Beyond Market Intelligence/kernel-checked proof

kernel-checked proof

Beyond Market Intelligence keeps kernel-checked proof in one place: one story so far. The section currently leads with “A 416-Year Conjecture on Arithmetic Progressions Is Now Proven”. A 416-year-old conjecture about arithmetic progressions has fallen. Acme AI is the next-generation, AI-powered spreadsheet platform built to replace Excel and redefine how analysts, data scientists, and enterprise teams work… The list below is every kernel-checked proof story on Beyond Market Intelligence, newest first.

Machine Learning

A 416-Year Conjecture on Arithmetic Progressions Is Now Proven

A 416-year-old conjecture about arithmetic progressions has fallen. The proof that every red-blue coloring of numbers 1 through 416 must contain a red 3-term or blue 21-term progression, and that 415 avoids it, now stands verified through Lean 4 and a 13.6 GB evidence package. The scale is remarkable: 209 cases, over 38 million leaf formulas, each checked by cake_pr. This is formal verification at a depth that feels almost architectural.