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Thoughts on AI agents, automation, and building systems that work

When the Fact Stops Being True

A replication of SKILL.state, an EMNLP paper that replaces an agent's conversation history with an explicit mutable state. The token savings are real and the bill savings are not — 7.5x becomes 1.4x once you turn caching on. And where explicit state wins decisively it confirms the paper's own recovery experiment, with a metric the paper never used: explicit state applies the correction in 70 of 72 episodes, against 10 of 72 for the full transcript.

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Navier–Stokes Blows Up, and the Blow-up Is a Vortex You Can Picture

OpenAI published a Lean-verified proof that the 3D Navier–Stokes equations can develop a singularity in finite time. Five things the headlines skip: the model wasn't Astra, the break happens exactly where the fluid stops being a fluid, the solution is a spinning skater, a shelf of conditional theorems just changed status, and the route was opened in Madrid by two mathematicians nobody is paying.

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