Run 05: sequence contract and companion alignment

Date: 23 September 2026

Contents

Scope

This run compares the later sequence-implementation chain against the current direct and causal papers, then checks whether the transfer and unary papers depend on that chain. It is a statement-level dependency review, not a new proof of the sequence implementation or the palindrome theorem.

The four circulated paper bodies and PDFs were not changed.

Finding

The current direct paper separates two claims correctly:

Theorem 12.2 is a mathematical construction conditional on a persistent sequence implementation satisfying the contract in Section 11.1.
Appendix D gives informal source-level evidence that a pinned, length-free OCaml sequence variant satisfies that contract.

The paper explicitly says that its automated analysis does not yet establish complete old/fresh pointer provenance and that the source evidence is distinct from the generic conditional construction. The numerical access radius and scaffold distance remain withdrawn.

The whole-client normalization theorem is not the unresolved part. It proves that a bounded sequential client satisfying its hypotheses can be partially evaluated into one simultaneous old-dependent plan. What remains below a full source-to-scaffold certificate is the premise that the concrete sequence implementation satisfies every source-record clause, especially complete pointer provenance.

The causal paper’s generic simultaneous-batch compiler remains independent of that source question. Its palindrome example is explicitly scoped to the companion’s abstract model. However, the example says the companion supplies “an explicit strict source-record implementation” and “its resource certificate.” That phrase compresses a conditional theorem and informal implementation evidence into language that can be read as a completed source certificate. The causal bibliography also still identifies the companion as Draft 4, while the linked current paper is Draft 5.

This is an edition-alignment issue, not a newly found counterexample. The next coordinated causal edition should describe the companion at its actual assurance level and cite the numbered edition used. No prominent correction notice or immediate paper rewrite is warranted.

Source-evidence boundary reproduced

The existing certificate programs were rerun successfully:

the typed-call inventory covers 3 units, 3,912 expressions, and 454 direct calls and reproduces the endpoint-call ceilings;
the cat closure resolves 81 bindings and admits all 952 constructor slots;
474 polymorphic source sites still require contextual type specialization;
zero of those sites have been resolved by a real specialization run;
no old/fresh interpretation has executed and no numerical radius has been derived.

The programs establish real source coverage while also recording their own boundary. They do not turn the OCaml evidence into a complete provenance proof.

Dependency trace

Direct palindrome: the theorem remains conditional on the Section 11.1 sequence contract; source evidence remains informal and needs-work.
Causal algebra: its generic compiler is unaffected. Only the wording and edition reference for the companion palindrome application need alignment.
Real-time multitape transfer: no dependency on the direct sequence implementation; it remains a separate proof route.
Unary coherence: no dependency on the sequence implementation or direct palindrome client was found.

Evidence

check_sequence_contract_alignment.py checks the exact current statement markers and the machine-readable certificate boundaries.
sequence-contract-alignment-output.json records its output.
The repository’s existing typed-call, typed-flow, cat-frontier, and context-specialization checkers all passed in this run.

Finish the remaining statement ledger for historical sequence-contract changes, then resume the native-observation comparison. Any paper changes should be made only as matching numbered PDF and HTML editions with a concise cumulative history at the end.