bibkey: ahmedkunjwal2026quasiprocess authors: Nasra Daher Ahmed, Ravi Kunjwal year: 2026 title: “Characterizing unitaries via quasi-process functions” doi: 10.48550/arXiv.2610.00579 url: https://arxiv.org/html/2610.00579v1 claim: “Conjecture V.1 asks for an all-direction partition into maximal cliques of every mixed-alphabet Hamming graph with more than three coordinates and all alphabet sizes at least two.” strata_touched:

• D5/S3/Combinatorics/Hamming/HammingMultipartitePartition license: citation-only triage: anchor

Mixed-alphabet Hamming clique partitions

Verified locator

DOI: 10.48550/arXiv.2610.00579 URL: https://arxiv.org/html/2610.00579v1

Ahmed and Kunjwal, arXiv:2610.00579v1, Section V.2, Conjecture V.1. Definition V.1 fixes the vertex set as a product of independent finite alphabets and adjacency as disagreement at exactly one position. Section V uses alphabet sizes at least two. The paragraph before Section V.1 defines genuine multipartiteness by the occurrence of every coordinate direction.

The source attributes the binary-alphabet case to J. Erde, Matchings in the hypercube with specified edges, arXiv:2404.03950. The internal binary construction does not carry a novelty claim. The new result addresses the complete mixed-alphabet statement. These notes paraphrase the mathematical contract; no source proof code or licensed prose is transferred.

Accessible-source boundary

Preregistration issue #13221 records the accessible literature check: the source lists only v1 and labels the assertion a conjecture; INSPIRE and OpenAlex report zero citations; the published project problem page and the searched formal-conjectures snapshot contain no exact target. MathDB was inaccessible with HTTP 403, Semantic Scholar with HTTP 429, and search engines were unavailable. This establishes only absence in the searched scope, not exhaustive novelty or priority.

The current source fetch returned HTTP 200 and has SHA-256 fc6ddc3bd0b39de98867fc4cad646a2c1e6725c6e460d5ca3c0cfabe67715106, matching the preregistered source identity. The quantum-circuit and quasi-process interpretations are not part of the Lean graph theorem.