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Anthropic's 3-SAT claim comes with a Lean proof
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◆ Braid Daily · 2026-10-29

Anthropic's 3-SAT claim comes with a Lean proof

Proof checks, Gemini 4 Carbon's ranking, and the costs of verifying and running coding agents.

A mathematical sculpture and its offset glass reflection under a yellow light in a dark research chamber.

The lead

1

Anthropic says Claude found a subexponential algorithm for 3-SAT, contradicting the Exponential Time Hypothesis. Its repository includes an AI-written Lean proof, but no machine check confirms that the formal statement matches the paper. The result says nothing about practical SAT-solving performance.

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Lean checks a proof against a formal statement; the match between that statement and the paper has no machine check.
Anthropic's repository separates proof checking from checking that the formal statement matches the paper.

Formal proofs and frontier models

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Gemini 4 Carbon leads the Artificial Analysis index

Google

Google announces gains in coding, agentic tasks, and cybersecurity. Artificial Analysis's current table confirms Carbon's top ranking on its Intelligence Index; that aggregate ranking doesn't establish performance on a particular workload.

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Four talks on verification and recovery

4

Running agents and managing their costs

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Revolut reports a coding AI bill one-tenth as large

AI Engineer · Revolut

Following this week's open-weight cost discussion, Revolut describes a production deployment of a self-hosted GLM model. The bank reports cutting its provider bill to one-tenth of previous spending, with sandboxes and human approval restricting autonomous actions; the figures are self-reported.

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Financing and local costs

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Companion episode

Anthropic Says Claude Refuted the Exponential Time Hypothesis, and Shipped a Lean Proof to Check

· 00:30:37