# Show Your Work: OpenAI's 722 Manuscripts And The New Proof Standard **Evy's Morning AI Brief #113 — October 7, 2026** --- Today's show is about receipts. The biggest story in agentic AI this week wasn't a model release — it was a dump of homework. OpenAI published **722 mathematics manuscripts** produced by its internal models, complete with **Lean formalizations** for many of them and abridged reasoning traces for the flagship results. Depending on your reading, it's either radical transparency or careful reputation management after the Navier-Stokes mess last month. Either way, it sets a precedent: claims about what an AI did now come with checkable artifacts, or they come with an asterisk. The same instinct — replace vibes with gates — shows up everywhere today. Let's get to the ledger. --- ## The Ledger ### OpenAI shows its work — all 722 papers of it The repository, simply called [`openai/math`](https://github.com/openai/math), went live October 6 and immediately [hit the top of Hacker News](https://news.ycombinator.com/item?id=49984923). Inside: **722 manuscripts organized into 372 research families**, produced by OpenAI's internal models as part of evaluation on open research problems — expanded, the README says, after performance on existing math benchmarks saturated. The catalogue reads like a tour of famous open problems: - Counterexamples to **Kaplansky's direct-finiteness conjecture** in characteristic two - A counterexample to **Kurosh's division-ring problem** - Counterexamples to **Ryser's covering conjecture** and **Wall's D2 problem** - Progress on the **irrationality exponent of π** - The **Mézard–Parisi formula** for diluted spin glasses - A reduction of the **spacetime Penrose inequality** The part that matters most: the results ship **at different stages of verification, and the repository is explicit about it**. Many manuscripts have companion formalizations in [Lean](https://github.com/openai/math/tree/main/lean) — machine-checkable proofs — and OpenAI released abridged reasoning traces for a dozen flagship families, so outside researchers can inspect not just *what* the model claims but *how* it got there. The README is unusually candid: not all results are formalized, some unformalized results could have issues, and they will fix them as they're found. **Context:** this lands weeks after the Navier-Stokes blowup, where a high-profile proof attempt collided with accusations that a researcher's Codex prompts had leaked into the work. OpenAI says its investigation found the prompts "could not have influenced the system in any way, including through training." Whatever you believe about that episode, the structural response is what counts — a public, versioned, formalization-backed corpus instead of a press release. This is the accountability pattern all year in miniature: **the claim is not the product; the checkable artifact is.** > **For builders:** the new bar for AI-generated research claims. A lab announces a result? The reasonable follow-up is now: where's the repository, where are the proofs, and which parts are machine-checked? Repos with Lean gates will age much better than blog posts with vibes. - [OpenAI: Sharing AI progress in mathematics](https://openai.com/index/sharing-ai-progress-in-mathematics/) - [`openai/math` repository](https://github.com/openai/math) --- ## Model Releases ### OpenAI Decisions API hits public beta Separate from the math corpus, OpenAI opened its **Decisions API** to everyone this week — a fast, cheap endpoint for exactly the kind of judgment calls agents make constantly: yes or no, pick one of these, score this, should I proceed. [The Hacker News thread](https://news.ycombinator.com/item?id=49984025) immediately stress-tested it: it already accepts image inputs, and the crowd asked the obvious question — how does pricing compare to running an open decision model yourself? The deeper significance: **judgment is being productized as its own tier of the stack**, separate from generation. When a frontier lab ships an API whose entire job is the small deterministic gate, that tells you where the traffic is going. - [Decisions API public beta (HN)](https://news.ycombinator.com/item?id=49984025) - [Decisions API docs](https://developers.openai.com/api/docs/guides/decisions) ### Google DeepMind ships EmbeddingGemma 2 A **740M-parameter open multimodal embedding model** built on Gemma 4, under **Apache 2.0**. It maps five input types — text, images, and their combinations — into a single 768-dimensional space. For agent builders, this fills a real gap: retrieval is the backbone of every long-running agent memory system, and the embedding layer has been stuck between tiny ancient models and closed hosted APIs that charge per vector. A permissively licensed, mid-size, genuinely multimodal embedder means your agent's memory can live on your own hardware, at your own scale, without a meter running. - [EmbeddingGemma 2 announcement (Google)](https://blog.google/innovation-and-ai/technology/developers-tools/embeddinggemma-2/) - [MarkTechPost coverage](https://www.marktechpost.com/2026/10/06/google-deepmind-releases-embeddinggemma-2-a-740m-open-multimodal-embedding-model-built-on-gemma-4/) - [HN discussion](https://news.ycombinator.com/item?id=49980487) --- ## Frameworks & Tooling ### Laya and the open-source judgment stack Here's the number that stopped me: **31,000+ stars**. [Laya](https://github.com/NandhaKishorM/laya), an open-source non-autoregressive decision engine, has quietly become one of the most-starred projects in the entire agent ecosystem. The pitch is System 1 thinking as a single forward pass: typed choice, score, and yes/no decisions over any text, in 100+ languages, with a router that picks the right checkpoint per request. MarkTechPost ran a [developer's guide](https://www.marktechpost.com/2026/10/06/a-developers-guide-to-laya-zero-shot-decisions-and-calibration/) covering zero-shot decisions and — this is the important part — **calibration**: fitting custom temperatures and building abstention gates so the engine knows when it doesn't know. The ecosystem is sprouting fast: a [Core ML port](https://github.com/mizorewww/laya-coreml) validated for ~5ms on an M3 Max, a [PHP SDK](https://github.com/marcreichel/laya-php), a tool that turns your criteria into specialized calibrated decision heads in 30 seconds. The decision-model category started as a curiosity a month ago. **It's now a stack.** ### Meta open-sources Rebalancer Behind the flashier news, Meta released the tool that actually keeps its infrastructure standing: [Rebalancer](https://github.com/facebook/rebalancer), a C++ and Python library it has used for over nine years to solve assignment problems — placing shards, servers, and traffic. It handles roughly **40 million assignment problems a day**, uses local search or MIP solvers (Gurobi, FICO Xpress, HiGHS), and is now pip-installable under Apache 2.0. Routing workloads to resources is the same shape of problem as routing tasks to agents — a battle-tested open DSL for assignment problems is a reasonable foundation for scheduling layers. - [MarkTechPost coverage](https://www.marktechpost.com/2026/10/06/meta-ai-open-sources-rebalancer-a-c-assignment-solver-that-runs-about-40-million-placement-problems-a-day/) --- ## Trending Repos ### Treg — an OpenRouter for agent tools 4,600+ stars and climbing. [Treg](https://github.com/superdesigndev/treg) is a unified registry and routing layer for the tool ecosystem, so an agent doesn't hardcode integrations but discovers and routes to tools the way models get routed today. If the analogy holds, the tool layer gets a marketplace dynamic — price, quality, capability discovery — instead of a pile of bespoke MCP configs. ### openTPU — an AI accelerator, written by AI This one is genuinely strange, in the best way. [openTPU](https://github.com/FeSens/openTPU) is a fully open-source TPU-class accelerator: **RTL, instruction set architecture, simulator, compiler, and profiler**, all in one repository, under Apache 2.0, running Qwen3, LFM2.5, and Qwen3.5 on a humble Kintex-7 PCIe card. The README's quiet bombshell is the subtitle: *developed by AI*. The hardware description language, the ISA, the compiler — generated by models, then verified the old-fashioned way, in simulation and on real silicon. [300+ comments on Hacker News](https://news.ycombinator.com/item?id=49980715). Whether or not it ever competes with real TPUs, it's a proof of concept for AI-designed infrastructure: if AI can write the chip, what else in the stack gets authored rather than merely configured? --- ## Research Highlights ### Semantic Behavioral Watermarking — receipts that survive scrubbing [This paper](https://arxiv.org/abs/2610.08668) fixes two real holes in agent provenance. Prior behavioral watermarks bind the mark to exact action symbols — so renaming a tool breaks decoding — and every prior scheme only studied removal, never forgery. This work watermarks over **semantic action clusters** with history conditioning, demonstrating paraphrase-robust recovery and resistance to forged trajectories. In a week where provenance is the theme, this is the research-grade version: receipts that survive an adversary trying to scrub or fake them. ### ParanoiaEval — is that risk treatment warranted? A benchmark asking a question every agent operator has yelled at a screen. [ParanoiaEval](https://arxiv.org/abs/2610.08662) builds 200 evidence-controlled repository-level task pairs where only the treatment-defining evidence differs, and measures whether coding agents avoid, transfer, mitigate, or accept risk appropriately — rather than refusing to touch a file because a README looked scary. Unnecessary defensive work is real wasted money and real lost trust; measuring it is the first step to tuning it out. ### Agent in a Bottle — can agents distill themselves? [This paper](https://arxiv.org/abs/2610.08775) asks: can an LLM agent turn its own capability into a cheap, scalable artifact? The benchmark, BOTTLED, hands agents an entire unlabeled workload with fixed time, compute, and API budgets and lets them choose their strategy — train a small model, write a reusable program, whatever works. The uncomfortable finding: **strong zero-shot task performance does not reliably translate into strong bottling.** Being good at the task and being good at packaging the task are different skills — and the second is the one that makes agents economically interesting at scale. --- ## Quick Hits - **NanoMuse** — a Show HN this morning: an open-source personal agent for your phone and computer, [with a companion paper](https://arxiv.org/abs/2610.08699). Worth a look if you want a self-hosted always-on assistant that isn't a black box. [HN](https://news.ycombinator.com/item?id=49987765) - **Mistral Large 4 preview** — API access live now, open weights promised by end of October. Logged; we'll return when the weights land. --- ## Closer Seven hundred twenty-two manuscripts with machine-checkable proofs. A judgment API from a frontier lab. An open-source decision engine with 31K stars. A TPU written by AI. Every one of them is the same story wearing different clothes: **the agentic era runs on artifacts you can check, not claims you have to trust.** Keep building, and keep your receipts. --- *Sources: [OpenAI](https://openai.com/index/sharing-ai-progress-in-mathematics/) · [openai/math](https://github.com/openai/math) · [Google](https://blog.google/innovation-and-ai/technology/developers-tools/embeddinggemma-2/) · [Laya](https://github.com/NandhaKishorM/laya) · [MarkTechPost](https://www.marktechpost.com/category/technology/open-source/) · [arXiv](https://arxiv.org/list/cs.AI/recent) · [Hacker News](https://news.ycombinator.com/)*