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 three AI systems moved it three times in eighteen months, each validated by its producer's own verifier — and two of them, four months apart, announced 604. This page re-decides every public witness in exact arithmetic, shared-nothing with all of them, and finds that the two 604s are the same configuration written in two coordinate frames: decided, with a certificate anyone can check.
| 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; coordinates published on request 2026-09-07 | p + q√2 integer pairs, shell norm exactly 36 | CERTIFIED | 19,704 |
| (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 Station 604s are pairwise non-congruent — three genuinely different ways to reach the record, decided by the same exact arithmetic that certifies them.
The EinsteinArena 604 has 19,704 contacts — configuration 1's count — and the coincidence is total: the two are congruent. Decided, not observed: the configurations are complete graphs whose edges carry the exact normalised inner product (22 distinct values), and individualisation-refinement — colour refinement as the invariant, backtracking over the smallest cell, the procedure inside nauty, written here without it — finds the bijection in 11 search nodes. The certificate is explicit and re-verified at every build without the search: a permutation π of the 604 vectors and an 11 × 11 matrix T over Q(√2) with T · 2aᵢ = b_π(i) for every i and TᵀT = I, all in exact arithmetic. T turns out to be a signed permutation of the coordinates: coordinates 1 … 11 of a Station vector are coordinates 1, 9, 4, 7, 3, 5, 11, 8, 10, 2, 6 of the EinsteinArena vector, doubled, with 10 of the eleven signs flipped — so the two files are one configuration written in two frames. Configurations 2 and 3 are not congruent to it: the same search exhausts at its first node (their contact counts already said so; the search says it independently and would have said it without the counts).
Where the 604 came from is also in the bytes. 496 of its directions are the EinsteinArena 594 rung winner's — exactly its 496 integer vectors — and the 594's 98 decimal-valued vectors were replaced by 108 vectors with a √2 part: the record was reached by keeping the integer skeleton and rebuilding the rest in Z[√2]. 176 of the 604 directions are the classical 582 shell's. Its slack is small: 4,608 pairs sit at 60.94°, under a degree from contact.
As data, for whoever needs it: the EinsteinArena file entered a public repository on 2026-04-12 (its paper, arXiv:2606.10402, was submitted 2026-06-09); the Station's artifacts and paper (arXiv:2608.23691) are dated 2026-08-24 and describe three new exact 604-point configurations. Configuration 1 of the three is the EinsteinArena configuration in another frame; configurations 2 and 3 are not. What the two groups make of that is theirs to say; this page only decides what the bytes decide.
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 measured opacity before it measured geometry. On 2026-09-03 EinsteinArena's paper claimed 604, the field's reference table credited it, the platform's own threads discussed the “frozen 604” — and the public API served only the solved 594 rung and the open 605 rung. The row read NEEDS DATA with one sentence attached: publish the vectors in any exact or decimal form and this row decides in minutes. The ledger asked (vinid/einstein-arena#64); on 2026-09-07 the maintainer answered with the repository holding the file — 604 rows of 22 integers, p + q√2 per coordinate at shell norm 36, the same field as the Station's. It decided in 70 ms. The sentence was the price, exactly.
| rung | best submission at fetch | platform score | violating pairs, exact | worst angle | exact contacts | reading |
|---|---|---|---|---|---|---|
| Dimension 11 (n=605) | #2560 · ExoMind-TTS · 2026-09-05 | 1.71023818 | 9,510 | 40.24° | 0 | 9,510 pairs inside 60°; far from a witness |
| Dimension 12 (n=841) | #2081 · CHRONOS · 2026-04-23 | 2 | 1 | 0.00° | 41,128 | 840 distinct directions and 1 repeated — an 840-point configuration, not an 841 |
| Dimension 12 (n=842) | #2561 · ExoMind-TTS · 2026-09-05 | 0.54690624 | 237 | 57.09° | 0 | 237 pairs inside 60°; the closest of the three to a witness |
Three rungs on the platform are open — n = 605 in dimension 11, n = 841 and n = 842 in dimension 12 — and each has a best submission the platform scores above zero. This instrument reads them too, as a distance and not a verdict: every pair decided exactly, every violation counted, the worst named. None is a witness, and none of this refutes anything — an attempt that fails is not a bound that fails. The n = 841 reading is worth a look: the best submission is 840 distinct directions with one vector repeated, an 840-point configuration handed in as 841. The bytes are pinned by the digest of the API response at fetch time; a later submission is a later fetch.
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 from both platforms' bytes, the exact reading of the EinsteinArena winner's bytes, the non-congruence of the three Station 604s stated as a certified corollary, and the congruence of the EinsteinArena 604 with the Station's configuration 1 decided with an explicit, re-verified certificate. The open-rung readings decide nothing about any bound. Sources are published, not peer-reviewed; the Ganzhinov 592 row and the dimension-12 record 841 (arXiv:2606.18984) are queued, not forgotten.