# AI-use statement

**Paper:** Strongly regular graphs on 306, 400, 576, 784 and 1296 vertices from multi-orbit coset fusion and Bush-type Hadamard matrices

**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) designed and ran the two-orbit search with its controls and rebuilt the hits (one Claude Code session); a separate session, coordinating the project, re-verified the hits with independent checkers; a third session found the explicit constructions, the symmetric Hadamard matrix construction and its proof, wrote the builders, the standalone verifier and the remaining computations, did the literature check, and drafted the first version of the paper. These sessions used the same model family, so their agreement is evidence of correct computation but not an independent mathematical review.
- The first version was reviewed by a referee session of a different model (Claude Fable), which re-derived the proofs, re-implemented every computation from scratch, and pointed out the closest prior work, the generalization to all Hadamard orders and gaps that were corrected. A further session compared the graphs with known constructions and wrote the corresponding computations.
- The second version was reviewed in a second referee round by a Claude Fable session with its own code (coclique counts, exact-cover result, own SAT model for n=12, symmetry-breaking argument); its citation and notation corrections are in version 3, which is the version deposited.

## 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_new_srgs_multiorbit_fable_2026_10_11.md`: referee report, round 1 (Claude Fable)
- `referee_new_srgs_multiorbit_v2_fable_2026_10_12.md`: referee report, round 2 (Claude Fable)
