Claimed Search scaffold

Épi agent reports 120 record bounds and constructions, with released certificates

Bake AI's Épi agent, running GPT-5.6 Sol and GPT-6 Astra against fixed verifiers, reports 20 improved numerical bounds and 100 record constructions, including certificates that the Cohn–Elkies sphere-packing bound cannot be sharp in dimensions 10 and 11, an upper bound of 4.29569 on Klarner's polyomino growth constant against 4.5238, and a computer-assisted extension of Tuza's conjecture for a class of split graphs.

Lab: Bake AI
Model: GPT-5.6 Sol and GPT-6 Astra in the Épi agent
Field: Mathematics
Date: 2026-10-18
Human collaborators: Yue Huang, Zhangchen Xu, Zichen Chen

Sources

What was found

Épi keeps a persistent research history across model sessions, branches and reviews its own work, and has each output scored by a fixed verifier, accepting an improvement only when it is feasible and clears a set margin over the literature value. The results repository lists 12 families of numerical bounds and 8 of constructions. The headline mathematics: dual certificates giving lower bounds on the Cohn–Elkies linear programme of about 0.0564 and 0.0577 in dimensions 10 and 11, above the known upper bounds on sphere-packing density there, so the method cannot be sharp in either; the bound $\lambda \le 4.29569$ for Klarner's constant, whose previous record was 4.5238 and whose empirical value is about 4.06; an interval for the n-queens constant about 84 times narrower than before; and a proof that $\tau_\triangle(G) \le 2 \nu_\triangle(G)$ for split graphs with an eight-vertex clique part and at most three active neighbourhood types, up from two. The construction records are mostly circle and ball packings, 46 of them circles in a quarter disk.

Novelty check

Each record is stated against a cited prior value, and the ones checked hold: the Klarner comparison is arXiv 2511.00461, which gives $\lambda \le 4.5238$ , and the Tuza base case is Zeng's two-type theorem with the threshold-graph case of arXiv 2105.09871. arXiv, 2026-10-29: abs:"Cohn-Elkies" AND abs:"sharp" returned 4 records and abs:"Tuza" AND abs:"split graphs" returned 5, none settling these cases before this paper; abs:"n-queens" AND abs:"constant" returned 3, the earlier ones being the 2021 asymptotic count and a 2026 statistical-mechanics estimate. Within this registry 2025-11-03-alphaevolve-at-scale and the packing entries record comparable search-scaffold records, none for these problems; 2026-10-02-squares-in-circle-packings concerns a different packing problem.

Caveats and known objections

Entered at claimed: a technical report from the developer, not refereed, and no mathematician outside the authors is on record as having checked any result. The certificates are what lifts it above a press claim, and they vary. Only the Tuza result ships a checker; this registry wrote its own from the proof's description and confirmed the finite certificate, but that does not cover the proof's prose steps, the truncation lemma or Zeng's two-type theorem, an unrefereed preprint. The Cohn–Elkies certificates are exact discrete measures checked, the README says, by a separate implementation, and the Klarner certificate is an exact recurrence and supersolution, but neither ships a verifier and neither has been rechecked here. The Klarner bound deserves the most care: it closes about half the gap between the previous record and the empirical value in one step, after five decades of small gains. The paper says published methods and constructions supplied starting points for several campaigns, so some records refine human work rather than start fresh. Autonomy is search-scaffold, as for AlphaEvolve: humans chose the problems, wrote the verifiers and set the margins and budgets, and the agent searched inside that loop.

Independent checks

whataifound.org (independent recomputation, Python): Wrote a checker from the proof's description, sharing no code with the repository. It regenerates the 872 classes of three neighbourhood types, splits them into 35 nested, 277 handled by the clique-cut argument and 560 remaining, confirms the certificate's profiles are exactly those 560, and checks all 18,444 boxes: each cover meets every triangle at the upper corner, each packing is edge-disjoint at the lower corner with $|F| \le 2|P|$ , and the boxes cover every multiplicity vector in $[0, 28]^3$ . Does not check the analytic steps.

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Entry history (1 event)

2026-10-29AddedEntered the registry graded Claimed and Search scaffold.

Entries are never deleted. A grade that does not hold up is downgraded on the record, with the reason beside it.

Graded claimed for verification and search scaffold for autonomy. What these mean.

Cite this entry

Plain text

whataifound.org. (2026). Épi agent reports 120 record bounds and constructions, with released certificates. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-10-18-epi-autonomous-research-records

BibTeX

@misc{whataifound-bakeai-2026-records,
  title        = {Épi agent reports 120 record bounds and constructions, with released certificates},
  author       = {{whataifound.org}},
  year         = {2026},
  howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
  note         = {Result by Bake AI. Verification: Claimed. Autonomy: Search scaffold.},
  url          = {https://whataifound.org/finding/2026-10-18-epi-autonomous-research-records}
}

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