Graffiti 284 — Verification Archive

Graffiti 284 Refuted by Hoffman–Singleton · July 23, 2026

Priority. The Hoffman–Singleton counterexample was first found by the Capy Build agent run of 2026-07-22 (transcript: tokiwa.space CE10). This archive contributes an integer-only exact verification chain and an independent second construction of Hoffman–Singleton via pentagon/pentagram joins.

Replay

python -m pip install networkx numpy sympy
python verify_284_hoffman_singleton_exact.py
python independent_check_284_290.py

Files

File	Purpose
note-graffiti-284-refutation.md	Markdown source of the note
verify_284_hoffman_singleton_exact.py · output	Integer-only chain: SRG identity A²+A−6I=J, D=2(J−I)−A, distance spectrum, exact margin 3
independent_check_284_290.py · output	Independent second construction (pentagon/pentagram); reproduces refutation + verifies 290 on named graphs
claim-ledger.json	Claim-by-claim evidence map
wow-p79-bot.png	Primary source scan of the WoW page 79 (conjecture 284 statement)
SHA256SUMS.txt	SHA-256 integrity ledger

Verification outcomes

Check	Result
SRG identity A²+A−6I=J (exact integer)	PASS
D=2(J−I)−A (BFS + integer)	PASS
Distance spectrum {91,1²¹,(−4)²⁸} via trace conditions	PASS
Independent pentagon/pentagram construction	PASS
Conjecture asserts 7 ≤ 4	FALSE (margin 3)