AI-Assisted Vacation Project Cracks Open 2008 Quantum Physics Puzzle

A security and infrastructure engineer at a medical-imaging company spent a family vacation pointing Claude at problems far outside his day job, eventually landing on "generalized Pauli constraints" — a 2008 result by Altunbulak and Klyachko that reshaped quantum occupation-number theory into a polytope, two corners of which had only ever been verified numerically, never constructed explicitly.

Using a disciplined loop — Claude proposes an attack, a home PC runs solvers, every claim gets re-derived in exact rational arithmetic, and a human audits adversarially — the pair closed both open corners. The first collapsed into a clean combinatorial design of seven integer-weighted determinants; the second required complex quantum amplitudes and yielded a proof that no real-valued state of its type can exist, a result the authors believe is new to the literature.

The work is less a story about a chatbot doing physics and more about verification discipline: every key claim is backed by a certificate a third party can independently check, from hand-verifiable states to re-runnable infeasibility proofs. The takeaway for engineers experimenting with AI on hard technical problems is that the model's frequent, confident errors were only survivable because of an exact-arithmetic, zero-trust verification loop around it.