# AI-use statement

**Paper:** The Bannai–Munemasa–Venkov lattice method for strongly regular graphs: a uniform discriminant-form condition and new nonexistence results

**Author and sole contributor:** Anton Kovaľ (ORCID 0009-0009-3182-6626), VÚB banka, Bratislava, Slovakia. No AI system is a contributor or an author.

## How AI systems were used

Taken from the paper's acknowledgements and verification sections, which state these facts in full.

- Claude (Anthropic), in Claude Code sessions in the author's repository under the author's direction, produced the derivation, the hand proofs of the section on hand proofs (in their original form), the implementation V1 and the table scans, and drafted the text, including the parity corollary in its general form and its scan.
- A separate Claude session on a different model (Claude Fable) carried out a blind adversarial audit: it re-derived the obstruction from first principles before reading the derivation, wrote the independent decider V3, computed the actual discriminant forms of 254 real graphs as controls, and found the W(3)/Q(4,3) example of the paper.
- Codex (OpenAI's coding agent) independently reviewed the uniform lemma and the two main hand proofs, found a missing step in one lemma and supplied its repair, and wrote the fourth implementation V4.
- A further Claude Fable session made the literature check of the novelty section, and a fresh Claude Fable session acted as referee of the draft.

## Role of the author

The author directed the work, coordinated the AI sessions, checked the results and the mathematics, and is responsible for all content. No step of the argument is accepted on the judgement of an AI system: each claim is either proved in the text or is a finite computation that can be rerun from the deposited data archive.

## Records in this archive

These are the written outputs (reports) of the reviewing, auditing and refereeing AI sessions, copied unchanged from the author's working repository. File paths cited inside them are repository-relative; most of the cited scripts and logs are in the Zenodo data archive of the paper. Full session transcripts are not included.

- `referee_milgram_fable_2026_10_09.md`: referee report (Claude Fable, fresh session, own code)
- `audit_milgram_obstruction_fable_2026_10_09.md`: blind adversarial audit (Claude Fable)
- `codex_review_milgram_v2_2026_10_09.md`: review of the draft (Codex, OpenAI)
- `codex_audit_milgram_obstruction_2026_10_09.md`: audit of the lemma and hand proofs (Codex, OpenAI)
- `novelty_milgram_obstruction_2026_10_09.md`: literature / novelty check (Claude Fable session)