)
+		return ct.ParamsFlow()
 
 	####################
 	# - UI

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

@@ -29,11 +29,11 @@ class MaxwellMonitorBLSocket(base.MaxwellSimSocket):
 class MaxwellMonitorSocketDef(base.SocketDef):
 	socket_type: ct.SocketType = ct.SocketType.MaxwellMonitor
 
-	is_list: bool = False
-
 	def init(self, bl_socket: MaxwellMonitorBLSocket) -> None:
-		if self.is_list:
+		pass
-			bl_socket.active_kind = ct.FlowKind.Array
+
+	def local_compare(self, _: MaxwellMonitorBLSocket) -> None:
+		return True
 
 
 ####################

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

@@ -55,6 +55,16 @@ class MaxwellSimGridBLSocket(base.MaxwellSimSocket):
 			min_steps_per_wvl=self.min_steps_per_wl,
 		)
 
+	@bl_cache.cached_bl_property(depends_on={'value'})
+	def lazy_func(self) -> ct.FuncFlow:
+		return ct.FuncFlow(
+			func=lambda: self.value,
+		)
+
+	@bl_cache.cached_bl_property()
+	def params(self) -> ct.FuncFlow:
+		return ct.ParamsFlow()
+
 
 ####################
 # - Socket Configuration

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

@@ -29,11 +29,11 @@ class MaxwellSourceBLSocket(base.MaxwellSimSocket):
 class MaxwellSourceSocketDef(base.SocketDef):
 	socket_type: ct.SocketType = ct.SocketType.MaxwellSource
 
-	is_list: bool = False
-
 	def init(self, bl_socket: MaxwellSourceBLSocket) -> None:
-		if self.is_list:
+		pass
-			bl_socket.active_kind = ct.FlowKind.Array
+
+	def local_compare(self, _: MaxwellSourceBLSocket) -> None:
+		return True
 
 
 ####################

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

@@ -29,11 +29,11 @@ class MaxwellStructureBLSocket(base.MaxwellSimSocket):
 class MaxwellStructureSocketDef(base.SocketDef):
 	socket_type: ct.SocketType = ct.SocketType.MaxwellStructure
 
-	is_list: bool = False
-
 	def init(self, bl_socket: MaxwellStructureBLSocket) -> None:
-		if self.is_list:
+		pass
-			bl_socket.active_kind = ct.FlowKind.Array
+
+	def local_compare(self, _: MaxwellStructureBLSocket) -> None:
+		return True
 
 
 ####################

src/blender_maxwell/utils/bl_cache/__init__.py

@@ -16,10 +16,10 @@
 
 """Package providing various tools to handle cached data on Blender objects, especially nodes and node socket classes."""
 
+from ..keyed_cache import KeyedCache, keyed_cache
 from .bl_field import BLField
 from .bl_prop import BLProp, BLPropType
 from .cached_bl_property import CachedBLProperty, cached_bl_property
-from .keyed_cache import KeyedCache, keyed_cache
 from .managed_cache import invalidate_nonpersist_instance_id
 from .signal import Signal
 

src/blender_maxwell/utils/bl_instance.py

@@ -21,6 +21,7 @@ from types import MappingProxyType
 import bpy
 
 from blender_maxwell.utils import bl_cache, logger
+from blender_maxwell.utils.keyed_cache import keyed_cache
 
 InstanceID: typ.TypeAlias = str  ## Stringified UUID4
 
@@ -220,11 +221,14 @@ class BLInstance:
 		for str_search_prop_name in self.blfields_str_search:
 			setattr(self, str_search_prop_name, bl_cache.Signal.ResetStrSearch)
 
+	@keyed_cache(
+		exclude={'self'},  ## No dynamic elements of 'self' can be used.
+	)
 	def trace_blfields_to_clear(
 		self,
 		prop_name: str,
-		prev_blfields_to_clear: list[
+		prev_blfields_to_clear: tuple[
-			tuple[str, typ.Literal['invalidate', 'reset_enum', 'reset_strsearch']]
+			tuple[str, typ.Literal['invalidate', 'reset_enum', 'reset_strsearch']], ...
 		] = (),
 	) -> list[str]:
 		"""Invalidates all properties that depend on `prop_name`.
@@ -239,7 +243,7 @@ class BLInstance:
 			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()
+			blfields_to_clear = list(prev_blfields_to_clear)
 		else:
 			blfields_to_clear = []
 
@@ -268,7 +272,7 @@ class BLInstance:
 					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,
+							prev_blfields_to_clear=tuple(blfields_to_clear),
 						)
 
 		match (bool(prev_blfields_to_clear), bool(blfields_to_clear)):
@@ -297,7 +301,7 @@ class BLInstance:
 			## -> 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
+				return list(reversed(dict.fromkeys(reversed(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`.

src/blender_maxwell/utils/image_ops.py

@@ -17,6 +17,7 @@
 """Useful image processing operations for use in the addon."""
 
 import enum
+import functools
 import typing as typ
 
 import jax
@@ -26,7 +27,6 @@ import matplotlib
 import matplotlib.axis as mpl_ax
 import matplotlib.backends.backend_agg
 import matplotlib.figure
-import numpy as np
 import seaborn as sns
 
 from blender_maxwell import contracts as ct
@@ -138,7 +138,7 @@ def rgba_image_from_2d_map(
 ####################
 # - MPL Helpers
 ####################
-# @functools.lru_cache(maxsize=16)
+@functools.lru_cache(maxsize=4)
 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'

src/blender_maxwell/utils/keyed_cache.py

@@ -18,11 +18,15 @@ import functools
 import inspect
 import typing as typ
 
-from blender_maxwell.utils import bl_instance, logger, serialize
+from blender_maxwell.utils import logger, serialize
 
 log = logger.get(__name__)
 
 
+class BLInstance(typ.Protocol):
+	instance_id: str
+
+
 class KeyedCache:
 	def __init__(
 		self,
@@ -75,8 +79,8 @@ class KeyedCache:
 
 	def __get__(
 		self,
-		bl_instance: bl_instance.BLInstance | None,
+		bl_instance: BLInstance | None,
-		owner: type[bl_instance.BLInstance],
+		owner: type[BLInstance],
 	) -> typ.Callable:
 		_func = functools.partial(self, bl_instance)
 		_func.invalidate = functools.partial(
@@ -110,7 +114,7 @@ class KeyedCache:
 
 	def invalidate(
 		self,
-		bl_instance: bl_instance.BLInstance | None,
+		bl_instance: BLInstance | None,
 		**arguments: dict[str, typ.Any],
 	) -> dict[str, typ.Any]:
 		# Determine Wildcard Arguments

src/blender_maxwell/utils/sim_symbols.py

@@ -264,13 +264,16 @@ class SimSymbol(pyd.BaseModel):
 	interval_closed_im: tuple[bool, bool] = (False, False)
 
 	####################
-	# - Labels
+	# - Core
 	####################
 	@functools.cached_property
 	def name(self) -> str:
 		"""Usable name for the symbol."""
 		return self.sym_name.name
 
+	####################
+	# - Labels
+	####################
 	@functools.cached_property
 	def name_pretty(self) -> str:
 		"""Pretty (possibly unicode) name for the thing."""
@@ -307,6 +310,8 @@ class SimSymbol(pyd.BaseModel):
 	@functools.cached_property
 	def plot_label(self) -> str:
 		"""Pretty plot-oriented label."""
+		if self.unit is None:
+			return self.name_pretty
 		return f'{self.name_pretty} ({self.unit_label})'
 
 	####################
@@ -420,6 +425,11 @@ class SimSymbol(pyd.BaseModel):
 
 	@functools.cached_property
 	def is_nonzero(self) -> bool:
+		"""Whether or not the value of this symbol can ever be $0$.
+
+		Notes:
+			Most notably, this symbol cannot be used as the right hand side of a division operation when this property is `False`.
+		"""
 		if self.exclude_zero:
 			return True
 
@@ -441,6 +451,18 @@ class SimSymbol(pyd.BaseModel):
 			)
 		return check_real_domain(self.domain)
 
+	@functools.cached_property
+	def can_diff(self) -> bool:
+		"""Whether this symbol can be used as the input / output variable when differentiating."""
+		# Check Constants
+		## -> Constants (w/pinned values) are never differentiable.
+		if self.is_constant:
+			return False
+
+		# TODO: Discontinuities (especially across 0)?
+
+		return self.mathtype in [spux.MathType.Real, spux.MathType.Complex]
+
 	####################
 	# - Properties
 	####################
@@ -664,8 +686,10 @@ class SimSymbol(pyd.BaseModel):
 			res = spux.strip_unit_system(sp_obj)
 
 		# Broadcast Expansion
-		if self.rows > 1 or self.cols > 1 and not isinstance(res, spux.MatrixBase):
+		if (self.rows > 1 or self.cols > 1) and not isinstance(
-			res = sp_obj * sp.ImmutableMatrix.ones(self.rows, self.cols)
+			res, sp.MatrixBase | sp.MatrixSymbol
+		):
+			res = res * sp.ImmutableMatrix.ones(self.rows, self.cols)
 
 		return res
 
@@ -753,7 +777,9 @@ class SimSymbol(pyd.BaseModel):
 			unit = None
 
 		# Rows/Cols from Expr (if Matrix)
-		rows, cols = expr.shape if isinstance(expr, sp.MatrixBase) else (1, 1)
+		rows, cols = (
+			expr.shape if isinstance(expr, sp.MatrixBase | sp.MatrixSymbol) else (1, 1)
+		)
 
 		return SimSymbol(
 			sym_name=sym_name,