2026-08-31-faithful-semantic-preservation

Research round: Faithful Semantic Preservation and Grounded Slice Admission

Prompt-author model: unrecorded. Executor: GPT-5 Codex (OpenAI).

Work against the live alignment-workspace at current PR73. Inspect its actual head, PR72, PR71, settled Normative Continuity, and Legitimate Evolution grounding. This is a hostile refinement pass, not an architecture search.

Preserve unless refuted: matter identity, independently incurred slices, matter-and-slice-indexed issue loads, and the intended accounting plus authentication plus Continuity conservation result.

0–4. Persistent-carrier mutation

Reconstruct PR73 exactly and separate algebraic proof, semantic assumptions, Continuity structure, and finite-test support. Attack the induction with a live unresolved issue whose load silently changes from a to zero without resolution, Satisfaction, Disposition, or Transfer. If this satisfies current hypotheses, add an exact fixture and repair the live PR73 theorem.

Define semantically affected carriers to include every load change, even on persistent issues. Compare default stability, per-edit certificates, and one generalized batch equation over all changed old and post carriers. Prefer generalized Transfer. Give identity an explicit/default semantic case and restate Slice-wise Conservation so every mutation is covered and unchanged carriers preserve their authenticated loads. Avoid Continuity surgery.

5–10. Faithfulness and non-vacuity

Separate authentication soundness from faithfulness. Attack join-and-bottom preserving anchored maps that collapse relevant distinctions, including maps that hide strengthening or weakening. Compare global injectivity, order reflection, slice-relative quotient embeddings, and reflection restricted to admissible carrier representations.

Define a reusable slice-relative faithfulness property without making it tautological. Distinguish checker correctness from semantic adequacy. Determine whether equality reflection is enough for translation and whether order reflection is required for weakening/strengthening. Reprove No Semantic Laundering with every semantic assumption explicit and necessity-tested.

11–14. Grounded admission

Separate semantic authentication of what a slice means from normative grounding of why it becomes owed. Test Admission as SemanticAuth plus GroundedOrigin. Reuse Due rising edges, standing rules, issue anchors, and Grounded Replay where they fit; do not invent a second provenance graph.

Give late accretion a real origin: fact activation, conditional obligation, external criticism, stakeholder claim, authorized inquiry obligation, or a reason generated under a grounded rule. Analyze revisions to admission rules, reflexive answerability, the fixed-metalanguage boundary, and the seed-quality seam without infinite regress.

15–18. Composition and instances

Determine whether faithfulness composes across era bridges. Test quotient mismatch, context/target drift, and cumulative erosion. Verify exactly when the stable anchored codomain blocks gradual semantic collapse.

Instantiate adequacy independently for Coverage, preserving target, applicability, scope, unresolved/registration status, route quality, and registration conditions; and for Reasons, preserving provenance, target, answer mode, unresolved status, and adequate-answer criteria. Keep answerability faithfulness weaker than Progress comparison faithfulness.

19–23. Boundaries, cases, and theorem targets

Keep Progress, eventual response, liability, and multi-agent transfer out. Add 22 exact hostile fixtures: silent loss/change; accepted in-place translation, weakening, and strengthening; lossy join maps; noninjective faithful quotients; constant observation; failed order reflection; faithful and incompatible composition; cumulative erosion; semantically valid but ungrounded admission; grounded malformed meaning; fact activation; evaluator invention; Coverage and Reason laundering; and necessity of the weakest faithfulness condition.

State Fully Repaired Slice-wise Conservation over every semantic mutation, No Semantic Laundering under faithful authentication, and No Groundless Accretion. Be explicit about what is derived versus an interface assumption.

24–25. Discipline and deliverables

Prefer exact finite models; add no large Lean. Create IN_PLACE_MUTATION_AUDIT.md, FAITHFUL_AUTHENTICATION.md, AUTHENTICATION_ADEQUACY.md, GROUNDED_ADMISSION.md, COMPOSITION_AND_EROSION.md, COVERAGE_FAITHFULNESS.md, REASON_FAITHFULNESS.md, REPAIRED_CONSERVATION.md, NO_SEMANTIC_LAUNDERING.md, COUNTERMODELS.md, REPORT.md, and exact tests. Amend PR73's live theorem if the first defect is real.

26. Questions

Answer all 24 questions concerning the mutation gap and minimal repair, identity, repaired conservation, soundness versus faithfulness, lossy maps, global injectivity, equality/order reflection, admissible domains, composition/erosion, Coverage and Reason distinctions, semantic versus normative admission, grounding by Due/Legitimate Evolution, evaluator self-declaration, Continuity surgery, seed assumptions, and the strongest justified laundering theorem.

27. Verdict

End with exactly one primary verdict: PR73-CONSERVATION-NEEDS-IN-PLACE-MUTATION-REPAIR, PR73-CONSERVATION-SURVIVES-AS-WRITTEN, AUTHENTICATION-NEEDS-SLICE-FAITHFULNESS, SOUND-AUTHENTICATION-IS-SUFFICIENT, GROUNDED-SLICE-ADMISSION-REQUIRED, or ANSWERABILITY-SEMANTICS-NEEDS-RETHINK.

Secondary verdicts are encouraged. Prevent carrier laundering, semantic laundering, and provenance laundering. Do not accept constant or otherwise vacuous interpretations as adequate preservation.

Report: faithful semantic preservation and grounded slice admission

Result

All three attacks survive, with local repairs that preserve the architecture.

First, PR73's original induction has a real gap: settled outstanding evolution does not constrain the load of a persistent issue. Generalized Transfer must cover every semantic mutation, including in-place edits, with an identity frame for carriers outside the affected batch. PR73's live theorem statement is amended accordingly. No Continuity change is needed.

Second, authentication soundness relative to a denotation is insufficient for the strong No Semantic Laundering claim. A join-preserving map can collapse a slice-relevant distinction. The weakest reusable strong condition is order reflection on admissible carrier representations modulo a domain-supplied slice-relative equivalence. Equality reflection suffices only for exact translation. Global injectivity is unnecessary.

Third, semantic authentication of a new slice and normative grounding of its admission are independent. Existing Due and Grounded Replay can realize the standing-authorizer lineage, but they do not derive the domain evidence or semantic meaning of every admission. No Groundless Accretion is an interface condition above that machinery.

Answers

1. Does PR73 fail under in-place mutation? Yes. A persistent issue can change \(a\to0\) while every original resolution-batch premise is vacuous.
2. Minimal repair? One generalized affected batch per transition and slice, plus an identity frame outside it.
3. Must Transfer cover every semantic change? Yes, including changes on structurally persistent carriers.
4. Explicit semantic identity? Identity is the default frame condition and may be reified as a trivial certificate for composition.
5. Does repaired conservation survive? Yes by a finite-prefix partition and substitution induction.
6. Is soundness alone sufficient for laundering? No.
7. Can a join-preserving anchored map be lossy? Yes; mapping a relevant token to bottom hides both strengthening and weakening.
8. Global injectivity? Not necessary.
9. Weakest useful faithfulness? An order embedding of admissible representations modulo anchored slice-relative equivalence.
10. Is equality reflection enough? For exact translation only.
11. Is order reflection required? For the strong weakening/strengthening classification, yes.
12. Only admissible representations? Yes. This avoids freezing irrelevant or unreachable ontology.
13. Does faithfulness compose? Yes with compatible relevance quotients, targets, contexts, and a shared anchored domain.
14. Can repeated revisions erode meaning? They can if local quotients drift or maps are merely sound.
15. Does the stable codomain prevent erosion? Only together with anchored quotient compatibility and order reflection.
16. Coverage distinctions? Target, applicability, scope, unresolved and registration status, route quality, and qualifying registration conditions.
17. Reason distinctions? Provenance, target/content, answer mode, unresolved status, and adequate-answer criterion.
18. Authentication versus grounding? Distinct and jointly necessary.
19. What grounds a slice? Domain origin evidence acted on by a currently standing permitted authorizer with strict-prefix lineage.
20. Can Legitimate Evolution / Due supply it? They supply a clean realization of authorizer ancestry and rising-edge representation, not the entire domain or semantic certificate.
21. Evaluator declaration alone? No.
22. Continuity surgery? None.
23. Seed-quality assumptions? Genesis standing, adequacy of relevance quotients, checker soundness, admission-rule validity/completeness, and authenticated revision of those rules.
24. Strongest justified laundering theorem? Repaired slice conservation plus sound, order-reflecting authentication and grounded admission prevents carrier, semantic, and provenance laundering modulo explicitly anchored slice irrelevance.

Theorem dependency

grounded origin + authenticated meaning [domain / seed interface] | v faithful admissible quotient into L_alpha [semantic adequacy] | v generalized Transfer for every mutation + identity frame outside affected batch [local accounting] | v outstanding evolution / birth / ancestry [settled Continuity] | v repaired Slice-wise Conservation [finite-prefix induction] | v No Semantic Laundering + No Groundless Accretion

Progress/fairness, liability, and eventual response are not used.

Verification

Run:

python3 tests/run.py

The runner executes 22 exact finite hostile cases. It checks the three laundering counterexamples, accepted repairs, noninjective faithful quotients, failed order reflection, bridge compatibility, cumulative erosion, grounded and ungrounded admissions, and independent Coverage/Reason instances. These are test-supported unregistered paper results, not registered claims.

Provisional names

Provisional names introduced: generalized Transfer, identity frame, slice-relative faithfulness, authentication adequacy, grounded admission, and No Groundless Accretion.

Deviations

No Lean was added because the repaired hypothesis is semantic and requires no new Continuity field. The round amended PR73's open theorem and report rather than leaving the known counterexample only in a follow-up. The prompt record compresses repeated displays and framing while preserving every numbered requirement, hostile case, deliverable, question, and verdict option.

What is not shown

The round does not prove that the chosen relevance preorder is morally adequate, that admission rules discover all valid new obligations, or that a response eventually occurs. It does not derive domain evidence, seed standing, or checker correctness from the calculus. Infinite traces are covered only prefix by prefix. No result is registered.

Outstanding maintainer actions

None.

IN-PLACE-REPAIR-LOCAL

SLICE-RELATIVE-FAITHFULNESS-SUFFICES

FULL-INJECTIVITY-TOO-STRONG

ADMISSION-GROUNDING-SEPARATE-FROM-SEMANTICS

PR73-CONSERVATION-NEEDS-IN-PLACE-MUTATION-REPAIR

Faithful semantic preservation and grounded slice admission

Unregistered hostile refinement of PR73. It repairs the in-place mutation gap, separates authentication correctness from slice-relative adequacy, and separates semantic authentication of a fresh slice from normative grounding of its origin.

Read REPORT.md first. Run the exact fixtures with:

python3 tests/run.py

The round amends PR73's open paper theorem but changes no settled Continuity definition, Lean declaration, or registered claim.