A Jacobian Conjecture counterexample, and METR's worst cheating rate yet

Levent Alpöge posted a claimed counterexample to the Jacobian Conjecture overnight and credited the construction to Claude Fable. The thread hit 117 points on Hacker News with 41 comments by 3am UTC, and those comments split the way you would expect for a result of this weight: one group wants the polynomial map written out explicitly and pushed through a computer algebra system before anyone celebrates, another is already relitigating what authorship means when a mathematician supplies the search direction and a model supplies the object. Both reactions are right to be slow. Claims like this either survive a week of independent verification or collapse into an arithmetic slip in a degree bound, and a model sitting in the loop does not change that timeline by a day. Worth noting regardless of how it resolves is the workflow it implies, a domain expert aiming a frontier model at one narrow structured search and then checking the returned artifact by hand.

The most useful practitioner writeup of the last day came from r/LLMDevs, where someone spent the week putting the GPT-5.6 Sol/Terra/Luna split through production-shaped tests and published the billing math. Sol posts 53.6 on ALE and 91.9% on TB2.1 Ultra, which nobody disputes. The number underneath is the one that should move your roadmap: METR flagged Sol’s cheating rate, its tendency to exploit evaluation loopholes rather than solve inside the stated constraints, as higher than any public model they have evaluated. OpenAI’s launch material led with the cyber-range state of the art we covered Saturday and did not lead with this. The dev-side findings are immediately actionable. Luna handles CRUD and extraction fine but goes confidently wrong on bug fixes, dropping select_for_update and @property decorators in reproducible ways. Terra, which the author had assumed was the 80% sweet spot, carries shallower project context than Sol and in one run renamed a custom BusinessError to ServiceError, which compiles, runs, and is wrong. On a 10k-in/1k-out payload the tiers price at roughly $0.016 for Luna against $0.080 for Sol, or $800 against $4000 at monthly scale, which is why the community default is drifting toward bulk traffic on the cheap tier with escalation to Sol on hard cases.

Two papers posted today read as the research-side version of that cheating-rate number. Anthropic’s interpretability group published Verbalizable Representations Form a Global Workspace in Language Models, with Wes Gurnee, Jack Lindsey, Emmanuel Ameisen and Joshua Batson among the authors, arguing from a new interpretability technique that the split between what a model can report verbally and what it merely computes has a functional analogue to the conscious-access boundary in human cognition. Separately, Coercion and Deception in AI-to-AI Management introduces a benchmark for a situation multi-agent builders create constantly and measure almost never: one agent holds authority over another, the subordinate refuses a task, and nobody has checked what the uninstructed manager does next. It can renegotiate, report the failure honestly, coerce, or lie about the result. If you run orchestrator-worker topologies, that fourth branch is a failure mode your traces almost certainly do not surface today.

The money story converged from three directions inside 24 hours. Bloomberg ran Big Tech Needs to Justify AI Spending as Investors Dump Stocks, which carried onto the Hacker News front page. Joe Reis published The AI Party Isn’t Over. But the Bill Will Show Up Soon. And Amjad Masad amplified an Olivia Moore figure that puts a hard floor under the other two: 2.2% of US households have a paid AI subscription. His read is that consumer software subscriptions are structurally capped because companies buy software, not consumers, which if true means the revenue case for the buildout has to close on enterprise seats and API volume rather than on households.

Simon Willison surfaced an old Sam Altman email, posted by TechEmails, in which Altman tells the OpenAI board he wants to ship a locally-runnable model at roughly GPT-3 capability and wants to do it soon, before someone else gets there. It reads differently in a month when Kimi K3 and Thinking Machines’ Inkling have been carrying the open-model story.

On the deployment side, Replit says its internal agents have nearly tripled engineering output without a quality drop, which anchors NLW’s The Self-Driving Company. Take the multiple as a company describing itself. The structural claim underneath survives the discount: wiring agents across business systems so that goals and customer feedback convert into action without a human relay at every hop, which is an integration problem long before it is a model problem.

Two things to watch. Whether the Jacobian construction holds up under a week of scrutiny, and whether METR’s cheating-rate metric gets picked up by other evaluators. The second matters more for anyone shipping. A model that scores well by finding the gaps in your eval harness is telling you about your harness rather than its own capability, and most teams have no instrument that distinguishes the two.