AI Proof WatchKeep up with AI contributions

On hold: outside the current catalog. The source attributes mathematical and formal-proof collaboration broadly; identify the retained model-origin classification idea rather than infer it from agent reviews. Reviewed 2026-10-29. This page preserves the publication history.

AI-assisted classification of depth-labeled substitutions in Sacchetti logics

The modal-depth project reports that, for positive n in wGL_n, arbitrary simultaneous formula substitutions indexed by atom and depth label preserve theoremhood exactly when c(k+n)=c(k) for every positive depth k. Structural interpolation equivalences pair this periodicity with the corresponding ordinary interpolation properties.

Sources for this record

What was already known

Ordinary interpolation results for Sacchetti’s logics and familiar depth/congruence restrictions provide the setting. The project classifies arbitrary labels rather than only one chosen congruence labeling.

AI involvement Not rated

JD Jones directed the project. GPT-6/Codex and GPT-6 Pro assisted with mathematical arguments, Lean proofs, review and verification; separate internal checks are not outside assessments.

The source attributes mathematical and formal-proof collaboration broadly; identify the retained model-origin classification idea rather than infer it from agent reviews.

Importance Notable

Gives an exact structural criterion, with supporting positive transfers and negative obstructions, for this modal substitution/interpolation setup.

Limitations

The source atom type must be nonempty for the substitution characterization. Ordinary uniform/Lyndon/Craig interpolation properties remain explicit inputs where used; they are not proved by this project. This concerns the disclosed Hilbert calculus and labeling conventions, not arbitrary modal logics. Worldwide priority and independent human specialist review are not established. AIProofWatch read the exact challenge and disclosure but did not rebuild the proof or audit every formal definition.

Technical verification Formal

A completed rigorous check is documented for the scoped statement. Palomar: Lean, NanoDa and con-ron (reported): The registered depth-labeling, simultaneous-substitution and structural interpolation contracts at 8c5fc2afd424a0fc593c97031ada788befdc5b10. Ordinary interpolation remains explicit; only propext, Quot.sound and Classical.choice permitted.

Formal checking

Reported checking of the stated formal scope; not reproduced by AIProofWatch. Separate kernels and author-produced checkers do not establish outside researcher review.

Checker
Palomar: Lean, NanoDa and con-ron (reported)
Scope
The registered depth-labeling, simultaneous-substitution and structural interpolation contracts at 8c5fc2afd424a0fc593c97031ada788befdc5b10. Ordinary interpolation remains explicit; only propext, Quot.sound and Classical.choice permitted.
Basis
Reported by the linked checker
Check date
2026-10-15
Evidence source

Checking a formal statement does not establish that it matches the original problem.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No sufficient account of a named human explaining the scoped central reasoning is established in this assessment. Missing disclosure is not evidence of little understanding.

Correction and publication history

2026-10-16 · publication

Primary statement, hypotheses, prior bounds, AI role and evidence scope reviewed on 16 October 2026 against every current catalog/update page and existing immutable revisions. New recent scoped contribution; ordinary notifying editor publication.

Read this published revision