I’m Carlos. I check published results exactly, whoever printed them: an AI lab, a journal, a simulation, a spreadsheet. You get one word back, and a file you can run.
They touch.Still touching.Still touching?They overlap.They overlap, by 0.0000003.
At ×1.6 millionThey overlap.
Three words. That’s the whole product.
It holds. Here’s the file that proves it.
It fails. Here’s the thing that breaks it.
I can’t decide it, and here’s why. No guessing.
Dashed means someone printed it, or it was computed and not proved.Plain means I decided it.Dotted means I picked the test mix.
OpenAI and Anthropic each published a proof that it is false. Each on a computer of its own design. With AI agents, I carried both proofs to the textbook computer.
Solid lines are checked by machine; the first is Daniel Hawkley’s proof, replayed here. The last step has no line. It takes a human to read a definition, and I won’t draw what I didn’t decide.
The full story“with no code shared with the claimants, by C. Toledo”
The optimization-constants registry of Davis, Ivanisvili and Tao. Ten asterisks came off on my replays.
In the registry’s README“independently verified the complete configurations in all 19 dimensions”
The Qiushi Engine authors, after I asked for their data and checked every pair. All 9.75 × 10¹⁵ of them.
In their README“It covers much of the same ground, carefully”
maximusrufus, an outside replayer. Four of them have re-run my work eight times. Same verdict every time.
On the threadI was a designer first. So every stroke on this site says how much it knows.
A proof, a record, a benchmark, a number in a report. Gaps listed first.
See VerifyThe answer key is a proof. Wrong answers don’t slip through on a tolerance.
See the gradersIt’s one person and rented machines. Compute, credits or a grant go a long way.
Write to meIndependent exact certification of machine-generated mathematics — exact arithmetic, no code shared with the claimant, refusal as a verdict.