Épi posts 120 verifier-backed records across sessions of autonomous maths research

Épi's wager is that the investigation can remember itself when the session ends.

On 20-21 October 2026, Bake AI introduced Épi as a self-evolving framework for autonomous research, and the accompanying paper (arXiv:2610.24944) spelled out the mechanism: persistent research history, hierarchical memory, branching, independent review, long-running sandbox experiments, and a verifier that stays fixed while the agent changes strategy. The claimed haul is 120 record-setting results plus one theorem extension, produced in verifiable environments on Bake's Breadboard infrastructure.

Persistence across sessions is the product claim

Épi's authors argue that frontier models already have enough capability to move some research problems, and that the missing piece is a process that keeps verified wins, failed approaches, and unfinished questions available when a session ends. Within an investigation, the environment configuration and verifier are frozen so every candidate faces the same test. Across investigations, verified advances can change the starting point and reshape the environment.

Agents develop methods as evidence accumulates, revisit earlier ideas, and take independent review that challenges assumptions. Breadboard runs many isolated sandboxes in parallel so long experiments can continue while other branches explore. That package is the claimed novelty relative to single-session coding agents that forget the trail.

One hundred twenty records, one Tuza case, and a coding side path

Bake's table groups 20 numerical bound records across 12 families, 100 construction records across eight families, and a Tuza conjecture proof for split graphs with an eight-vertex clique part and at most three triangle-active neighbourhood types with arbitrary multiplicities. A problem family groups related instances; each distinct instance or parameter setting counts once; repeated improvements to the same instance contribute one record.

Standout numerical claims, as stated by Bake and the paper abstract, include an enclosing interval for the n-queens constant narrowed to width 3.9367×10⁻⁹, about 84× narrower than the published Nobel-Agrawal-Boyd interval, with exact feasibility checks on millions of projected coordinates. Klarner's polyomino growth upper bound moved from 4.5238 to 4.29569 by extending a recurrence to 1,186 neighbourhood types. The quartic Feigenbaum attractor dimension interval is more than 3.6 million times narrower than the Burbanks-Osbaldestin-Thurlby rigorous enclosure. Cohn-Elkies LP lower bounds in dimensions 10 and 11 exceed known packing-density upper bounds, so the method cannot be sharp even at its limit (gaps of about 0.35% and 1.92% respectively).

Bake also lists MAX-4-CUT hardness-ratio tightening, Spencer discrepancy raised via an exhaustive 8×8 sign certificate, Ramsey multiplicity c4,5 on 1,024 vertices, quantum-capacity noise-threshold lifts on two channels, and a waterund36 global lower bound within about 0.00001001 of a known feasible value.

A 56-minute session on packing 34 regular pentagons into an equilateral triangle produced 17 successive verified improvements from Hyra's reference arrangement, cutting triangle side length from 12.98141 to 12.97564. The first two candidates carried most of the gain; fifteen later submissions still cleared the same verifier. Construction records overall span eight families, including 46 circle packings in a quadrant and 36 ball packings in four dimensions, scored against Packomania, Friedman's pages, CVRPLIB, and related registries per Bake. On the algorithmic side, Épi-turbo, a lighter coding configuration, reports a 5.4% higher total score than Codex on 30 FrontierOR tasks (vehicle routing, scheduling, production planning) at 64% of Codex's model cost, using the same underlying model and reasoning effort.

Bake also publishes a negative case: seven hours on flat polynomials, 31 approaches, 20 scored candidates, zero improvements. The tree of abandoned branches stays in the research history. That failure log is part of the product claim. Persistence without salvageable dead ends would be marketing amnesia.

Fixed verifiers make comparisons local; vendor benches stay vendor benches

Inside each investigation, freezing the verifier is the right honesty move: improvement means beating a stated reference under a stated check. Across families, "120 records" aggregates very different kinds of progress (tighter upper bounds, narrower enclosures, higher noise thresholds, new constructions). Readers should score families individually rather than treat the sum as a single scientific IQ.

The Cohn-Elkies results deserve a separate fairness note. Crossing a packing-density upper bound with a certified lower bound on the LP optimum shows a method ceiling. It does not exhibit a denser packing. Bake is clear that dimensions 8 and 24 remain the exact Cohn-Elkies successes, and that closing the new gaps needs a stronger method.

The FrontierOR comparison is same-model, same-effort against Codex, which is fairer than a cross-lab bake-off, and still sits inside Bake's harness and cost accounting. Related-work notes on Bake's page say most reported results used OpenAI GPT-5.6 Sol and GPT-6 Astra. Independent groups have not yet published a reproduction of the full 120-record ledger from the paper's artifacts alone.

Open-ended science without a grader remains outside the claim

Épi's design assumes a reliable way to check whether a candidate is valid and improves on a reference. That fits bounds, constructions, and many OR tasks. Bake's own roadmap says the next evaluations will ask how efficiently Épi explores approaches, whether it can combine discoveries, and how far it can move past tasks whose objectives are already defined. Open-ended question formation, contested empirical graders, and programmes where the verifier must change mid-stream remain outside the published haul. How much of the gain is persistence versus raw model strength versus Breadboard concurrency is not separated in a public ablation that outsiders can rerun cold.

Paper and Bake post are public; full reproduce bundles vary by family

Primary materials are the Bake research article and arXiv:2610.24944. Bake publishes per-family numerical tables and describes certificates (exact dual certificates for Cohn-Elkies non-sharpness in dimensions 10 and 11; exact recurrence certificates for Klarner). The degree to which every construction ships as a one-click reproduce package is family-dependent and should be checked against the paper supplements before claiming independent verification.

Use Épi as a pattern for verifier-backed research loops

Labs building science agents should copy the frozen-verifier discipline and cross-session memory before they copy the marketing total. Maths and OR groups can mine the published bound tables and Tuza case for methods worth re-checking. Buyers evaluating "autonomous research" vendors should ask which problems have a fixed grader, how records are counted, and whether failed branches remain inspectable.

Do not read Épi as proof that AI has replaced mathematical taste. The Tuza extension and Cohn-Elkies limits are interesting precisely because they still need human-readable arguments attached to machine search.

Épi sits with the 2026 wave of agents that treat research as a multi-session system

Relative to single-shot paper-writing agents and coding copilots, Épi's lineage is closer to systems that keep experiments running and score them under a stable check. It pairs naturally with harness-level recursion work elsewhere this week: those rewrite the outer loop; Épi insists the inner loop survive session death. The next decisive artifact is an independent reproduction of one numerical family end to end, or a public Breadboard-scale rerun log that outsiders can audit.