What was already known
Classical extended Reed–Solomon and hyperoval constructions attain the proposed lengths. Prime-field and restricted-dimension results did not supply the full even-field range; a recent two-transitive-automorphism result concerns a special class of codes.
AI involvement
Kumar devised the argument. Claude assisted its original Lean translation; Claude Opus 5.5 later ported the development, prepared the challenge and report, and produced supplementary checks.
Kumar devised the mathematical argument. Claude translated and ported it and prepared checking material; no new model-origin mathematics is documented.
Importance
If correct and novel as scoped, supplies a substantial sharp coding-theory bound across all even finite fields, with an AI-assisted formalization checkpoint.
Limitations
The mathematical argument is attributed to Kumar, not to AI discovery. Odd-order fields, nonlinear codes and classification of extremizers are outside the claim. The project’s literature comparison is bounded and novelty has not been independently established; no human specialist review is reported. The formal challenge uses literal subspaces, attained Hamming minimum distance and IsGreatest. AIProofWatch read the exact challenge and provenance but has not rebuilt the proof or audited all dependencies. The reported date is the registry checkpoint; an earlier first mathematical report date is unestablished.
Technical verification
Reported is the default when evidence for a higher level is insufficient. No qualifying AI mathematical contribution remains in the proposed scope. Existing checks of the human result or its translation are retained as current evidence, without transferring them to an invented included AI contribution.
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
- EvenOrderMDS.maximum_length_of_MDS_code at 1e7d9f0fc719de64230edd473411b23e2a8ed72b; literal subspaces of K^N, attained Hamming minimum distance, 2≤k≤q, even field cardinality; only propext, Quot.sound and Classical.choice permitted.
- Basis
- Reported by the linked checker
- Check date
- 2026-10-15
Checking a formal statement does not establish that it matches the original problem.
Human understanding
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
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