fix: Inching closer.

I'm of the belief that the correct abstractions are now actually
available, and that most-to-all of the required functionality actually
already exists within the code base.
The art is bringing it together!

TODO.md

@@ -1,5 +1,5 @@
 # Working TODO
-- [ ] Wave Constant
+- [x] Wave Constant
 - Bounds
 	- [ ] Boundary Conds
 	- [ ] PML
@@ -18,8 +18,8 @@
 	- [ ] Data File Import
 	- [ ] DataFit Medium
 - Monitors
-	- [ ] EH Field
+	- [x] EH Field
-	- [ ] Power Flux
+	- [x] Power Flux
 	- [ ] Permittivity
 	- [ ] Diffraction
 - Structures
@@ -49,9 +49,9 @@
 - Integration
 	- [ ] Simulation and Analysis of Maxim's Cavity
 - Constants
-	- [ ] Number Constant
+	- [x] Number Constant
-	- [ ] Vector Constant
+	- [x] Vector Constant
-	- [ ] Physical Constant
+	- [x] Physical Constant
 
 - [ ] Fix many problems by persisting `_enum_cb_cache` and `_str_cb_cache`.
 
@@ -70,7 +70,7 @@
 		- [ ] Pol SocketType: 3D Poincare sphere visualization of Stokes vectors.
 
 - [x] Math / Map Math
-	- [ ] Remove "By x" socket set let socket sets only be "Function"/"Expr"; then add a dynamic enum underneath to select "By x" based on data support.
+	- [x] Remove "By x" socket set let socket sets only be "Function"/"Expr"; then add a dynamic enum underneath to select "By x" based on data support.
 	- [ ] Filter the operations based on data support, ex. use positive-definiteness to guide cholesky.
 	- [ ] Implement support for additional symbols via `Expr`.
 - [x] Math / Filter Math
@@ -81,8 +81,6 @@
 
 ## Inputs
 - [x] Wave Constant
-	- [ ] Fix the LazyValueRange (again!)
-	- [ ] Document
 - [x] Scene
 	- [ ] Implement export of scene time via. Blender unit system.
 	- [ ] Implement optional scene-synced time exporting, so that the simulation definition and scene definition match for analysis needs.
@@ -90,14 +88,14 @@
 - [x] Constants / Expr Constant
 	- See IDEAS.
 - [x] Constants / Number Constant
-	- [ ] Fix non-integer sockets
+- [x] Constants / Vector Constant
-- [ ] Constants / Vector Constant
+- [x] Constants / Physical Constant
-- [ ] Constants / Physical Constant
 - [x] Constants / Scientific Constant
 	- [ ] Nicer (boxed?) node information, maybe centered headers, in a box, etc. .
-- [x] Constants / Unit System Constant
+- [ ] Constants / Unit System Constant
+	- [ ] Re-implement with `PhysicalType`.
 	- [ ] Implement presets, including "Tidy3D" and "Blender", shown in the label row.
-- [x] Constants / Blender Constant
+- [ ] Constants / Blender Constant
 	- [ ] Fix it!
 
 - [ ] Web / Tidy3D Web Importer

src/blender_maxwell/assets/geonodes.py

@@ -168,13 +168,13 @@ class GeoNodes(enum.StrEnum):
 			GN.StructurePrimitiveCapsule: GN_INTERNAL_STRUCTURES_PATH,
 			GN.StructurePrimitiveCone: GN_INTERNAL_STRUCTURES_PATH,
 			## Monitor
-			GN.MonitorEHField: GN_INTERNAL_STRUCTURES_PATH,
+			GN.MonitorEHField: GN_INTERNAL_MONITORS_PATH,
-			GN.MonitorPowerFlux: GN_INTERNAL_STRUCTURES_PATH,
+			GN.MonitorPowerFlux: GN_INTERNAL_MONITORS_PATH,
-			GN.MonitorEpsTensor: GN_INTERNAL_STRUCTURES_PATH,
+			GN.MonitorEpsTensor: GN_INTERNAL_MONITORS_PATH,
-			GN.MonitorDiffraction: GN_INTERNAL_STRUCTURES_PATH,
+			GN.MonitorDiffraction: GN_INTERNAL_MONITORS_PATH,
-			GN.MonitorProjCartEHField: GN_INTERNAL_STRUCTURES_PATH,
+			GN.MonitorProjCartEHField: GN_INTERNAL_MONITORS_PATH,
-			GN.MonitorProjAngEHField: GN_INTERNAL_STRUCTURES_PATH,
+			GN.MonitorProjAngEHField: GN_INTERNAL_MONITORS_PATH,
-			GN.MonitorProjKSpaceEHField: GN_INTERNAL_STRUCTURES_PATH,
+			GN.MonitorProjKSpaceEHField: GN_INTERNAL_MONITORS_PATH,
 			## Simulation
 			GN.SimulationSimDomain: GN_INTERNAL_SIMULATIONS_PATH,
 			GN.SimulationBoundConds: GN_INTERNAL_SIMULATIONS_PATH,
@@ -225,7 +225,7 @@ def import_geonodes(
 	if import_method == 'link' and geonodes in bpy.data.node_groups:
 		return bpy.data.node_groups[geonodes]
 
-	filename = geonodes
+	filename = str(geonodes)
 	filepath = str(geonodes.parent_path / (geonodes + '.blend') / 'NodeTree' / geonodes)
 	directory = filepath.removesuffix(geonodes)
 	log.info(

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

@@ -25,58 +25,60 @@ class BLSocketInfo:
 	bl_isocket_identifier: spux.ScalarUnitlessRealExpr
 
 
-@blender_type_enum.prefix_values_with('NodeSocket')
 class BLSocketType(enum.StrEnum):
-	Virtual = 'Virtual'
+	Virtual = 'NodeSocketVirtual'
 	# Blender
-	Image = 'Image'
+	Image = 'NodeSocketImage'
-	Shader = 'Shader'
+	Shader = 'NodeSocketShader'
-	Material = 'Material'
+	Material = 'NodeSocketMaterial'
-	Geometry = 'Material'
+	Geometry = 'NodeSocketGeometry'
-	Object = 'Object'
+	Object = 'NodeSocketObject'
-	Collection = 'Collection'
+	Collection = 'NodeSocketCollection'
 	# Basic
-	Bool = 'Bool'
+	Bool = 'NodeSocketBool'
-	String = 'String'
+	String = 'NodeSocketString'
-	Menu = 'Menu'
+	Menu = 'NodeSocketMenu'
 	# Float
-	Float = 'Float'
+	Float = 'NodeSocketFloat'
-	FloatUnsigned = 'FloatUnsigned'
+	FloatUnsigned = 'NodeSocketFloatUnsigned'
-	FloatAngle = 'FloatAngle'
+	FloatAngle = 'NodeSocketFloatAngle'
-	FloatDistance = 'FloatDistance'
+	FloatDistance = 'NodeSocketFloatDistance'
-	FloatFactor = 'FloatFactor'
+	FloatFactor = 'NodeSocketFloatFactor'
-	FloatPercentage = 'FloatPercentage'
+	FloatPercentage = 'NodeSocketFloatPercentage'
-	FloatTime = 'FloatTime'
+	FloatTime = 'NodeSocketFloatTime'
-	FloatTimeAbsolute = 'FloatTimeAbsolute'
+	FloatTimeAbsolute = 'NodeSocketFloatTimeAbsolute'
 	# Int
-	Int = 'Int'
+	Int = 'NodeSocketInt'
-	IntFactor = 'IntFactor'
+	IntFactor = 'NodeSocketIntFactor'
-	IntPercentage = 'IntPercentage'
+	IntPercentage = 'NodeSocketIntPercentage'
-	IntUnsigned = 'IntUnsigned'
+	IntUnsigned = 'NodeSocketIntUnsigned'
 	# Vector
-	Color = 'Color'
+	Color = 'NodeSocketColor'
-	Rotation = 'Rotation'
+	Rotation = 'NodeSocketRotation'
-	Vector = 'Vector'
+	Vector = 'NodeSocketVector'
-	VectorAcceleration = 'Acceleration'
+	VectorAcceleration = 'NodeSocketAcceleration'
-	VectorDirection = 'Direction'
+	VectorDirection = 'NodeSocketDirection'
-	VectorEuler = 'Euler'
+	VectorEuler = 'NodeSocketEuler'
-	VectorTranslation = 'Translation'
+	VectorTranslation = 'NodeSocketTranslation'
-	VectorVelocity = 'Velocity'
+	VectorVelocity = 'NodeSocketVelocity'
-	VectorXYZ = 'XYZ'
+	VectorXYZ = 'NodeSocketXYZ'
 
 	@staticmethod
 	def from_bl_isocket(
 		bl_isocket: bpy.types.NodeTreeInterfaceSocket,
 	) -> typ.Self:
-		return BLSocketType[bl_isocket.bl_socket_idname]
+		return BLSocketType(bl_isocket.bl_socket_idname)
 
 	@staticmethod
 	def info_from_bl_isocket(
 		bl_isocket: bpy.types.NodeTreeInterfaceSocket,
 	) -> typ.Self:
-		return BLSocketType.from_bl_isocket(bl_isocket).parse(
+		bl_socket_type = BLSocketType.from_bl_isocket(bl_isocket)
+		if bl_socket_type.has_support:
+			return bl_socket_type.parse(
 				bl_isocket.default_value, bl_isocket.description, bl_isocket.identifier
 			)
+		return bl_socket_type.parse(None, bl_isocket.description, bl_isocket.identifier)
 
 	####################
 	# - Direct Properties
@@ -288,7 +290,7 @@ class BLSocketType(enum.StrEnum):
 		)
 
 		# Parse the Default Value
-		if self.mathtype is not None:
+		if self.mathtype is not None and bl_default_value is not None:
 			if self.size == spux.NumberSize1D.Scalar:
 				default_value = self.mathtype.pytype(bl_default_value)
 			elif description.startswith('2D'):

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

@@ -57,19 +57,22 @@ class FlowKind(enum.StrEnum):
 	Info = enum.auto()
 
 	@classmethod
-	def scale_to_unit_system(cls, kind: typ.Self, value, socket_type, unit_system):
+	def scale_to_unit_system(
-		if kind == cls.Value:
+		cls,
-			return spux.sympy_to_python(
+		kind: typ.Self,
-				spux.scale_to_unit(
 		value,
-					unit_system[socket_type],
+		unit_system: spux.UnitSystem,
-				)
+	):
+		if kind == cls.Value:
+			return spux.scale_to_unit_system(
+				value,
+				unit_system,
 			)
 		if kind == cls.LazyArrayRange:
-			return value.rescale_to_unit(unit_system[socket_type])
+			return value.rescale_to_unit_system(unit_system)
 
 		if kind == cls.Params:
-			return value.rescale_to_unit(unit_system[socket_type])
+			return value.rescale_to_unit_system(unit_system)
 
 		msg = 'Tried to scale unknown kind'
 		raise ValueError(msg)
@@ -187,6 +190,9 @@ class ArrayFlow:
 		msg = f'Tried to rescale unitless LazyDataValueRange to unit {unit}'
 		raise ValueError(msg)
 
+	def rescale_to_unit_system(self, unit: spu.Quantity) -> typ.Self:
+		raise NotImplementedError
+
 
 ####################
 # - Lazy Value Func
@@ -469,14 +475,13 @@ class LazyArrayRangeFlow:
 
 		# Get Stop Mathtype
 		if isinstance(self.stop, spux.SympyType):
-			stop_mathtype = spux.MathType.from_expr(type(self.stop))
+			stop_mathtype = spux.MathType.from_expr(self.stop)
 		else:
-			stop_mathtype = spux.MathType.from_pytype(type(self.stop))
+			stop_mathtype = spux.MathType.from_pytype(self.stop)
 
 		# Check Equal
 		if start_mathtype != stop_mathtype:
-			msg = "Mathtypes of start and stop don't agree. Please fix!"
+			return spux.MathType.combine(start_mathtype, stop_mathtype)
-			raise ValueError(msg)
 
 		return start_mathtype
 
@@ -525,8 +530,8 @@ class LazyArrayRangeFlow:
 		"""
 		if self.unit is not None:
 			return LazyArrayRangeFlow(
-				start=spu.scale_to_unit(self.start * self.unit, unit),
+				start=spux.scale_to_unit(self.start * self.unit, unit),
-				stop=spu.scale_to_unit(self.stop * self.unit, unit),
+				stop=spux.scale_to_unit(self.stop * self.unit, unit),
 				steps=self.steps,
 				scaling=self.scaling,
 				unit=unit,
@@ -536,6 +541,39 @@ class LazyArrayRangeFlow:
 		msg = f'Tried to rescale unitless LazyDataValueRange to unit {unit}'
 		raise ValueError(msg)
 
+	def rescale_to_unit_system(self, unit_system: spux.Unit) -> typ.Self:
+		"""Replaces the units, **with** rescaling of the bounds.
+
+		Parameters:
+			unit: The unit to convert the bounds to.
+
+		Returns:
+			A new `LazyArrayRangeFlow` with replaced unit.
+
+		Raises:
+			ValueError: If the existing unit is `None`, indicating that there is no unit to correct.
+		"""
+		if self.unit is not None:
+			return LazyArrayRangeFlow(
+				start=spux.strip_unit_system(
+					spux.convert_to_unit_system(self.start * self.unit, unit_system),
+					unit_system,
+				),
+				stop=spux.strip_unit_system(
+					spux.convert_to_unit_system(self.start * self.unit, unit_system),
+					unit_system,
+				),
+				steps=self.steps,
+				scaling=self.scaling,
+				unit=unit_system[spux.PhysicalType.from_unit(self.unit)],
+				symbols=self.symbols,
+			)
+
+		msg = (
+			f'Tried to rescale unitless LazyDataValueRange to unit system {unit_system}'
+		)
+		raise ValueError(msg)
+
 	####################
 	# - Bound Operations
 	####################

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

@@ -16,6 +16,7 @@ class FlowSignal(enum.StrEnum):
 
 	"""
 
+	FlowInitializing = enum.auto()
 	FlowPending = enum.auto()
 	NoFlow = enum.auto()
 

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

@@ -110,26 +110,23 @@ class ManagedBLMesh(base.ManagedObj):
 
 		If it's already included, do nothing.
 		"""
-		if (bl_object := bpy.data.objects.get(self.name)) is not None:
+		bl_object = bpy.data.objects.get(self.name)
+		if bl_object is None:
+			bl_object = self.bl_object()
+
 		if bl_object.name not in preview_collection().objects:
 			log.info('Moving "%s" to Preview Collection', bl_object.name)
 			preview_collection().objects.link(bl_object)
-		else:
-			msg = 'Managed BLMesh does not exist'
-			raise ValueError(msg)
 
 	def hide_preview(self) -> None:
 		"""Removes the managed Blender object from the preview collection.
 
 		If it's already removed, do nothing.
 		"""
-		if (bl_object := bpy.data.objects.get(self.name)) is not None:
+		bl_object = bpy.data.objects.get(self.name)
-			if bl_object.name in preview_collection().objects:
+		if bl_object is not None and bl_object.name in preview_collection().objects:
 			log.info('Removing "%s" from Preview Collection', bl_object.name)
 			preview_collection().objects.unlink(bl_object)
-		else:
-			msg = 'Managed BLMesh does not exist'
-			raise ValueError(msg)
 
 	def bl_select(self) -> None:
 		"""Selects the managed Blender object, causing it to be ex. outlined in the 3D viewport."""

src/blender_maxwell/node_trees/maxwell_sim_nodes/node_tree.py

@@ -206,6 +206,8 @@ class MaxwellSimTree(bpy.types.NodeTree):
 		"""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
@@ -229,7 +231,9 @@ class MaxwellSimTree(bpy.types.NodeTree):
 	@contextlib.contextmanager
 	def repreview_all(self) -> None:
 		all_nodes_with_preview_active = {
-			node.instance_id: node for node in self.nodes if node.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 = {}

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

@@ -1,40 +1,37 @@
-# from . import kitchen_sink
-# from . import bounds
 from . import (
 	analysis,
+	# bounds,
 	inputs,
-	mediums,
+	# mediums,
 	monitors,
 	outputs,
-	simulations,
+	# simulations,
-	sources,
+	# sources,
-	structures,
+	# structures,
-	utilities,
+	# utilities,
 )
 
 BL_REGISTER = [
-	# *kitchen_sink.BL_REGISTER,
 	*analysis.BL_REGISTER,
 	*inputs.BL_REGISTER,
 	*outputs.BL_REGISTER,
-	*sources.BL_REGISTER,
+	# *sources.BL_REGISTER,
-	*mediums.BL_REGISTER,
+	# *mediums.BL_REGISTER,
-	*structures.BL_REGISTER,
+	# *structures.BL_REGISTER,
 	# *bounds.BL_REGISTER,
 	*monitors.BL_REGISTER,
-	*simulations.BL_REGISTER,
+	# *simulations.BL_REGISTER,
-	*utilities.BL_REGISTER,
+	# *utilities.BL_REGISTER,
 ]
 BL_NODES = {
-	# **kitchen_sink.BL_NODES,
 	**analysis.BL_NODES,
 	**inputs.BL_NODES,
 	**outputs.BL_NODES,
-	**sources.BL_NODES,
+	# **sources.BL_NODES,
-	**mediums.BL_NODES,
+	# **mediums.BL_NODES,
-	**structures.BL_NODES,
+	# **structures.BL_NODES,
 	# **bounds.BL_NODES,
 	**monitors.BL_NODES,
-	**simulations.BL_NODES,
+	# **simulations.BL_NODES,
-	**utilities.BL_NODES,
+	# **utilities.BL_NODES,
 }

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

@@ -401,7 +401,7 @@ class MapMathNode(base.MaxwellSimNode):
 		run_on_init=True,
 	)
 	def on_input_changed(self):
-		if self.operation not in MapOperation.by_element_shape(self.expr_output_shape):
+		# if self.operation not in MapOperation.by_element_shape(self.expr_output_shape):
 		self.operation = bl_cache.Signal.ResetEnumItems
 
 	@events.on_value_changed(

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

@@ -20,6 +20,10 @@ FUNCS = {
 	'MUL': lambda exprs: exprs[0] * exprs[1],
 	'DIV': lambda exprs: exprs[0] / exprs[1],
 	'POW': lambda exprs: exprs[0] ** exprs[1],
+	'ATAN2': lambda exprs: sp.atan2(exprs[1], exprs[0]),
+	# Vector | Vector
+	'VEC_VEC_DOT': lambda exprs: exprs[0].dot(exprs[1]),
+	'CROSS': lambda exprs: exprs[0].cross(exprs[1]),
 }
 
 SP_FUNCS = FUNCS
@@ -52,8 +56,8 @@ class OperateMathNode(base.MaxwellSimNode):
 	bl_label = 'Operate Math'
 
 	input_sockets: typ.ClassVar = {
-		'Expr L': sockets.ExprSocketDef(show_info_columns=False),
+		'Expr L': sockets.ExprSocketDef(),
-		'Expr R': sockets.ExprSocketDef(show_info_columns=False),
+		'Expr R': sockets.ExprSocketDef(),
 	}
 	output_sockets: typ.ClassVar = {
 		'Expr': sockets.ExprSocketDef(),
@@ -73,10 +77,12 @@ class OperateMathNode(base.MaxwellSimNode):
 	def search_categories(self) -> list[ct.BLEnumElement]:
 		"""Deduce and return a list of valid categories for the current socket set and input data."""
 		expr_l_info = self._compute_input(
-			'Expr L', kind=ct.FlowKind.Info, optional=True
+			'Expr L',
+			kind=ct.FlowKind.Info,
 		)
 		expr_r_info = self._compute_input(
-			'Expr R', kind=ct.FlowKind.Info, optional=True
+			'Expr R',
+			kind=ct.FlowKind.Info,
 		)
 
 		has_expr_l_info = not ct.FlowSignal.check(expr_l_info)
@@ -121,6 +127,10 @@ class OperateMathNode(base.MaxwellSimNode):
 			if expr_l_info.output_shape is None and expr_r_info.output_shape is None:
 				categories = [NUMBER_NUMBER]
 
+			## * | Number
+			elif expr_r_info.output_shape is None:
+				categories = []
+
 			## Number | Vector
 			elif (
 				expr_l_info.output_shape is None and len(expr_r_info.output_shape) == 1
@@ -170,13 +180,12 @@ class OperateMathNode(base.MaxwellSimNode):
 				('POW', 'L^R', 'Power'),
 				('ATAN2', 'atan2(L,R)', 'atan2(L,R)'),
 			]
-		if self.category in 'Vector | Vector':
+		if self.category == 'Vector | Vector':
 			if items:
 				items += [None]
 			items += [
 				('VEC_VEC_DOT', 'L · R', 'Vector-Vector Product'),
 				('CROSS', 'L x R', 'Cross Product'),
-				('PROJ', 'proj(L, R)', 'Projection'),
 			]
 		if self.category == 'Matrix | Vector':
 			if items:
@@ -364,9 +373,7 @@ class OperateMathNode(base.MaxwellSimNode):
 			'Expr R': ct.FlowKind.Params,
 		},
 	)
-	def compute_params(
+	def compute_params(self, props, input_sockets) -> ct.ParamsFlow | ct.FlowSignal:
-		self, props, input_sockets
-	) -> ct.ParamsFlow | ct.FlowSignal:
 		operation = props['operation']
 		params_l = input_sockets['Expr L']
 		params_r = input_sockets['Expr R']

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

@@ -2,8 +2,11 @@ import enum
 import typing as typ
 
 import bpy
+import jax
+import jax.numpy as jnp
 import jaxtyping as jtyp
 import matplotlib.axis as mpl_ax
+import sympy as sp
 
 from blender_maxwell.utils import bl_cache, image_ops, logger
 from blender_maxwell.utils import extra_sympy_units as spux
@@ -192,7 +195,10 @@ class VizNode(base.MaxwellSimNode):
 	# - Sockets
 	####################
 	input_sockets: typ.ClassVar = {
-		'Expr': sockets.ExprSocketDef(),
+		'Expr': sockets.ExprSocketDef(
+			symbols={_x := sp.Symbol('x', real=True)},
+			default_value=2 * _x,
+		),
 	}
 	output_sockets: typ.ClassVar = {
 		'Preview': sockets.AnySocketDef(),
@@ -221,8 +227,12 @@ class VizNode(base.MaxwellSimNode):
 	## - Mode Searcher
 	#####################
 	@property
-	def data_info(self) -> ct.InfoFlow:
+	def data_info(self) -> ct.InfoFlow | None:
-		return self._compute_input('Expr', kind=ct.FlowKind.Info)
+		info = self._compute_input('Expr', kind=ct.FlowKind.Info)
+		if not ct.FlowSignal.check(info):
+			return info
+
+		return None
 
 	def search_modes(self) -> list[ct.BLEnumElement]:
 		if not ct.FlowSignal.check(self.data_info):
@@ -298,7 +308,9 @@ class VizNode(base.MaxwellSimNode):
 		managed_objs={'plot'},
 		props={'viz_mode', 'viz_target', 'colormap'},
 		input_sockets={'Expr'},
-		input_socket_kinds={'Expr': {ct.FlowKind.Array, ct.FlowKind.Info}},
+		input_socket_kinds={
+			'Expr': {ct.FlowKind.Array, ct.FlowKind.LazyValueFunc, ct.FlowKind.Info}
+		},
 		stop_propagation=True,
 	)
 	def on_show_plot(

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

@@ -599,22 +599,28 @@ class MaxwellSimNode(bpy.types.Node):
 				It must be currently active.
 			kind: The data flow kind to compute.
 		"""
-		if (bl_socket := self.inputs.get(input_socket_name)) is not None:
+		bl_socket = self.inputs.get(input_socket_name)
+		if bl_socket is not None:
+			if bl_socket.instance_id:
 				return (
 					ct.FlowKind.scale_to_unit_system(
 						kind,
 						bl_socket.compute_data(kind=kind),
-					bl_socket.socket_type,
 						unit_system,
 					)
 					if unit_system is not None
 					else bl_socket.compute_data(kind=kind)
 				)
 
+			# No Socket Instance ID
+			## -> Indicates that socket_def.preinit() has not yet run.
+			## -> Anyone needing results will need to wait on preinit().
+			return ct.FlowSignal.FlowInitializing
+
 		if optional:
 			return ct.FlowSignal.NoFlow
 
-		msg = f'Input socket "{input_socket_name}" on "{self.bl_idname}" is not an active input socket'
+		msg = f'{self.sim_node_name}: Input socket "{input_socket_name}" cannot be computed, as it is not an active input socket'
 		raise ValueError(msg)
 
 	####################

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

@@ -3,6 +3,7 @@ import inspect
 import typing as typ
 from types import MappingProxyType
 
+from blender_maxwell.utils import extra_sympy_units as spux
 from blender_maxwell.utils import logger
 
 from .. import contracts as ct
@@ -10,7 +11,6 @@ from .. import contracts as ct
 log = logger.get(__name__)
 
 UnitSystemID = str
-UnitSystem = dict[ct.SocketType, typ.Any]
 
 
 ####################
@@ -70,7 +70,7 @@ def event_decorator(
 	all_loose_input_sockets: bool = False,
 	all_loose_output_sockets: bool = False,
 	# Request Unit System Scaling
-	unit_systems: dict[UnitSystemID, UnitSystem] = MappingProxyType({}),
+	unit_systems: dict[UnitSystemID, spux.UnitSystem] = MappingProxyType({}),
 	scale_input_sockets: dict[ct.SocketName, UnitSystemID] = MappingProxyType({}),
 	scale_output_sockets: dict[ct.SocketName, UnitSystemID] = MappingProxyType({}),
 ):
@@ -213,7 +213,6 @@ def event_decorator(
 						kind=kind,
 						optional=output_sockets_optional.get(output_socket_name, False),
 					),
-					node.outputs[output_socket_name].socket_type,
 					unit_systems.get(scale_output_sockets.get(output_socket_name)),
 				)
 
@@ -269,9 +268,21 @@ def event_decorator(
 				else {}
 			)
 
+			# Propagate Initialization
+			## If there is a FlowInitializing, then the method would fail.
+			## Therefore, propagate FlowInitializing if found.
+			if any(
+				ct.FlowSignal.FlowInitializing in sockets.values()
+				for sockets in [
+					method_kw_args.get('input_sockets', {}),
+					method_kw_args.get('loose_input_sockets', {}),
+					method_kw_args.get('output_sockets', {}),
+					method_kw_args.get('loose_output_sockets', {}),
+				]
+			):
+				return ct.FlowSignal.FlowInitializing
+
 			# Call Method
-			## If there is a FlowPending, then the method would fail.
-			## Therefore, propagate FlowPending if found.
 			return method(
 				node,
 				**method_kw_args,

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

@@ -1,18 +1,22 @@
-# from . import scientific_constant
+from . import (
-# from . import physical_constant
+    blender_constant,
-from . import blender_constant, expr_constant, number_constant, scientific_constant
+    expr_constant,
+    number_constant,
+    physical_constant,
+    scientific_constant,
+)
 
 BL_REGISTER = [
 	*expr_constant.BL_REGISTER,
 	*scientific_constant.BL_REGISTER,
 	*number_constant.BL_REGISTER,
-	# *physical_constant.BL_REGISTER,
+	*physical_constant.BL_REGISTER,
 	*blender_constant.BL_REGISTER,
 ]
 BL_NODES = {
 	**expr_constant.BL_NODES,
 	**scientific_constant.BL_NODES,
 	**number_constant.BL_NODES,
-	# **physical_constant.BL_NODES,
+	**physical_constant.BL_NODES,
 	**blender_constant.BL_NODES,
 }

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

@@ -44,7 +44,7 @@ class NumberConstantNode(base.MaxwellSimNode):
 	####################
 	# - UI
 	####################
-	def draw_value(self, col: bpy.types.UILayout) -> None:
+	def draw_props(self, _, col: bpy.types.UILayout) -> None:
 		row = col.row(align=True)
 		row.prop(self, self.blfields['mathtype'], text='')
 		row.prop(self, self.blfields['size'], text='')
@@ -56,7 +56,7 @@ class NumberConstantNode(base.MaxwellSimNode):
 	def on_mathtype_size_changed(self, props) -> None:
 		"""Change the input/output expression sockets to match the mathtype declared in the node."""
 		self.inputs['Value'].mathtype = props['mathtype']
-		self.inputs['Value'].shape = props['mathtype'].shape
+		self.inputs['Value'].shape = props['size'].shape
 
 	####################
 	# - FlowKind

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

@@ -1,6 +1,6 @@
-import enum
 import typing as typ
 
+import bpy
 import sympy as sp
 
 from blender_maxwell.utils import bl_cache
@@ -10,7 +10,7 @@ from .... import contracts, sockets
 from ... import base, events
 
 
-class PhysicalConstantNode(base.MaxwellSimTreeNode):
+class PhysicalConstantNode(base.MaxwellSimNode):
 	"""A number of configurable unit dimension, ex. time, length, etc. .
 
 	Attributes:
@@ -36,12 +36,12 @@ class PhysicalConstantNode(base.MaxwellSimTreeNode):
 		prop_ui=True,
 	)
 
-	mathtype: enum.Enum = bl_cache.BLField(
+	mathtype: spux.MathType = bl_cache.BLField(
 		enum_cb=lambda self, _: self.search_mathtypes(),
 		prop_ui=True,
 	)
 
-	size: enum.Enum = bl_cache.BLField(
+	size: spux.NumberSize1D = bl_cache.BLField(
 		enum_cb=lambda self, _: self.search_sizes(),
 		prop_ui=True,
 	)
@@ -62,16 +62,25 @@ class PhysicalConstantNode(base.MaxwellSimTreeNode):
 			if spux.NumberSize1D.supports_shape(shape)
 		]
 
+	####################
+	# - UI
+	####################
+	def draw_props(self, _, col: bpy.types.UILayout) -> None:
+		row = col.row(align=True)
+		row.prop(self, self.blfields['mathtype'], text='')
+		row.prop(self, self.blfields['size'], text='')
+
 	####################
 	# - Events
 	####################
 	@events.on_value_changed(
 		prop_name={'physical_type', 'mathtype', 'size'},
+		run_on_init=True,
 		props={'physical_type', 'mathtype', 'size'},
 	)
 	def on_mathtype_or_size_changed(self, props) -> None:
 		"""Change the input/output expression sockets to match the mathtype and size declared in the node."""
-		shape = spux.NumberSize1D(props['size']).shape
+		shape = props['size'].shape
 
 		# Set Input Socket Physical Type
 		if self.inputs['Value'].physical_type != props['physical_type']:
@@ -90,9 +99,9 @@ class PhysicalConstantNode(base.MaxwellSimTreeNode):
 	####################
 	# - Callbacks
 	####################
-	@events.computes_output_socket('value')
+	@events.computes_output_socket('Value', input_sockets={'Value'})
-	def compute_value(self: contracts.NodeTypeProtocol) -> sp.Expr:
+	def compute_value(self, input_sockets) -> sp.Expr:
-		return self.compute_input('value')
+		return input_sockets['Value']
 
 
 ####################

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

@@ -2,7 +2,7 @@ import typing as typ
 
 import bpy
 
-from blender_maxwell.utils import sci_constants as constants
+from blender_maxwell.utils import bl_cache, sci_constants
 
 from .... import contracts as ct
 from .... import sockets
@@ -20,63 +20,43 @@ class ScientificConstantNode(base.MaxwellSimNode):
 	####################
 	# - Properties
 	####################
-	sci_constant: bpy.props.StringProperty(
+	sci_constant: str = bl_cache.BLField(
-		name='Sci Constant',
+		'',
-		description='The name of a scientific constant',
+		prop_ui=True,
-		default='',
+		str_cb=lambda self, _, edit_text: self.search_sci_constants(edit_text),
-		search=lambda self, _, edit_text: self.search_sci_constants(edit_text),
-		update=lambda self, context: self.on_update_sci_constant(context),
 	)
 
-	cache__units: bpy.props.StringProperty(default='')
-	cache__uncertainty: bpy.props.StringProperty(default='')
-
 	def search_sci_constants(
 		self,
 		edit_text: str,
 	):
 		return [
 			name
-			for name in constants.SCI_CONSTANTS
+			for name in sci_constants.SCI_CONSTANTS
 			if edit_text.lower() in name.lower()
 		]
 
-	def on_update_sci_constant(
-		self,
-		context: bpy.types.Context,
-	):
-		if self.sci_constant:
-			self.cache__units = str(
-				constants.SCI_CONSTANTS_INFO[self.sci_constant]['units']
-			)
-			self.cache__uncertainty = str(
-				constants.SCI_CONSTANTS_INFO[self.sci_constant]['uncertainty']
-			)
-		else:
-			self.cache__units = ''
-			self.cache__uncertainty = ''
-
-		self.on_prop_changed('sci_constant', context)
-
 	####################
 	# - UI
 	####################
 	def draw_props(self, _: bpy.types.Context, col: bpy.types.UILayout) -> None:
-		col.prop(self, 'sci_constant', text='')
+		col.prop(self, self.blfields['sci_constant'], text='')
 
 	def draw_info(self, _: bpy.types.Context, col: bpy.types.UILayout) -> None:
 		if self.sci_constant:
-			col.label(text=f'Units: {self.cache__units}')
+			col.label(
-			col.label(text=f'Uncertainty: {self.cache__uncertainty}')
+				text=f'Units: {sci_constants.SCI_CONSTANTS_INFO[self.sci_constant]["units"]}'
-
+			)
-		col.label(text=f'Ref: {constants.SCI_CONSTANTS_REF[0]}')
+			col.label(
+				text=f'Uncertainty: {sci_constants.SCI_CONSTANTS_INFO[self.sci_constant]["uncertainty"]}'
+			)
 
 	####################
-	# - Callbacks
+	# - Output
 	####################
 	@events.computes_output_socket('Value', props={'sci_constant'})
 	def compute_value(self, props: dict) -> typ.Any:
-		return constants.SCI_CONSTANTS[props['sci_constant']]
+		return sci_constants.SCI_CONSTANTS[props['sci_constant']]
 
 
 ####################

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/wave_constant.py

@@ -33,6 +33,7 @@ class WaveConstantNode(base.MaxwellSimNode):
 	input_socket_sets: typ.ClassVar = {
 		'Wavelength': {
 			'WL': sockets.ExprSocketDef(
+				active_kind=ct.FlowKind.Value,
 				physical_type=spux.PhysicalType.Length,
 				# Defaults
 				default_unit=spu.nm,
@@ -58,18 +59,18 @@ class WaveConstantNode(base.MaxwellSimNode):
 	output_sockets: typ.ClassVar = {
 		'WL': sockets.ExprSocketDef(
 			active_kind=ct.FlowKind.Value,
-			unit_dimension=spux.Dims.length,
+			physical_type=spux.PhysicalType.Length,
 		),
 		'Freq': sockets.ExprSocketDef(
 			active_kind=ct.FlowKind.Value,
-			unit_dimension=spux.Dims.frequency,
+			physical_type=spux.PhysicalType.Freq,
 		),
 	}
 
 	####################
 	# - Properties
 	####################
-	use_range: bool = bl_cache.BLField(False)
+	use_range: bool = bl_cache.BLField(False, prop_ui=True)
 
 	####################
 	# - UI
@@ -80,14 +81,14 @@ class WaveConstantNode(base.MaxwellSimNode):
 		Parameters:
 			col: Target for defining UI elements.
 		"""
-		col.prop(self, self.blfields['use_range'], toggle=True)
+		col.prop(self, self.blfields['use_range'], toggle=True, text='Range')
 
 	####################
 	# - Events
 	####################
 	@events.on_value_changed(
 		prop_name={'active_socket_set', 'use_range'},
-		props='use_range',
+		props={'use_range'},
 		run_on_init=True,
 	)
 	def on_use_range_changed(self, props: dict) -> None:
@@ -128,7 +129,8 @@ class WaveConstantNode(base.MaxwellSimNode):
 	)
 	def compute_wl_value(self, input_sockets: dict) -> sp.Expr:
 		"""Compute a single wavelength value from either wavelength/frequency."""
-		if input_sockets['WL'] is not None:
+		has_wl = not ct.FlowSignal.check(input_sockets['WL'])
+		if has_wl:
 			return input_sockets['WL']
 
 		return sci_constants.vac_speed_of_light / input_sockets['Freq']
@@ -141,7 +143,8 @@ class WaveConstantNode(base.MaxwellSimNode):
 	)
 	def compute_freq_value(self, input_sockets: dict) -> sp.Expr:
 		"""Compute a single frequency value from either wavelength/frequency."""
-		if input_sockets['Freq'] is not None:
+		has_freq = not ct.FlowSignal.check(input_sockets['Freq'])
+		if has_freq:
 			return input_sockets['Freq']
 
 		return sci_constants.vac_speed_of_light / input_sockets['WL']
@@ -158,11 +161,20 @@ class WaveConstantNode(base.MaxwellSimNode):
 	)
 	def compute_wl_range(self, input_sockets: dict) -> sp.Expr:
 		"""Compute wavelength range from either wavelength/frequency ranges."""
-		if input_sockets['WL'] is not None:
+		has_wl = not ct.FlowSignal.check(input_sockets['WL'])
+		if has_wl:
 			return input_sockets['WL']
 
-		return input_sockets['Freq'].rescale_bounds(
+		freq = input_sockets['Freq']
-			lambda bound: sci_constants.vac_speed_of_light / bound, reverse=True
+		return ct.LazyArrayRangeFlow(
+			start=spux.scale_to_unit(
+				sci_constants.vac_speed_of_light / (freq.stop * freq.unit), spu.um
+			),
+			stop=spux.scale_to_unit(
+				sci_constants.vac_speed_of_light / (freq.start * freq.unit), spu.um
+			),
+			steps=freq.steps,
+			unit=spu.um,
 		)
 
 	@events.computes_output_socket(
@@ -177,11 +189,20 @@ class WaveConstantNode(base.MaxwellSimNode):
 	)
 	def compute_freq_range(self, input_sockets: dict) -> sp.Expr:
 		"""Compute frequency range from either wavelength/frequency ranges."""
-		if input_sockets['Freq'] is not None:
+		has_freq = not ct.FlowSignal.check(input_sockets['Freq'])
+		if has_freq:
 			return input_sockets['Freq']
 
-		return input_sockets['WL'].rescale_bounds(
+		wl = input_sockets['WL']
-			lambda bound: sci_constants.vac_speed_of_light / bound, reverse=True
+		return ct.LazyArrayRangeFlow(
+			start=spux.scale_to_unit(
+				sci_constants.vac_speed_of_light / (wl.stop * wl.unit), spux.THz
+			),
+			stop=spux.scale_to_unit(
+				sci_constants.vac_speed_of_light / (wl.start * wl.unit), spux.THz
+			),
+			steps=wl.steps,
+			unit=spux.THz,
 		)
 
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/inputs/web_importers/tidy_3d_web_importer.py

@@ -35,7 +35,7 @@ class LoadCloudSim(bpy.types.Operator):
 		node = context.node
 
 		# Try Loading Simulation Data
-		node.sim_data = bl_cache.Signal.InvalidateCache
+		#node.sim_data = bl_cache.Signal.InvalidateCache
 		sim_data = node.sim_data
 		if sim_data is None:
 			self.report(
@@ -70,18 +70,26 @@ class Tidy3DWebImporterNode(base.MaxwellSimNode):
 			should_exist=True,
 		),
 	}
+	output_sockets: typ.ClassVar = {
+		'Sim Data': sockets.MaxwellFDTDSimDataSocketDef(),
+	}
 
+	####################
+	# - Properties
+	####################
 	sim_data_loaded: bool = bl_cache.BLField(False)
 
-	@bl_cache.cached_bl_property()
+	####################
+	# - Computed
+	####################
+	@property
 	def sim_data(self) -> td.SimulationData | None:
 		cloud_task = self._compute_input(
 			'Cloud Task', kind=ct.FlowKind.Value, optional=True
 		)
+		has_cloud_task = not ct.FlowSignal.check(cloud_task)
 		if (
-			# Check Flow
+			has_cloud_task
-			not ct.FlowSignal.check(cloud_task)
-			# Check Task
 			and cloud_task is not None
 			and isinstance(cloud_task, tdcloud.CloudTask)
 			and cloud_task.status == 'success'
@@ -97,7 +105,7 @@ class Tidy3DWebImporterNode(base.MaxwellSimNode):
 	####################
 	# - UI
 	####################
-	def draw_operators(self, context, layout):
+	def draw_operators(self, _: bpy.types.Context, layout: bpy.types.UILayout):
 		if self.sim_data_loaded:
 			layout.operator(ct.OperatorType.NodeLoadCloudSim, text='Reload Sim')
 		else:
@@ -106,11 +114,6 @@ class Tidy3DWebImporterNode(base.MaxwellSimNode):
 	####################
 	# - Events
 	####################
-	@events.on_value_changed(socket_name='Cloud Task')
-	def on_cloud_task_changed(self):
-		self.inputs['Cloud Task'].on_cloud_updated()
-		## TODO: Must we babysit sockets like this?
-
 	@events.on_value_changed(
 		prop_name='sim_data_loaded', run_on_init=True, props={'sim_data_loaded'}
 	)

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

@@ -33,6 +33,7 @@ class EHFieldMonitorNode(base.MaxwellSimNode):
 		'Size': sockets.ExprSocketDef(
 			shape=(3,),
 			physical_type=spux.PhysicalType.Length,
+			default_value=sp.Matrix([1, 1, 1]),
 		),
 		'Spatial Subdivs': sockets.ExprSocketDef(
 			shape=(3,),
@@ -124,11 +125,30 @@ class EHFieldMonitorNode(base.MaxwellSimNode):
 	# - Preview
 	####################
 	@events.on_value_changed(
-		socket_name={'Center', 'Size'},
+		# Trigger
 		prop_name='preview_active',
+		# Loaded
+		managed_objs={'mesh'},
 		props={'preview_active'},
 		input_sockets={'Center', 'Size'},
+	)
+	def on_preview_changed(self, managed_objs, props, input_sockets):
+		"""Enables/disables previewing of the GeoNodes-driven mesh, regardless of whether a particular GeoNodes tree is chosen."""
+		mesh = managed_objs['mesh']
+
+		# Push Preview State to Managed Mesh
+		if props['preview_active']:
+			mesh.show_preview()
+		else:
+			mesh.hide_preview()
+
+	@events.on_value_changed(
+		# Trigger
+		socket_name={'Center', 'Size'},
+		run_on_init=True,
+		# Loaded
 		managed_objs={'mesh', 'modifier'},
+		input_sockets={'Center', 'Size'},
 		unit_systems={'BlenderUnits': ct.UNITS_BLENDER},
 		scale_input_sockets={
 			'Center': 'BlenderUnits',
@@ -136,7 +156,6 @@ class EHFieldMonitorNode(base.MaxwellSimNode):
 	)
 	def on_inputs_changed(
 		self,
-		props: dict,
 		managed_objs: dict,
 		input_sockets: dict,
 		unit_systems: dict,
@@ -153,9 +172,6 @@ class EHFieldMonitorNode(base.MaxwellSimNode):
 				},
 			},
 		)
-		# Push Preview State
-		if props['preview_active']:
-			managed_objs['mesh'].show_preview()
 
 
 ####################

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

@@ -31,6 +31,7 @@ class PowerFluxMonitorNode(base.MaxwellSimNode):
 		'Size': sockets.ExprSocketDef(
 			shape=(3,),
 			physical_type=spux.PhysicalType.Length,
+			default_value=sp.Matrix([1, 1, 1]),
 		),
 		'Samples/Space': sockets.ExprSocketDef(
 			shape=(3,),
@@ -123,11 +124,29 @@ class PowerFluxMonitorNode(base.MaxwellSimNode):
 	# - Preview - Changes to Input Sockets
 	####################
 	@events.on_value_changed(
-		socket_name={'Center', 'Size'},
+		# Trigger
 		prop_name='preview_active',
+		# Loaded
+		managed_objs={'mesh'},
 		props={'preview_active'},
-		input_sockets={'Center', 'Size'},
+	)
+	def on_preview_changed(self, managed_objs, props):
+		"""Enables/disables previewing of the GeoNodes-driven mesh, regardless of whether a particular GeoNodes tree is chosen."""
+		mesh = managed_objs['mesh']
+
+		# Push Preview State to Managed Mesh
+		if props['preview_active']:
+			mesh.show_preview()
+		else:
+			mesh.hide_preview()
+
+	@events.on_value_changed(
+		# Trigger
+		socket_name={'Center', 'Size'},
+		run_on_init=True,
+		# Loaded
 		managed_objs={'mesh', 'modifier'},
+		input_sockets={'Center', 'Size'},
 		unit_systems={'BlenderUnits': ct.UNITS_BLENDER},
 		scale_input_sockets={
 			'Center': 'BlenderUnits',
@@ -135,7 +154,6 @@ class PowerFluxMonitorNode(base.MaxwellSimNode):
 	)
 	def on_inputs_changed(
 		self,
-		props: dict,
 		managed_objs: dict,
 		input_sockets: dict,
 		unit_systems: dict,
@@ -152,9 +170,6 @@ class PowerFluxMonitorNode(base.MaxwellSimNode):
 				},
 			},
 		)
-		# Push Preview State
-		if props['preview_active']:
-			managed_objs['mesh'].show_preview()
 
 
 ####################

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

@@ -1,12 +1,13 @@
-from . import file_exporters, viewer, web_exporters
+#from . import file_exporters, viewer, web_exporters
+from . import viewer
 
 BL_REGISTER = [
 	*viewer.BL_REGISTER,
-	*file_exporters.BL_REGISTER,
+	#*file_exporters.BL_REGISTER,
-	*web_exporters.BL_REGISTER,
+	#*web_exporters.BL_REGISTER,
 ]
 BL_NODES = {
 	**viewer.BL_NODES,
-	**file_exporters.BL_NODES,
+	#**file_exporters.BL_NODES,
-	**web_exporters.BL_NODES,
+	#**web_exporters.BL_NODES,
 }

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

@@ -217,7 +217,7 @@ class MaxwellSimSocket(bpy.types.NodeSocket):
 			Called by `self.on_prop_changed()` when `self.active_kind` was changed.
 		"""
 		self.display_shape = (
-			'SQUARE' if self.active_kind == ct.FlowKind.LazyValueRange else 'CIRCLE'
+			'SQUARE' if self.active_kind == ct.FlowKind.LazyArrayRange else 'CIRCLE'
 		)  # + ('_DOT' if self.use_units else '')
 		## TODO: Valid Active Kinds should be a subset/subenum(?) of FlowKind
 

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

@@ -2,6 +2,7 @@ import enum
 import typing as typ
 
 import bpy
+import pydantic as pyd
 import sympy as sp
 
 from blender_maxwell.utils import bl_cache, logger
@@ -63,6 +64,7 @@ class InfoDisplayCol(enum.StrEnum):
 class ExprBLSocket(base.MaxwellSimSocket):
 	socket_type = ct.SocketType.Expr
 	bl_label = 'Expr'
+	use_info_draw = True
 
 	####################
 	# - Properties
@@ -70,7 +72,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	shape: tuple[int, ...] | None = bl_cache.BLField(None)
 	mathtype: spux.MathType = bl_cache.BLField(spux.MathType.Real, prop_ui=True)
 	physical_type: spux.PhysicalType | None = bl_cache.BLField(None)
-	symbols: frozenset[spux.Symbol] = bl_cache.BLField(frozenset())
+	symbols: frozenset[sp.Symbol] = bl_cache.BLField(frozenset())
 
 	active_unit: enum.Enum = bl_cache.BLField(
 		None, enum_cb=lambda self, _: self.search_units(), prop_ui=True
@@ -102,7 +104,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	)
 
 	# UI: LazyArrayRange
-	steps: int = bl_cache.BLField(2, abs_min=2)
+	steps: int = bl_cache.BLField(2, abs_min=2, prop_ui=True)
 	## Expression
 	raw_min_spstr: str = bl_cache.BLField('', prop_ui=True)
 	raw_max_spstr: str = bl_cache.BLField('', prop_ui=True)
@@ -125,6 +127,15 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Computed: Raw Expressions
 	####################
+	@property
+	def sorted_symbols(self) -> list[sp.Symbol]:
+		"""Retrieves all symbols and sorts them by name.
+
+		Returns:
+			Repeateably ordered list of symbols.
+		"""
+		return sorted(self.symbols, key=lambda sym: sym.name)
+
 	@property
 	def raw_value_sp(self) -> spux.SympyExpr:
 		return self._parse_expr_str(self.raw_value_spstr)
@@ -140,7 +151,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	####################
 	# - Computed: Units
 	####################
-	def search_units(self, _: bpy.types.Context) -> list[ct.BLEnumElement]:
+	def search_units(self) -> list[ct.BLEnumElement]:
 		if self.physical_type is not None:
 			return [
 				(sp.sstr(unit), spux.sp_to_str(unit), sp.sstr(unit), '', i)
@@ -163,33 +174,38 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		return None
 
 	@unit.setter
-	def unit(self, unit: spux.Unit) -> None:
+	def unit(self, unit: spux.Unit | None) -> None:
 		"""Set the unit, without touching the `raw_*` UI properties.
 
 		Notes:
 			To set a new unit, **and** convert the `raw_*` UI properties to the new unit, use `self.convert_unit()` instead.
 		"""
+		if self.physical_type is not None:
 			if unit in self.physical_type.valid_units:
 				self.active_unit = sp.sstr(unit)
-
+			else:
 				msg = f'Tried to set invalid unit {unit} (physical type "{self.physical_type}" only supports "{self.physical_type.valid_units}")'
 				raise ValueError(msg)
+		elif unit is not None:
+			msg = f'Tried to set invalid unit {unit} (physical type is {self.physical_type}, and has no unit support!)")'
+			raise ValueError(msg)
 
 	def convert_unit(self, unit_to: spux.Unit) -> None:
-		if self.active_kind == ct.FlowKind.Value:
 		current_value = self.value
-			self.unit = unit_to
-			self.value = current_value
-		elif self.active_kind == ct.FlowKind.LazyArrayRange:
 		current_lazy_array_range = self.lazy_array_range
-			self.unit = unit_to
+
+		self.unit = bl_cache.Signal.InvalidateCache
+
+		self.value = current_value
 		self.lazy_array_range = current_lazy_array_range
 
 	####################
 	# - Property Callback
 	####################
 	def on_socket_prop_changed(self, prop_name: str) -> None:
-		if prop_name == 'unit' and self.active_unit is not None:
+		if prop_name == 'physical_type':
+			self.active_unit = bl_cache.Signal.ResetEnumItems
+		if prop_name == 'active_unit' and self.active_unit is not None:
 			self.convert_unit(spux.unit_str_to_unit(self.active_unit))
 
 	####################
@@ -200,23 +216,23 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	) -> tuple[spux.MathType, tuple[int, ...] | None, spux.UnitDimension]:
 		# Parse MathType
 		mathtype = spux.MathType.from_expr(expr)
-		if self.mathtype != mathtype:
+		if not self.mathtype.is_compatible(mathtype):
 			msg = f'MathType is {self.mathtype}, but tried to set expr {expr} with mathtype {mathtype}'
 			raise ValueError(msg)
 
 		# Parse Symbols
-		if expr.free_symbols:
+		if expr.free_symbols and not expr.free_symbols.issubset(self.symbols):
-			if self.mathtype is not None:
-				msg = f'MathType is {self.mathtype}, but tried to set expr {expr} with free symbols {expr.free_symbols}'
-				raise ValueError(msg)
-
-			if not expr.free_symbols.issubset(self.symbols):
 			msg = f'Tried to set expr {expr} with free symbols {expr.free_symbols}, which is incompatible with socket symbols {self.symbols}'
 			raise ValueError(msg)
 
 		# Parse Dimensions
 		shape = spux.parse_shape(expr)
-		if shape != self.shape:
+		if shape != self.shape and not (
+			shape is not None
+			and self.shape is not None
+			and len(self.shape) == 1
+			and 1 in shape
+		):
 			msg = f'Expr {expr} has shape {shape}, which is incompatible with the expr socket (shape {self.shape})'
 			raise ValueError(msg)
 
@@ -238,7 +254,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		# Try Parsing and Returning the Expression
 		try:
 			self._parse_expr_info(expr)
-		except ValueError(expr) as ex:
+		except ValueError:
 			log.exception(
 				'Couldn\'t parse expression "%s" in Expr socket.',
 				expr_spstr,
@@ -270,6 +286,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			expr = self.raw_value_sp
 			if expr is None:
 				return ct.FlowSignal.FlowPending
+			return expr
 
 		MT_Z = spux.MathType.Integer
 		MT_Q = spux.MathType.Rational
@@ -312,7 +329,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		Notes:
 			Called to set the internal `FlowKind.Value` of this socket.
 		"""
-		mathtype, shape = self._parse_expr_info(expr)
+		_mathtype, _shape = self._parse_expr_info(expr)
 		if self.symbols or self.shape not in [None, (2,), (3,)]:
 			self.raw_value_spstr = sp.sstr(expr)
 
@@ -321,32 +338,33 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			MT_Q = spux.MathType.Rational
 			MT_R = spux.MathType.Real
 			MT_C = spux.MathType.Complex
-			if shape is None:
+			if self.shape is None:
-				if mathtype == MT_Z:
+				if self.mathtype == MT_Z:
 					self.raw_value_int = self._to_raw_value(expr)
-				elif mathtype == MT_Q:
+				elif self.mathtype == MT_Q:
 					self.raw_value_rat = self._to_raw_value(expr)
-				elif mathtype == MT_R:
+				elif self.mathtype == MT_R:
 					self.raw_value_float = self._to_raw_value(expr)
-				elif mathtype == MT_C:
+				elif self.mathtype == MT_C:
 					self.raw_value_complex = self._to_raw_value(expr)
-			elif shape == (2,):
+			elif self.shape == (2,):
-				if mathtype == MT_Z:
+				if self.mathtype == MT_Z:
 					self.raw_value_int2 = self._to_raw_value(expr)
-				elif mathtype == MT_Q:
+				elif self.mathtype == MT_Q:
 					self.raw_value_rat2 = self._to_raw_value(expr)
-				elif mathtype == MT_R:
+				elif self.mathtype == MT_R:
 					self.raw_value_float2 = self._to_raw_value(expr)
-				elif mathtype == MT_C:
+				elif self.mathtype == MT_C:
 					self.raw_value_complex2 = self._to_raw_value(expr)
-			elif shape == (3,):
+			elif self.shape == (3,):
-				if mathtype == MT_Z:
+				log.critical(expr)
+				if self.mathtype == MT_Z:
 					self.raw_value_int3 = self._to_raw_value(expr)
-				elif mathtype == MT_Q:
+				elif self.mathtype == MT_Q:
 					self.raw_value_rat3 = self._to_raw_value(expr)
-				elif mathtype == MT_R:
+				elif self.mathtype == MT_R:
 					self.raw_value_float3 = self._to_raw_value(expr)
-				elif mathtype == MT_C:
+				elif self.mathtype == MT_C:
 					self.raw_value_complex3 = self._to_raw_value(expr)
 
 	####################
@@ -404,7 +422,6 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			Called to compute the internal `FlowKind.LazyArrayRange` of this socket.
 		"""
 		self.steps = value.steps
-		self.unit = value.unit
 
 		if self.symbols:
 			self.raw_min_spstr = sp.sstr(value.start)
@@ -416,21 +433,26 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			MT_R = spux.MathType.Real
 			MT_C = spux.MathType.Complex
 
+			unit = value.unit if value.unit is not None else 1
 			if value.mathtype == MT_Z:
 				self.raw_range_int = [
-					self._to_raw_value(bound) for bound in [value.start, value.stop]
+					self._to_raw_value(bound * unit)
+					for bound in [value.start, value.stop]
 				]
 			elif value.mathtype == MT_Q:
 				self.raw_range_rat = [
-					self._to_raw_value(bound) for bound in [value.start, value.stop]
+					self._to_raw_value(bound * unit)
+					for bound in [value.start, value.stop]
 				]
 			elif value.mathtype == MT_R:
 				self.raw_range_float = [
-					self._to_raw_value(bound) for bound in [value.start, value.stop]
+					self._to_raw_value(bound * unit)
+					for bound in [value.start, value.stop]
 				]
 			elif value.mathtype == MT_C:
 				self.raw_range_complex = [
-					self._to_raw_value(bound) for bound in [value.start, value.stop]
+					self._to_raw_value(bound * unit)
+					for bound in [value.start, value.stop]
 				]
 
 	####################
@@ -441,8 +463,8 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		# Lazy Value: Arbitrary Expression
 		if self.symbols or self.shape not in [None, (2,), (3,)]:
 			return ct.LazyValueFuncFlow(
-				func=sp.lambdify(self.symbols, self.value, 'jax'),
+				func=sp.lambdify(self.sorted_symbols, self.value, 'jax'),
-				func_args=[spux.MathType.from_expr(sym) for sym in self.symbols],
+				func_args=[spux.MathType.from_expr(sym) for sym in self.sorted_symbols],
 				supports_jax=True,
 			)
 
@@ -482,8 +504,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 				unit=self.unit,
 			)
 
-		msg = "Expr socket can't produce array from expression with free symbols"
+		return ct.FlowSignal.NoFlow
-		raise ValueError(msg)
 
 	####################
 	# - FlowKind: Info
@@ -496,6 +517,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			output_mathtype=self.mathtype,
 			output_unit=self.unit,
 		)
+		## TODO: When expression can be used w/arrays, then allow directly outputting a LazyArrayRange pumped through the given expression. Or something like that.
 
 	####################
 	# - FlowKind: Capabilities
@@ -520,10 +542,11 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			_row.label(text=text)
 
 			_col = split.column(align=True)
-			_col.prop(self, 'active_unit', text='')
+			_col.prop(self, self.blfields['active_unit'], text='')
+		else:
+			row.label(text=text)
 
 	def draw_value(self, col: bpy.types.UILayout) -> None:
-		# Property Interface
 		if self.symbols:
 			col.prop(self, self.blfields['raw_value_spstr'], text='')
 
@@ -575,6 +598,27 @@ class ExprBLSocket(base.MaxwellSimSocket):
 			for sym in self.symbols:
 				col.label(text=spux.pretty_symbol(sym))
 
+	def draw_lazy_array_range(self, col: bpy.types.UILayout) -> None:
+		if self.symbols:
+			col.prop(self, self.blfields['raw_min_spstr'], text='')
+			col.prop(self, self.blfields['raw_max_spstr'], text='')
+
+		else:
+			MT_Z = spux.MathType.Integer
+			MT_Q = spux.MathType.Rational
+			MT_R = spux.MathType.Real
+			MT_C = spux.MathType.Complex
+			if self.mathtype == MT_Z:
+				col.prop(self, self.blfields['raw_range_int'], text='')
+			elif self.mathtype == MT_Q:
+				col.prop(self, self.blfields['raw_range_rat'], text='')
+			elif self.mathtype == MT_R:
+				col.prop(self, self.blfields['raw_range_float'], text='')
+			elif self.mathtype == MT_C:
+				col.prop(self, self.blfields['raw_range_complex'], text='')
+
+		col.prop(self, self.blfields['steps'], text='')
+
 	def draw_input_label_row(self, row: bpy.types.UILayout, text) -> None:
 		info = self.compute_data(kind=ct.FlowKind.Info)
 		has_dims = not ct.FlowSignal.check(info) and info.dim_names
@@ -630,7 +674,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 		_row.label(text=text)
 
 	def draw_info(self, info: ct.InfoFlow, col: bpy.types.UILayout) -> None:
-		if info.dim_names and self.show_info_columns:
+		if self.show_info_columns:
 			row = col.row()
 			box = row.box()
 			grid = box.grid_flow(
@@ -696,19 +740,87 @@ class ExprSocketDef(base.SocketDef):
 	default_unit: spux.Unit | None = None
 
 	# FlowKind: Value
-	default_value: spux.SympyExpr = sp.S(0)
+	default_value: spux.SympyExpr = sp.RealNumber(0)
 
 	# FlowKind: LazyArrayRange
-	default_min: spux.SympyExpr = sp.S(0)
+	default_min: spux.SympyExpr = sp.RealNumber(0)
-	default_max: spux.SympyExpr = sp.S(1)
+	default_max: spux.SympyExpr = sp.RealNumber(1)
 	default_steps: int = 2
 	## TODO: Configure lin/log/... scaling (w/enumprop in UI)
 
-	## TODO: Buncha validation :)
-
 	# UI
 	show_info_columns: bool = False
 
+	####################
+	# - Validators - Coersion
+	####################
+	@pyd.model_validator(mode='after')
+	def shape_value_coersion(self) -> str:
+		if self.shape is not None and not isinstance(self.default_value, sp.MatrixBase):
+			if len(self.shape) == 1:
+				self.default_value = self.default_value * sp.Matrix.ones(
+					self.shape[0], 1
+				)
+			if len(self.shape) == 2:
+				self.default_value = self.default_value * sp.Matrix.ones(*self.shape)
+
+		return self
+
+	@pyd.model_validator(mode='after')
+	def unit_coersion(self) -> str:
+		if self.physical_type is not None and self.default_unit is None:
+			self.default_unit = self.physical_type.default_unit
+
+		return self
+
+	####################
+	# - Validators - Assertion
+	####################
+	@pyd.model_validator(mode='after')
+	def valid_shapes(self) -> str:
+		if self.active_kind == ct.FlowKind.LazyArrayRange and self.shape is not None:
+			msg = "Can't have a non-None shape when LazyArrayRange is set as the active kind."
+			raise ValueError(msg)
+
+		return self
+
+	@pyd.model_validator(mode='after')
+	def mathtype_value(self) -> str:
+		default_value_mathtype = spux.MathType.from_expr(self.default_value)
+		if not self.mathtype.is_compatible(default_value_mathtype):
+			msg = f'MathType is {self.mathtype}, but tried to set default value {self.default_value} with mathtype {default_value_mathtype}'
+			raise ValueError(msg)
+
+		return self
+
+	@pyd.model_validator(mode='after')
+	def symbols_value(self) -> str:
+		if (
+			self.default_value.free_symbols
+			and not self.default_value.free_symbols.issubset(self.symbols)
+		):
+			msg = f'Tried to set default value {self.default_value} with free symbols {self.default_value.free_symbols}, which is incompatible with socket symbols {self.symbols}'
+			raise ValueError(msg)
+
+		return self
+
+	@pyd.model_validator(mode='after')
+	def shape_value(self) -> str:
+		shape = spux.parse_shape(self.default_value)
+		if shape != self.shape and not (
+			shape is not None
+			and self.shape is not None
+			and len(self.shape) == 1
+			and 1 in shape
+		):
+			msg = f'Default value {self.default_value} has shape {shape}, which is incompatible with the expr socket (shape {self.shape})'
+			raise ValueError(msg)
+
+		return self
+
+	####################
+	# - Initialization
+	####################
 	def init(self, bl_socket: ExprBLSocket) -> None:
 		bl_socket.active_kind = self.active_kind
 
@@ -718,11 +830,12 @@ class ExprSocketDef(base.SocketDef):
 		bl_socket.physical_type = self.physical_type
 		bl_socket.symbols = self.symbols
 
-		# Socket Units
+		# Socket Units & FlowKind.Value
-		if self.default_unit is not None:
+		log.critical(self)
+		if self.physical_type is not None:
 			bl_socket.unit = self.default_unit
-
+			bl_socket.value = self.default_value * self.default_unit
-		# FlowKind: Value
+		else:
 			bl_socket.value = self.default_value
 
 		# FlowKind: LazyArrayRange

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

@@ -96,6 +96,23 @@ class Tidy3DCloudTaskBLSocket(base.MaxwellSimSocket):
 
 	new_task_name: str = bl_cache.BLField('', prop_ui=True)
 
+	####################
+	# - Property Changes
+	####################
+	def on_socket_prop_changed(self, prop_name: str) -> None:
+		if prop_name in [
+			'api_key',
+			'existing_folder_id',
+			'existing_task_id',
+			'new_task_name',
+			'should_exist',
+		]:
+			self.existing_folder_id = bl_cache.Signal.ResetEnumItems
+			self.existing_task_id = bl_cache.Signal.ResetEnumItems
+
+	####################
+	# - FlowKinds
+	####################
 	@property
 	def capabilities(self) -> ct.CapabilitiesFlow:
 		return ct.CapabilitiesFlow(
@@ -122,7 +139,7 @@ class Tidy3DCloudTaskBLSocket(base.MaxwellSimSocket):
 				return (self.new_task_name, cloud_folder)
 
 			# No Task Selected: Return None
-			if self.existing_task_id == 'NONE':
+			if self.existing_task_id is None:
 				return None
 
 			# Retrieve Cloud Task
@@ -135,7 +152,7 @@ class Tidy3DCloudTaskBLSocket(base.MaxwellSimSocket):
 
 			return cloud_task
 
-		return None
+		return ct.FlowSignal.FlowPending
 
 	####################
 	# - Searchers
@@ -158,7 +175,7 @@ class Tidy3DCloudTaskBLSocket(base.MaxwellSimSocket):
 		return []
 
 	def search_cloud_tasks(self) -> list[ct.BLEnumElement]:
-		if self.existing_folder_id == 'NONE' or not tdcloud.IS_AUTHENTICATED:
+		if self.existing_folder_id is None or not tdcloud.IS_AUTHENTICATED:
 			return []
 
 		# Get Cloud Folder
@@ -221,10 +238,6 @@ class Tidy3DCloudTaskBLSocket(base.MaxwellSimSocket):
 	def on_prepare_new_task(self):
 		self.should_exist = False
 
-	def on_cloud_updated(self):
-		self.existing_folder_id = bl_cache.Signal.ResetEnumItems
-		self.existing_task_id = bl_cache.Signal.ResetEnumItems
-
 	####################
 	# - UI
 	####################

src/blender_maxwell/nodeps/utils/blender_type_enum.py

@@ -13,6 +13,7 @@ def prefix_values_with(prefix: str) -> type[enum.Enum]:
 	Returns:
 		A new StrEnum class with altered member values.
 	"""
+	## TODO: DO NOT USE FOR ENUMS WITH METHODS
 
 	def _decorator(cls: enum.StrEnum):
 		new_members = {

src/blender_maxwell/utils/bl_cache.py

@@ -547,6 +547,9 @@ class BLField:
 		self._str_cb = str_cb
 		self._enum_cb = enum_cb
 
+		## Type Coercion
+		self._coerce_output_to = None
+
 		## Vector/Matrix Identity
 		## -> Matrix Shape assists in the workaround for Matrix Display Bug
 		self._is_vector = False
@@ -797,7 +800,11 @@ class BLField:
 			}
 
 		## StrEnum
-		elif inspect.isclass(AttrType) and issubclass(AttrType, enum.StrEnum):
+		elif (
+			inspect.isclass(AttrType)
+			and issubclass(AttrType, enum.StrEnum)
+			and self._enum_cb is None
+		):
 			default_value = self._default_value
 			BLProp = bpy.props.EnumProperty
 			kwargs_prop |= {
@@ -814,9 +821,14 @@ class BLField:
 			}
 			if self._enum_many:
 				kwargs_prop['options'].add('ENUM_FLAG')
+			self._coerce_output_to = AttrType
 
 		## Dynamic Enum
-		elif AttrType is enum.Enum and self._enum_cb is not None:
+		elif (
+			AttrType is enum.Enum
+			or (inspect.isclass(AttrType) and issubclass(AttrType, enum.StrEnum))
+			and self._enum_cb is not None
+		):
 			if self._default_value is not None:
 				msg = 'When using dynamic enum, default value must be None'
 				raise ValueError(msg)
@@ -828,6 +840,8 @@ class BLField:
 			}
 			if self._enum_many:
 				kwargs_prop['options'].add('ENUM_FLAG')
+			if AttrType is not enum.Enum:
+				self._coerce_output_to = AttrType
 
 		## BL Reference
 		elif AttrType in typ.get_args(ct.BLIDStruct):
@@ -888,6 +902,9 @@ class BLField:
 	def __get__(
 		self, bl_instance: BLInstance | None, owner: type[BLInstance]
 	) -> typ.Any:
+		if bl_instance is None:
+			return None
+
 		value = self._cached_bl_property.__get__(bl_instance, owner)
 
 		# enum.Enum: Cast Auto-Injected Dynamic Enum 'NONE' -> None
@@ -913,7 +930,7 @@ class BLField:
 		## -> Reject modernity. Return to tuple[].
 		if self._is_vector:
 			## -> tuple()ify the np.array to respect tuple[] type annotation.
-			return tuple(np.array(value))
+			return tuple(value)
 
 		if self._is_matrix:
 			# Matrix Display Bug: Correctly Read Row-Major Values w/Reshape
@@ -921,6 +938,13 @@ class BLField:
 				map(tuple, np.array(value).flatten().reshape(self._matrix_shape))
 			)
 
+		# Coerce Output
+		## -> Mainly useful for getting the "real" StrEnum back.
+		if self._coerce_output_to is not None and value is not None:
+			if self._enum_many:
+				return {self._coerce_output_to(v) for v in value}
+			return self._coerce_output_to(value)
+
 		return value
 
 	def __set__(self, bl_instance: BLInstance | None, value: typ.Any) -> None:

src/blender_maxwell/utils/extra_sympy_units.py

@@ -25,6 +25,10 @@ from pydantic_core import core_schema as pyd_core_schema
 
 from blender_maxwell import contracts as ct
 
+from . import logger
+
+log = logger.get(__name__)
+
 SympyType = (
 	sp.Basic
 	| sp.Expr
@@ -47,21 +51,42 @@ class MathType(enum.StrEnum):
 	Real = enum.auto()
 	Complex = enum.auto()
 
+	@staticmethod
 	def combine(*mathtypes: list[typ.Self]) -> typ.Self:
 		if MathType.Complex in mathtypes:
 			return MathType.Complex
-		elif MathType.Real in mathtypes:
+		if MathType.Real in mathtypes:
 			return MathType.Real
-		elif MathType.Rational in mathtypes:
+		if MathType.Rational in mathtypes:
 			return MathType.Rational
-		elif MathType.Integer in mathtypes:
+		if MathType.Integer in mathtypes:
 			return MathType.Integer
-		elif MathType.Bool in mathtypes:
+		if MathType.Bool in mathtypes:
 			return MathType.Bool
 
+		msg = f"Can't combine mathtypes {mathtypes}"
+		raise ValueError(msg)
+
+	def is_compatible(self, other: typ.Self) -> bool:
+		MT = MathType
+		return (
+			other
+			in {
+				MT.Bool: [MT.Bool],
+				MT.Integer: [MT.Integer],
+				MT.Rational: [MT.Integer, MT.Rational],
+				MT.Real: [MT.Integer, MT.Rational, MT.Real],
+				MT.Complex: [MT.Integer, MT.Rational, MT.Real, MT.Complex],
+			}[self]
+		)
+
 	@staticmethod
 	def from_expr(sp_obj: SympyType) -> type:
-		## TODO: Support for sp.Matrix
+		if isinstance(sp_obj, sp.MatrixBase):
+			return MathType.combine(
+				*[MathType.from_expr(v) for v in sp.flatten(sp_obj)]
+			)
+
 		if isinstance(sp_obj, sp.logic.boolalg.Boolean):
 			return MathType.Bool
 		if sp_obj.is_integer:
@@ -172,7 +197,7 @@ class NumberSize1D(enum.StrEnum):
 			None: NS.Scalar,
 			(2,): NS.Vec2,
 			(3,): NS.Vec3,
-			(4,): NS.Vec3,
+			(4,): NS.Vec4,
 		}[shape]
 
 	@property
@@ -182,7 +207,7 @@ class NumberSize1D(enum.StrEnum):
 			NS.Scalar: None,
 			NS.Vec2: (2,),
 			NS.Vec3: (3,),
-			NS.Vec3: (4,),
+			NS.Vec4: (4,),
 		}[self]
 
 
@@ -702,7 +727,6 @@ def scale_to_unit(sp_obj: SympyType, unit: spu.Quantity) -> Number:
 	Raises:
 		ValueError: If the result of unit-conversion and -stripping still has units, as determined by `uses_units()`.
 	"""
-	## TODO: An LFU cache could do better than an LRU.
 	unitless_expr = spu.convert_to(sp_obj, unit) / unit
 	if not uses_units(unitless_expr):
 		return unitless_expr
@@ -739,7 +763,7 @@ def unit_str_to_unit(unit_str: str) -> Unit | None:
 	if unit_str in _UNIT_STR_MAP:
 		return _UNIT_STR_MAP[unit_str]
 
-	msg = 'No valid unit for unit string {unit_str}'
+	msg = f'No valid unit for unit string {unit_str}'
 	raise ValueError(msg)
 
 
@@ -802,7 +826,7 @@ class PhysicalType(enum.StrEnum):
 			# Global
 			PT.Time: Dims.time,
 			PT.Angle: Dims.angle,
-			PT.SolidAngle: Dims.steradian,  ## MISSING
+			PT.SolidAngle: spu.steradian.dimension,  ## MISSING
 			PT.Freq: Dims.frequency,
 			PT.AngFreq: Dims.angle * Dims.frequency,
 			# Cartesian
@@ -836,7 +860,7 @@ class PhysicalType(enum.StrEnum):
 			PT.HField: Dims.current / Dims.length,
 			# Luminal
 			PT.LumIntensity: Dims.luminous_intensity,
-			PT.LumFlux: Dims.luminous_intensity * Dims.steradian,
+			PT.LumFlux: Dims.luminous_intensity * spu.steradian.dimension,
 			PT.Illuminance: Dims.luminous_intensity / Dims.length**2,
 			# Optics
 			PT.OrdinaryWaveVector: Dims.frequency,
@@ -1263,12 +1287,23 @@ def convert_to_unit_system(sp_obj: SympyExpr, unit_system: UnitSystem) -> SympyE
 	return spu.convert_to(sp_obj, _flat_unit_system_units(unit_system))
 
 
+def strip_unit_system(sp_obj: SympyExpr, unit_system: UnitSystem) -> SympyExpr:
+	"""Strip units occurring in the given unit system from the expression.
+
+	Unit stripping is a "dumb" operation: "Substitute any `sympy` object in `unit_system.values()` with `1`".
+	Obviously, the semantic correctness of this operation depends entirely on _the units adding no semantic meaning to the expression_.
+
+	Notes:
+		You should probably use `scale_to_unit_system()` or `convert_to_unit_system()`.
+	"""
+	return sp_obj.subs({unit: 1 for unit in unit_system.values()})
+
+
 def scale_to_unit_system(
 	sp_obj: SympyExpr, unit_system: UnitSystem, use_jax_array: bool = False
 ) -> int | float | complex | tuple | jax.Array:
 	"""Convert an expression to the units of a given unit system, then strip all units of the unit system.
 
-	Unit stripping is "dumb": Substitute any `sympy` object in `unit_system.values()` with `1`.
 	Afterwards, it is converted to an appropriate Python type.
 
 	Notes:
@@ -1287,8 +1322,6 @@ def scale_to_unit_system(
 		If the returned type is array-like, and `use_jax_array` is specified, then (and **only** then) will a `jax.Array` be returned instead of a nested `tuple`.
 	"""
 	return sympy_to_python(
-		convert_to_unit_system(sp_obj, unit_system).subs(
+		strip_unit_system(convert_to_unit_system(sp_obj, unit_system), unit_system),
-			{unit: 1 for unit in unit_system.values()}
-		),
 		use_jax_array=use_jax_array,
 	)

src/blender_maxwell/utils/serialize.py

@@ -81,6 +81,7 @@ _NaivelyEncodableTypeSet = frozenset(typ.get_args(NaivelyEncodableType))
 class TypeID(enum.StrEnum):
 	Complex: str = '!type=complex'
 	SympyType: str = '!type=sympytype'
+	SympyExpr: str = '!type=sympyexpr'
 	SocketDef: str = '!type=socketdef'
 	ManagedObj: str = '!type=managedobj'