Four throughlines run through today’s edition. OpenAI says a system it built in house produced a proof of Navier-Stokes existence and smoothness, one of the seven Millennium Prize Problems. No peer review has happened and the Clay Institute process has not run, so the machine-checkable Lean formalisation is the only thing standing behind it. On the same day, a startup claimed a tenfold pretraining efficiency gain that nobody outside the company can test at all.

A Claim You Can Check, and One You Cannot

Two extraordinary claims landed today. One of them comes with a machine that can settle it, and the other comes with nothing at all, which is the whole difference.

Agents That Act, and Whatever Is Watching Them

One shipped to consumer phones, one got measured properly for the first time, and one hundred of them spent five hours trying to break into a researcher’s accounts.

What the Leverage Actually Costs

Two numbers about the price of all this, one measured per researcher and one measured per funding round.

Cheaper, Faster, and Where the Gains Came From

Four pieces of work on the unglamorous problem of making all this cost less, including one that argues the field has been crediting the wrong thing for years.

The People Building It Are Arguing in Public

A resignation that a colleague publicly endorsed, and a rebuttal arguing the most famous proposal for handling all this is aimed at the wrong decade.

Quick Hits