MLWave

Minimum quartet tree cost (@cilibrar-Vitanyi) at n = 1,000: handwritten digits and random colours, 41,417,124,750 quartets each, one tree, about a minute on 2 cores. Hat-tip Claude (Anthropic). 30k30.github.io/mqtc/

Me: We did "Reasoning with Neural Cellular Automata" (arxiv.org/abs/2609.36126) and Mapper on mazes. There anything you want to research? Maybe fixed points/paradox? Claude: "every sentence I point at is false" The thermodynamics of truth Me: Please continue however you see fit

Me: I want to have a look at the #21 Jacobsthal upper bound in the latest OpenAI maths batch. It includes a Lean proof and a paper on the Github repo. Please familiarize. Claude: This answers Erdős #687 (the “$1000 or half my savings”). Want a Lean proof? github.com/30k30/scholia/tre…

Having fun asking for mash-up games, here Opus 5.5 made Flapshot, inspired by Yeti Sports Pingu smash, Joust mechanics, and Worms weapons. No link needed, just make your own games ;)

After that, it designed code to run AI agents with harness on @vast_ai, to design models for a meta-ensemble, complete with ledger, referee, and leakage-control. Still trying to grok what it did with α-investing (Foster and Stine, 2008). And treating ML calibration like unit test

Asked Opus 5.5 extra to design a novel SKLearn-API compatible classifier and regressor, and it one-shotted HoraClassifier and HoraRegressor. It's competitive and even wins on Wine :). It also adds diversity to a blending model, since so different from NN, Tree, or Linear models.

"pls fix rotating triangle impossible physics"

Opus 5.5 "demo of dessert seapunk: no dolphins but camels. make AI-eigen"

Claude Opus 5.5 Scene Demo: Q.E.D (made in ~22 minutes, ~22kb Python code)

This is how AI learns about philosophy of science:

Archimedes' Spiral Arms.

Segmented "Twin Towers" Sieve.

Prime Summation Pairs Automata.

Projective Geometry for Addition/Multiplication.

Interval Coverage as Connected Paths.

Prime Bitstrings.

Modular Arithmetic Wrap-Around Patterns.