E.18.2:4 - Solution

Write a TransformationFlowMathematicalDescription@Context only when the mathematical expression changes the current transformation-flow description move. Name exactly one described ontic subject: one E.18 TFS or one E.18.NET network. Keep that subject reference, the mathematical description, any C.29 lens-use judgment, and any E.17 publication face separate. Then decide whether the C.29 lens-use card is needed for adequacy, payoff, preserved/lost structure, or boundary.

E.18.2:4.1 - First-use record

Use this compact record for ordinary cases:

TransformationFlowMathematicalDescription@Context:
  # exactly one described ontic subject branch is present:
  DescribedTransformationFlowStructureRef?:
  DescribedTransformationFlowStructureNetworkRef?:
  DescribedSliceOrLocusRef?:
  CandidateMathObject:
  ExpressionKind:
  MappingMode:
  PreservedStructure:
  LostStructure:
  DeclaredUse:
  BoundaryStop:
  C29LensUseRef?:
  PublicationFaceRef?:

Exactly one of DescribedTransformationFlowStructureRef? and DescribedTransformationFlowStructureNetworkRef? is present. The first points to one E.18 TFS; the second points to one already selected E.18.NET network. DescribedSliceOrLocusRef? may cite an existing path, slice, FlowPositionRef, ExposedFlowPositionRef, member path, E.18.NET NetworkCrossFlowRelationRowRef, or other independently identified part without copying the fields that define that object. CandidateMathObject and ExpressionKind name the graph, algebra, category, tuple, morphism, quotient, fold, refinement, factorization, wiring, matrix, network expression, or related mathematical object. PreservedStructure, LostStructure, DeclaredUse, and BoundaryStop follow the C.29 discipline when the expression is claim-bearing. PublicationFaceRef? points to a separate E.17 publication face. The compact record has no generic neighboring-object reference. When a neighboring claim is materially needed, cite its exact C.2.1 claim-bearing episteme in the subject-specific account; identify an ontic subject or relation occurrence only through a separately named, correctly typed reference supplied by the pattern for that claim.

E.18.2:4.2 - Expression families

These families are prompts for recovery, not a taxonomy of new FPF kinds. A local expression may combine several families; the record still names exactly one selected TFS or network subject, one current described part when relevant, and the declared use.

E.18.2:4.3 - Five-way subject, description, lens, and publication discriminator

Use this discriminator before writing or accepting a mathematical description:

If the claim selects one TFS or its internal flow structure, use E.18.
If the claim selects independently identified TFS or nested-network members plus exact cross-member relations, use E.18.NET.
If the claim describes exactly one selected TFS or network with mathematics, use E.18.2.
If the claim evaluates that mathematical lens use, use C.29 with the E.18.2 description reference.
If the claim publishes a graph, table, equation, diagram, card, or other face, use E.17 and the relevant view or architecture-description pattern.

The same visible source may require several records, but each E.18.2 description chooses one described ontic subject branch. A refrigerator principle scheme may include an E.17 publication face, a functional-architecture view, one selected E.18 TFS, a thermodynamic mechanism claim, and an E.18.2 graph or equation description. A network diagram may similarly publish an E.18.2 description of one already selected E.18.NET network. If the expression is evaluated as a lens, apply the C.29 adequacy test; if it is rendered or published, identify the E.17 publication face and any current view or architecture-description membership. Neither record reidentifies the TFS or network.

E.18.2:4.4 - Related claims

E.18.2 defines only the mathematical-description relation. For any neighboring claim, use the row below that names the exact contribution needed now: