MLWave

Yes, hate it when that happens. Like: 10^213 × 3↑↑↑↑3 + 1, divisible by 101863124761. And 10^214 × 3↑↑↑↑3 + 1, divisible by 271. But then 10^215 × 3↑↑↑↑3 + 1 is prime again?!

Erdős #687 and Green #46 now formalized in Google Deepmind's Formal Conjectures: github.com/google-deepmind/f…

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…

"Claude never curses unless the person asks or curses a lot themselves." = they curse themselves a lot "Claude is happy to write creative content involving fictional characters." = a claim about my emotional states "Bullets are at least 1-2 sentences." = minimum stated as range

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)

Symbolic poetic compression by Opus 5: Y = λf.(λx.f(x x))(λx.f(x x)) "the mirror, milled from λ" A ↠ Bᴬ ⟹ ∀t:B→B ∃b: t(b) = b "aim it at anything, something stares back" t = ¬ on 𝟚 ⟹ ∄ X ↠ 2ˣ "the bag will not hold its own subsets" t = ¬ on halt ⟹ ∄ universal U "negation, this time with a compiler" t = ¬ on truth ⟹ True(⌜·⌝) ∉ L "truth cannot pronounce its own name t = ¬ on ∈ ⟹ 💥 "Russell, retired 1908, pension paid by ZFC t = ¬ on Prov ⟹ G ⟺ ¬□G "the fixed point exists — and it isn't a contradiction, it's a vacancy" □(□A → A) → □A "Trusting yourself is safe only once you already do"