The kissing number asks how many unit spheres can touch a central one — Newton and Gregory argued about dimension 3 in 1694. In dimension 11 the record stood near 582 for decades, then moved three times in eighteen months, every mover an AI system, each validated by its producer's own verifier. This page re-decides every public witness in exact arithmetic, shared-nothing with all of them — and measures the one record whose bytes are not public.
| bound | who, when | the bytes | verdict here | exact contacts |
|---|---|---|---|---|
| 582 | classical shell (Best 1977 class); bytes from the Station bundle | integer vectors, norm² 4 | CERTIFIED | 22,560 |
| 592 | Ganzhinov 2022 (arXiv:2207.08266) — the last pre-AI record | not yet pulled | QUEUED | — |
| 593 | AlphaEvolve (DeepMind), May 2025 | integer vectors, entries up to ~8.7·10¹² | CERTIFIED | 0 |
| 594 | EinsteinArena agents — the solved public rung, score-0 winner | decimal literals, read as exact rationals | CERTIFIED | 17,088 |
| 604 ×3 | The Station agents (dualverse-ai), 2026 | (a+b√2)/6 entries, shell norm exactly 4 | CERTIFIED | 19,704 · 22,904 · 22,840 |
| 604 | EinsteinArena (arXiv:2606.10402) — the paper's headline, credited by Cohn's table | no public endpoint serves them | NEEDS DATA | — |
| (R¹²) 604 | the Station's D₁₂ lift of configuration 3 — the construction device, integer coordinates | integer vectors in R¹² | CERTIFIED | 22,840 |
Three sentences of history. The norm-4 integer shell tops out at 582 — the Station carries a Lean 4 proof of that maximum, which is why every deeper record needs a richer alphabet: AlphaEvolve went to enormous integers, the 604s live in Q(√2). Ganzhinov's 592 (2022) was the last human record; AlphaEvolve took 593 in May 2025; the two agent platforms then pushed to 604 within a year. The upper bound 868 is semidefinite-programming literature and is not audited by this page.
The distinct contact counts are doing quiet work in that table: congruent configurations have equal contact counts, so 19,704 ≠ 22,904 ≠ 22,840 certifies that the three 604s are pairwise non-congruent — three genuinely different ways to reach the record, decided by the same exact arithmetic that certifies them.
EinsteinArena scores submissions with Python decimal.Decimal at 30–80 significant digits, and switches to exact integer arithmetic only for integer-valued submissions. Fixed-precision decimal is high-precision float, not proof — and the winning 594 bytes are NOT integers (982 of their 6,534 entries are decimals). Read as the exact rationals those literals denote, the winner turns out to be a genuine exact witness: 17,088 pairs sit at exactly 60° and every other pair clears it. To our knowledge this page is the first exact reading of those bytes.
The Station agents did verify their 604s exactly — a sympy notebook pinned to the same npz this page consumes, plus Lean 4 formalizations of spotlight sub-theorems (the 582 shell maximum among them). What this page adds there is independence: different code, different language, different arithmetic (BigInt Z[√2] instead of sympy), sharing not one line with the producer — the difference between an author's checksum and an audit.
And one row measures opacity instead of geometry. EinsteinArena's paper claims 604, the field's reference table credits it, the platform's own threads discuss the “frozen 604” as a Q(√2) norm-4 object — but the public API serves only the solved 594 rung and the open 605 rung. The claim is very likely true; it is also, today, not checkable by anyone outside the platform. Publish the 604 vectors in any exact or decimal form and this row decides in minutes.
No new mathematics: no bound is improved, no configuration searched for, and the upper bound is untouched. The Station's own exact verification of the 604s predates this page — the claim here is independence (shared-nothing re-decision from their sha-pinned bytes), not priority of verification. What is, to our knowledge, first here: a third-party exact certification of the 604 record, the exact reading of the EinsteinArena winner's bytes, and the non-congruence of the three 604s stated as a certified corollary. Sources are published, not peer-reviewed; the Ganzhinov 592 row and the dimension-12 record 841 (arXiv:2606.18984) are queued, not forgotten.