FPRD LabShare an approach

← Claims

Theorem · full abstraction and minimization

FPRD-T129

Future-context full abstraction and canonical residual figures

Exact statement

Equality of rooted scaffold unfoldings is equivalent to equality of all finite neighborhoods and deterministic labelled bisimilarity, is preserved by every common finite scaffold continuation, and is separated when unequal by a finite distance-two unary continuation. Every finite rooted scaffold has a canonical minimal residual figure, unique up to rooted labelled port-graph isomorphism.

StatusProved, independently rederived, and finitely stress-tested
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

The unfolding of a rooted scaffold maps each finite port word to the label reached there or to a distinguished missing-edge value. Full abstraction says this observation is exactly the behavior respected by every common future row.

Definitions

  • A deterministic labelled bisimulation preserves the root label and matches every present or missing port recursively.
  • The minimal residual figure has one state for each distinct valid residual unfolding.

Hypotheses and scope

  • Rooted finite scaffolds of one fixed degree over the same working alphabet.
  • Common continuations append the same legal rows to both histories.

Proof or evidence

Finite neighborhoods are restrictions of the unfolding. Equality is a bisimulation and is preserved through one common row by induction on query words. A shortest distinguishing port word is exposed one symbol per row by a unary distance-two cursor. Residualization gives the canonical quotient. The replayed checker verified 86,832 common updates, 11,092 finite separators, and 78 canonical figures over its complete finite domain.

Future-context full abstraction →

Verification notes

The proof was independently reconstructed from the definitions and the checker was rerun successfully on 2026-08-26. The finite enumeration corroborates rather than proves the uniform theorem.

Limitations

  • Coalgebraic bisimulation quotients are inherited background; no novelty claim is made for them.
  • The scaffold-specific content is continuation stability plus the explicit distance-two separating context.
  • Behavioral equivalence does not preserve physical alias identity unless labels explicitly record it.

Open work

Compare the scaffold-specific continuation and separator statements with the closest coalgebraic testing and context-equivalence formulations.

Notes

Coalgebraic bisimulation quotients are inherited background. The scaffold-specific statements retained here are preservation by every common future row and the explicit distance-two separating context. Finite checks corroborate 86,832 common updates and do not prove the parameter-uniform result. No novelty claim is made.