Results ledger
Each note starts in plain language, then gives the claim, table, method, checker, limits, and baseline sources.
A Kesten-renewal certificate proves μ(Z²) ≥ 2.6273856, above Jensen's 2.625622 bound; the result was merged into Optimization Problems.
2.6273856 rigorous lower bound for μ(Z²)The certified side length 2.891999838304098 came from a different geometric basin than the familiar eight-corner construction.
2.8919998 certified container sideThe dated run spans autocorrelation, uncertainty, prime-number approximation, and two high-dimensional kissing configurations; later submissions have moved every leaderboard.
5 first-place milestones in four daysThe constructions independently reconstruct five cases of a family published by Korže and Vesel in 2012; they are useful witnesses, not a new theorem.
58–110 five explicit optimal witnessesA base-89 construction certifies a lower bound of 1.187326127925948, improving the merged value 1.183512932421861510... while remaining below every known upper barrier.
1.1873261 accepted 2026 lower boundA balanced monotone Boolean function on 18 variables moves the best-known lower bound from 6.514326913930565372 to 6.521845710923046575.
6.5218457 certified lower bound for C71More than 11,000 new verified table records across dimensions 3–32; 41 high-margin configurations were retained as explicit coordinate files.
11,000+ new verified recordsThe point is precise: larger explicit DNA codebooks under stated constraints; two small cells are proven optimal.
16 larger DNA codebooksThe result is about arithmetic cost, not a GPU speed claim: fewer transform additions under the standard Winograd counting convention.
289 adds for F(4x4,3x3)The improvements come from exact per-side straight-line programs, plus careful checks against the field's own reducers.
45 additive-complexity recordsThe report is deliberately narrow: it names the regimes that win and the regimes that lose.
2-4.5x small batched matmulThe output is raw circle coordinates, and the checker recomputes every overlap and wall clearance.
9 unit-square records beatenThe claims handle Friedman's displayed-plus truncation rule explicitly.
17 verified entriesA trusted table had source improvements that had not propagated into the derived cells. Numaro found the gap, built the witnesses, and checked the counts.
6,440 blocks savedThis is the array version of the covering-design result: a public snapshot lagged construction catalogues, so Numaro built the actual arrays and checked every required interaction.
40 array table improvementsThe object is simple: put as many 1s as possible in a 0/1 matrix without creating a 3 by 3 all-ones submatrix. Numaro found stronger matrices across the frontier.
31 lower bounds raisedThese are frontier extensions, not beats of AlphaEvolve's published cells.
13 first-known valuesThe search evolved the construction algorithm itself, but it did not beat AlphaEvolve's published n=64 or n=100 values.
54 first-known grid valuesThe main table mostly held. The win is one clean propagation cell, plus an exact fill of a less-policed object.
442 exact DCW valuesThis is a checking result, not a record beat.
19 exact certificatesThe result is explicitly about a computable proxy objective, not biological expression.
90/90 dominations reverified