cert-machine · the monthly ledger

Decided, September 2026

Every published claim this machine decided in September 2026, read from the register: what held, what did not, and what went wrong, in one closed vocabulary. The page is a dated diff of the records — nothing on it is typed.

The month is still running: this is September 2026 as of 2026-09-29 (git c56ab5f), and the page is rebuilt with every site build until the month closes. A row belongs to the month in which its deciding record first held it (the first commit, by git's pickaxe on the record). 18 claims were decided before September 2026 and are on the claims desk, not here.

tl;dr
  • The finding. 36 published claims decided in September 2026: 26 CERTIFIED, 4 REPAIRED, 4 MIXED, 1 PARTIAL, 1 NEEDS DATA. 10 of them name something that went wrong — 4 tolerance witness, 1 clause missing from formal statement, 1 not from the published data, 1 arithmetic slip, 1 not the optimum, 1 wrong quantity, 1 data not public; the other 26 hold as printed. 4 rows are one audit of many items (a dataset's keys, a benchmark's counts); the row counts once and names its most frequent defect.
  • The mechanism. Each row is derived from the record that decided it; a claim with no record gets no row. CERTIFIED and REFUTED are theorems; PARTIAL, MIXED, REPAIRED and NEEDS DATA are compositions of the three verdicts, named on the claims desk.
  • Check it. node tools/run-claims-ledger.js && node tools/build-report-monthly.js — the register is certs/claims-ledger.json.
decided this month
36
26 CERTIFIED, 4 REPAIRED, 4 MIXED, 1 PARTIAL, 1 NEEDS DATA.
held as printed
26
The row names nothing that went wrong. Most published claims hold, and the ledger says so first.
something went wrong
10
4 tolerance witness, 1 clause missing from formal statement, 1 not from the published data, 1 arithmetic slip, 1 not the optimum, 1 wrong quantity, 1 data not public.
decided before
18
Carried on the claims desk; the register holds 55 rows in all.
§1 · the rows

What was decided, in the order it was decided

recordedclaimclaimantverdictwhat went wrongwhere
2026‑09‑03K(11) >= 593 — the May 2025 recordAlphaEvolve (Novikov et al., DeepMind)CERTIFIED—the record
2026‑09‑03K(4) >= 24 — exact value, Musin 2003classical (generated here)CERTIFIED—the record
2026‑09‑03K(8) = 240 — exact value, Levenshtein / Odlyzko–Sloane 1979classical (generated here)CERTIFIED—the record
2026‑09‑03K(11) >= 594 — the solved n=594 rung, score-0 winner (solution #1492)EinsteinArena agents (Bianchi et al. platform)CERTIFIED—the record
2026‑09‑03K(11) >= 604 — the paper's headline result, credited by Cohn's reference table (2026-06-22)EinsteinArena (Bianchi, Kwon, Pappu, Zou — arXiv:2606.10402)CERTIFIED—the record
2026‑09‑03K(11) >= 592 — the 2022 record the AI ladder started fromM. Ganzhinov (arXiv:2207.08266, Highly symmetric lines)QUEUED—the record
2026‑09‑03K(11) >= 604 — configuration 1 of threeThe Station agents (dualverse-ai)CERTIFIED—the record
2026‑09‑03K(11) >= 604 — configuration 2 of threeThe Station agents (dualverse-ai)CERTIFIED—the record
2026‑09‑03K(11) >= 604 — configuration 3 of threeThe Station agents (dualverse-ai)CERTIFIED—the record
2026‑09‑03construction device: 604 integer D12 vectors whose oblique shadow is configuration 3 (also a valid 604-point direction set in R^12)The Station agents (dualverse-ai)CERTIFIED—the record
2026‑09‑03K(11) >= 582 — the pre-2022 record shell, integer norm-4 maximum (Lean-proved maximal by the Station)classical (Best 1977 class; bytes from the Station bundle)CERTIFIED—the record
2026‑09‑08f ≥ 0 as 600 values on [−1/4, 1/4]: C₁ ≤ 1.50529397AlphaEvolve (arXiv:2506.13131)CERTIFIED—the record
2026‑09‑08f ≥ 0 as 1319 values on [−1/4, 1/4]: C₁ ≤ (no value printed for this file)AlphaEvolve V2 (arXiv:2511.02864)CERTIFIED—the record
2026‑09‑08f ≥ 0 as 30000 values on [−1/4, 1/4]: C₁ ≤ 1.50286286Together AI agents (the EinsteinArena repository)CERTIFIED—the record
2026‑09‑08f ≥ 0 as 30000 values on [−1/4, 1/4]: C₁ ≤ 1.50286290TTT-Discover (arXiv:2601.16175)CERTIFIED—the record
2026‑09‑08n = 21 circles in a rectangle of perimeter 4 (bounding box w + h ≤ 2), no overlaps: Σ r = 2.3658321334AlphaEvolve V2 (Georgiev, Gómez-Serrano, Tao, Wagner — arXiv:2511.02864)CERTIFIED—the record
2026‑09‑08n = 21 circles in a rectangle of perimeter 4 (bounding box w + h ≤ 2), no overlaps: Σ r = 2.3658323759Together AI agents (the EinsteinArena repository)REPAIREDtolerance witnessthe record
2026‑09‑08100 rows of 20 weights → (edge density, triangle density) points; the platform's envelope score = -0.712494AlphaEvolve V2 (arXiv:2511.02864)CERTIFIED—the record
2026‑09‑08100 rows of 20 weights → (edge density, triangle density) points; the platform's envelope score = -0.712256Together AI agents (the EinsteinArena repository)CERTIFIED—the record
2026‑09‑0870 coefficients ±1: C⁺ = max_{|z|=1} |g(z)| / √71 = 1.340925AlphaEvolve V2 (arXiv:2511.02864)CERTIFIED—the record
2026‑09‑0870 coefficients ±1: C⁺ = max_{|z|=1} |g(z)| / √71 = 1.280932Together AI agents (the EinsteinArena repository)CERTIFIED—the record
2026‑09‑08n = 14 points, min triangle area / convex-hull area = 0.0278355715AlphaEvolve V2 (arXiv:2511.02864)CERTIFIED—the record
2026‑09‑08n = 14 points, min triangle area / convex-hull area = 0.0278355805Together AI agents (the EinsteinArena repository)CERTIFIED—the record
2026‑09‑0812 unit hexagons inside a hexagon of side 3.9419123, no overlaps, all inside: score = the outer sideAlphaEvolve V2 (arXiv:2511.02864)CERTIFIED—the record
2026‑09‑0812 unit hexagons inside a hexagon of side 3.9416523, no overlaps, all inside: score = the outer sideTogether AI agents (the EinsteinArena repository)CERTIFIED—the record
2026‑09‑08n = 16 points, (max distance / min distance)² = 12.889266AlphaEvolve (Novikov et al. — arXiv:2506.13131)CERTIFIED—the record
2026‑09‑08n = 16 points, (max distance / min distance)² = 12.889230Together AI agents (the EinsteinArena repository)CERTIFIED—the record
2026‑09‑08a step function h with 95 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380924AlphaEvolve (arXiv:2506.13131)REPAIREDtolerance witnessthe record
2026‑09‑08a step function h with 51 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380927J. K. Haugland (arXiv:1609.08000)CERTIFIED—the record
2026‑09‑08a step function h with 600 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380871Together AI agents (the EinsteinArena repository)REPAIREDtolerance witnessthe record
2026‑09‑08a step function h with 600 steps, 0 ≤ h ≤ 1, Σh = n/2: upper bound 0.380876TTT-Discover (Yuksekgonul et al. — arXiv:2601.16175)REPAIREDtolerance witnessthe record
2026‑09‑09finite-time blowup for the 3D Navier–Stokes equations with finite energy (Clay alternatives C and D)OpenAI (2026-09-08)PARTIALclause missing from formal statementthe record
2026‑09‑15the exceedance counts printed for the environmental-contour benchmark's 150 contoursthe benchmark's contributing teams (Haselsteiner et al., Ocean Eng. 2021)MIXEDnot from the published datathe record
2026‑09‑21the worked solutions of GSM8K's 8,792 test and train keysGSM8K (Cobbe et al., 2021)MIXEDarithmetic slipthe record
2026‑09‑22the time-horizon coefficients and 50% horizons METR prints for 23 modelsMETR (Time Horizon 1.1)MIXEDnot the optimumthe record
2026‑09‑27the 15 Hs marginal fits the benchmark teams printed for buoys A, B and Cthe environmental-contour benchmark's contributing teamsMIXEDwrong quantitythe record
2026‑09‑28the annual-maximum Hs fits of 20 printed rows for five South Atlantic lease areasBhaskaran et al. (Energies 16, 6935, 2023)NEEDS DATAdata not publicthe record
§2 · the vocabulary

What went wrong, in words

The vocabulary is closed: 12 kinds, defined once in tools/run-claims-ledger.js. A defect that fits none of them refuses the register until the vocabulary is decided on, never "other".

§3 · not here

What this page does not count