LLM Tech Briefing (Oct 26–28, 2026)

Overview

The news from October 26 to 28 falls into three threads. First, AI-originated mathematics has reached the "machine-checkable" stage: OpenAI and Anthropic each announced that their internal models independently refuted the Exponential Time Hypothesis (ETH), with Lean formal proofs attached; Axiom announced that AI agents completed a Lean formalization of the Classification of Finite Simple Groups in 24 days. Second, the range of open models keeps widening: from LFM3, an on-device model of about 1 GB, to the 560B-parameter Ling-3.1, to Unlimited-OCR-2, a 3B document model that parses a whole book in one request. Third, both evaluation and training are probing "implicit requirements": Cognition's FrontierCode 2.0 grades by "would a maintainer merge this," and the top score is only 45.5%; two widely discussed papers address "supervise only grounded actions" and "put a price on padding for points."

A caveat: all scores here are self-reported by vendors or authors, and as of October 27 the AI mathematics results had not been independently confirmed by peers. A GLM-5.5-Flash listing seen in the community had empty parameters and no official announcement, so it is not treated as fact in this issue.

1. AI-Originated Mathematics: From "Solving Problems" to "Delivering Machine-Checkable Research"

1. OpenAI: three results, three release strategies

What it is. On October 26, OpenAI announced three results produced by its internal models: a proof of Sogge's local smoothing conjecture in all dimensions (which implies the Kakeya conjecture and Stein's restriction conjecture), a refutation of ETH, and rigorous existence proofs for pure Yang–Mills and QCD [1]. OpenAI says it does not seek academic authorship; groups led by external experts handle review and interpretation.

Caveats. According to third-party analysis by Papex, the three leads of the ETH review group wrote in an open letter that "our involvement should not be read as a certification of the result"; the exponent in OpenAI's Lean formalization is slightly weaker than the paper's main result; and the physics result concerns existence and does not address the "mass gap" part of the Millennium Prize problem [3].

2. Anthropic: same conclusion, a different route

What it is. On October 27 (UTC), Anthropic published a paper and Lean 4 proof on GitHub: a deterministic algorithm solves 3-SAT in 2^o(n) time and counts satisfying assignments in 2^O(n·log log n/√log n) time [2]. The repository says the main results depend only on Lean's three standard axioms and were rechecked with a second, independently implemented kernel; it also states plainly that no machine checks whether the statement file matches the paper, so the statement file is kept deliberately short for human checking.

Why it matters. According to Papex's summary, the Anthropic paper says the core algorithm was found by an internal Claude research model on October 16 — "about 14 million output tokens, no human input" [3]. Both companies say their models independently reached this conclusion on October 16 and published within a day of each other — one of the strongest signals yet of "AI doing original mathematics." But the repository also stresses that "the result is purely asymptotic and says nothing about solving formulas in practice" [2].

3. Axiom: a complete formalization of the Classification of Finite Simple Groups

Key numbers (per official data). The original proof spans about 15,000 pages and more than 500 papers. Axiom divided the project into 108 milestones and about 380 small tasks; dozens of AI agents produced about 43.1 million lines of Lean code in 24 days and found 34 "notable discrepancies," including counterexamples that required rewriting proof routes [4].

Why it matters. Formalization is valuable not only for "proving new theorems" but also for "auditing old knowledge." The engineering lessons Axiom disclosed — managing unproven premises agents silently assume, distributed incremental verification, and traceable task decomposition — are instructive for any large-scale multi-agent project [4].

2. Model Releases

4. Genie 4: a division of labor between generative and reasoning models

On October 27, Google DeepMind released Genie 4, a new interactive world model: scenes can be rewritten in natural language in real time, human motion and physics are more realistic, and for the first time in the Genie series audio and character dialogue are generated natively; Gemini 3.8 Flash acts as a "guiding agent in the loop," continuously observing the scene, breaking down goals, and checking new frames [5]. DeepMind also lists limitations: object permanence drifts over time, and complex physical interactions, text rendering, and long-term consistency still need work. It is currently available as a research preview to trusted testers, and generated content carries a SynthID watermark. (A newsletter claim that "scene consistency lasts about two minutes, twice the previous generation" could not be verified on the official page and is not used here.)

5. Ling-3.1-flash-1019: 560B total parameters, MIT license

A hybrid linear-attention MoE from Ant Group's inclusionAI: about 560B total and about 25B active parameters, 1M context, MIT license, with a base model also released for enterprise post-training. According to the model card, further post-training alone raised the Artificial Analysis Intelligence Index from 41 to 44 and AutomationBench from 62% to 68% [6].

6. LFM3: an on-device agent model of about 1 GB

Liquid AI's LFM3-1.7B uses a "triple-hybrid" architecture of gated short convolutions, sliding-window attention, and global attention, pre-trained on 22T tokens, with 256K context and about 1 GB at 4-bit quantization [7]. According to the official table, it scores 71.39 on BFCL V4 and 38.42 on WebArena-Verified; the KV cache at 128K context is about 1.6 GB, versus 4.3 GB for Qwen3.5-4B in the same table. Liquid also acknowledges that larger models still have the edge in agentic coding and knowledge tasks. Note that it ships under Liquid's own license, not MIT or Apache.

7. Unlimited-OCR-2: parsing a whole book in one request

Baidu's open-source 3B document-parsing model (MIT license) is built around Sparse Reference Sliding Window Attention (SR-SWA): it compresses image–text attention interactions over ultra-long sequences into a fixed-size set of "working references" (e.g., 512 tokens), keeping per-step decoding latency and memory nearly constant regardless of document length [8]. The same day, Baidu released MarathonDocBench, a benchmark for ultra-long documents, and claims state-of-the-art results on both dozens-of-pages and hundred-page benchmarks. (Newsletter figures of "84.6 on MPDocBench, up to about 7× faster decoding" could not be verified on the model card and are not used here.)

3. Evaluation: FrontierCode 2.0

What it is. Cognition released FrontierCode 2.0 on October 27. It keeps the 1.0 methodology: more than 20 open-source maintainers wrote realistic tasks from the repositories they maintain, spending over 40 hours per task, graded by whether the code would be mergeable; prompts are deliberately incomplete, so agents must infer implicit constraints [9].

Key numbers (per official data). Compared with the previous version, tasks come from 55% more repositories and carry 43% more blocking criteria; reference solutions modify 67% more files and 89% more lines on average. "Thoroughness" blockers grew from 168 to 501; in 80% of tasks the reference solution differs from the upstream PR. The top score is 45.5% for Claude Opus 5.5, followed by 42.8% for GPT-6 Astra, 28.6% for Grok 4.7, and 17.7% for Kimi K3 [9].

Why it matters. On 1.1, eight models were bunched between 43.9% and 54.6%; on 2.0 they spread from 17.7% to 45.5% (Figure 3). Cognition also notes that open-source models still have significant room for improvement.

4. Training Methods: Two Widely Discussed Papers

8. Trajectory2Gym: supervise only decisions with visible grounds

This work from Ant International Research [10] stops treating "successful trajectories" as wholesale imitation targets. Instead it checks each action — is it supported by visible evidence, consistent with execution results, in the right procedural order? — and supervises only actions that pass, while giving every complete interaction equal weight in training. Per the paper, the post-trained 4B model reaches 69.17 on Tau2, above the 28.33 of a publicly initialized 30B-A3B model.

9. FORK: putting a price on padding for points

Targeting the problem that "rewarding rubric coverage makes models write ever longer," FORK [11] changes the reward from recall to an F-score combining recall and precision: every passage must be needed by some criterion and be factually correct. Per the paper, the win rate against the base model in the medical domain rises from 3.1% to 68.0%, and average length falls from 9,195 to 3,533 characters.

5. Three Key Concepts in Plain Language

① SR-SWA: why "unlimited pages" is possible

Intuition. Standard attention looks back at everything before it when generating each new token; the longer the document, the slower and more memory-hungry each step. SR-SWA lets the model look back only at "a recent window + a fixed-size set of working references," so the per-step cost is capped [8].

Analogy. A stenographer summarizing a thousand-page book does not flip back to page one for every sentence; they look at the few pages at hand plus a continually updated "key-points card." The card has a fixed size, so writing page 1,000 is as fast as writing page 10.

Worked example (illustrative). Suppose a page is about 1,000 tokens, so a 1,000-page book is about 1 million tokens. Standard attention, generating a token at the end, interacts with about 1 million previous tokens; if each step interacts only with 512 working references plus a local window, the per-step cost is essentially the same as at page 10. How the working references are selected and updated is not described in detail on the model card; refer to the official paper.

When it fails. A fixed-size reference set necessarily compresses information: whether long-range references across many pages (e.g., "see Table 2 in Chapter 3") survive depends on the selection mechanism; the official deployment notes also warn that too small a page window hurts cross-page merging [8].

② Blocking-criterion scoring: why "writing more code" does not necessarily add points

Intuition. A FrontierCode score is a weighted sum of rubric items, but failing any single "blocking criterion" scores the whole task 0 [9].

Analogy. A renovation inspection: no matter how nicely the walls are painted, the job fails if the wiring is not grounded.

Worked example (from the official case). In a Mock Service Worker task, the model fixed the "generator does not restart after reset" bug but simply discarded the old generator without closing it, so cleanup code the user wrote in a finally block never runs. The task did not explicitly ask for cleanup, but experienced developers expect it, and this triggers a "thoroughness" blocker [9].

Why it is interesting. Cognition observes that at higher reasoning effort, models tend to change more files and write more code, and on 1.1 the pass rate of "scope" criteria fell accordingly; 2.0 loosens scope criteria, lowering the scope-blocker failure rate from 9.0% to 3.8%, so that curves showing "thinking longer makes it worse" are more trustworthy [9].

③ Subexponential time: why refuting ETH does not mean "SAT got faster"

Intuition. 2^o(n) means the coefficient in the exponent tends to 0 as n grows, but perhaps so slowly that it is imperceptible at any realistic scale [2][3].

Worked example (illustrative; base 2, constants ignored). The coefficient in the new result can be written as log log n / √log n: about 0.97 at n = 10⁶ and about 0.84 at n = 10¹² — still close to 1. So it matters greatly for the theoretical landscape — many conditional lower bounds premised on ETH lose their footing — but has almost no direct effect on engineering practice.

6. Side-by-Side Comparison

Note: Tasks and evaluation conditions differ across items, so numbers are not directly comparable.

7. Our Views

1. "Machine-checkable" is becoming the entry ticket for AI scientific results. But one sentence in Anthropic's repository deserves to be remembered: no machine checks whether the statement matches the paper. The next bottleneck is "statement-faithfulness review," not the proof itself.
2. The focus of evaluation is shifting from "explicit specs" to "implicit requirements." FrontierCode 2.0's blockers, FORK's precision, and Trajectory2Gym's "grounded actions" point the same way: a good agent not only completes the literal task but also stays in scope and leaves no hidden defects.
3. Open models are tiering by scenario. On-device 1–2B models for workflows, large MoE for complex reasoning, specialized small models for ultra-long documents; enterprises should read the license first, then run pairing evaluations by task.
4. Stay restrained about "breakthroughs." Refuting ETH does not make SAT faster, the Yang–Mills result does not touch the mass gap, and unverified newsletter numbers should not be repeated as fact.

8. Implications for Enterprise Deployment

1. Check licenses and deployment form before leaderboards. The three open models in this issue have different licenses: Ling-3.1 and Unlimited-OCR-2 are MIT-licensed [6][8], while LFM3 uses Liquid's own license [7]. On that basis, assign models by tier: on-device workflows, complex reasoning, and ultra-long documents.
2. Ultra-long documents are worth a small pilot. Materials running to hundreds of pages, such as contracts, archives, and technical manuals, used to be split into chunks and stitched back together. Designs with a "fixed working reference," such as SR-SWA, make whole-document parsing possible [8], but the model card gives no specific scores, so enterprises should first measure accuracy and throughput on their own samples before replacing existing pipelines.
3. Add "implicit requirements" to internal evaluations. Following FrontierCode 2.0 [9], having the engineers who actually maintain a system write tasks and define "blocking criteria" comes closer to a production bar than unit-test pass rates alone.
4. Make training data "grounded in process." Whether for tool calling or report generation, admitting only actions with visible grounds and content that is necessary and correct into the training signal [10][11] reduces the chance that models learn to game the reward.
5. Build a verification process for external "breakthroughs." Two figures in this issue's news digest could not be verified on the original pages. Making "original link + official wording + independently confirmed or not" mandatory fields for technical intelligence is the cheapest form of risk control.

References

1. [1] OpenAI. Working with academic communities to build scientific understanding. OpenAI, 2026-10-26. https://openai.com/index/building-scientific-understanding-with-academic-communities
2. [2] Anthropic. anthropics/formal-math: the eth project (A 2^o(n) Time Algorithm for 3-SAT). GitHub, 2026-10-27. https://github.com/anthropics/formal-math
3. [3] Papex. OpenAI's Kakeya, ETH and Yang–Mills claims: what they say and what stays open. Papex Blog, 2026-10-27. (Third-party analysis.) https://papex.org/blog/claimed-verified-explained
4. [4] Axiom. Formalizing the Enormous Theorem. Axiom Math, 2026-10-26. https://axiommath.ai/research/the-enormous-theorem-formalized/
5. [5] Raia Hadsell, Diego Rivas, Hang Qi. Genie 4: A new generation of world simulation. Google DeepMind, 2026-10-27. https://deepmind.google/blog/genie-4-a-new-generation-of-world-simulation/
6. [6] inclusionAI. Ling-3.1-flash-1019 (model card). Hugging Face, 2026-10-19. https://huggingface.co/inclusionAI/Ling-3.1-flash-1019
7. [7] Liquid AI. Introducing LFM3: Every Modality for Specialized Intelligence. Liquid AI Blog, 2026-10-27. https://www.liquid.ai/blog/lfm3
8. [8] Baidu. Unlimited-OCR-2 (model card). Hugging Face, 2026-10-27. https://huggingface.co/baidu/Unlimited-OCR-2
9. [9] The Cognition Team. FrontierCode 2.0. Cognition Blog, 2026-10-27. https://cognition.com/blog/frontier-code-2.0
10. [10] Yihao Hu, Zhihao Wen, Yitong Lin, Siyuan Lu, et al. Trajectory2Gym: Decision-Grounded Compositional Interaction Synthesis for Tool-Use Agents. Ant International Research, 2026-10-24. https://arxiv.org/abs/2610.33568
11. [11] Hyun Ryu, Jong-Heon Kim, Yiqing Xie, Seungone Kim, et al. Eat Your Precision: Precision Objective Mitigates Reward Hacking in Rubric-based RL. KAIST, CMU, et al., 2026-10-24. https://arxiv.org/abs/2610.33512

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