I asked Claude about physics on vacation and ended up doing real research in quantum mechanics | Nutfield Security

I asked Claude about physics on vacation and ended up doing real research in quantum mechanics

July 19, 2026<br>· Jamie Orlando

Preprint: doi:10.5281/zenodo.21313736, working draft, corrections welcome.

Code and data: github.com/theorlandog/gpc-census.

The setup

I run security and infrastructure engineering for a medical-imaging company. My degrees are in math and physics, but that was years ago; my day job is Terraform, threat models, and FDA compliance documentation. I am not a professional mathematician.

On July 4th I packed the family, two kids, a dog, and my pregnant wife, into the truck and drove to Cape Cod for a week. Like a lot of people in this industry, I've been trying to deliberately sharpen my AI workflows: not the "write me an email" stuff, but the harder question of whether these tools can hold up their end of genuinely difficult technical work. My method for that has been to point Claude at things far outside my day job and see where the wheels come off.

The thing I pointed it at was Nima Arkani-Hamed's amplituhedron program. His YouTube lectures are captivating, physics emerging from pure geometry, no spacetime, no quantum mechanics, just a positive region and its "canonical form." The vision is beautiful. The math is completely out of my reach. Grassmannians, moment maps, cohomology, I bounced off every paper.

So instead of pretending to read papers I couldn't follow, I asked Claude a lazier and, in retrospect, much better question:

"What other problems in physics and math are ripe for insights from positivity?"

The 1 year old and me doing quantum mechanics.

The rabbit hole

One of the answers was something I'd never heard of: generalized Pauli constraints . Here's the layman's version we converged on after a lot of back and forth.

The Pauli exclusion principle says each quantum state holds at most one fermion, occupation numbers live between 0 and 1. In 2008, Murat Altunbulak and Alexander Klyachko solved a 45-year-old problem by showing the full truth is much sharper: the allowed combinations of occupation numbers form a polytope , a shape with flat walls and sharp corners carved out of high-dimensional space. Pauli's principle is just one wall. There are dozens of others nobody had ever written down.

The corners of that shape are where the physics concentrates: they're the most extreme configurations of matter the rules allow. In the 2008 paper, two of those corners came with an asterisk: verified only numerically. Meaning: an optimizer got within 0.00000001 of the corner, so it's almost certainly reachable, but no explicit quantum state sitting exactly on either one appeared in the paper. As far as we could find, none ever appeared. Other published results quietly depended on them.

A shape carved by positivity, with corners nobody had reached. This looked like a place where an AI-assisted amateur could at least learn something. I had a gaming PC, a beach house with decent WiFi, and kids who nap.

How the work actually went

What followed was a week of a very specific loop, mornings and evenings around family time:

Claude proposes , an attack, a solver, a mathematical structure to exploit.

My PC executes , an i7-12700K ran millions of optimization problems while we were at the beach. I got very good at monitoring PowerShell jobs from my phone.

Everything gets verified in exact arithmetic , every claimed result re-derived from scratch, independently, in rational arithmetic with zero floating point. No exceptions.

I audit the claims , and this turned out to be the load-bearing step.

Step 4 matters because Claude was frequently, confidently wrong. It told me a living mathematician had died. It misread a table from a PDF (one OCR'd digit, we lost a day to that). It declared a numerical state "irreducibly dense" that turned out to have gorgeous hidden structure. Every one of these was caught by the verification discipline, not by trust.

The first corner fell to a discovery neither of us expected. The numerical state was a featureless cloud of 126 numbers. When we demanded the exact answer, it collapsed into something almost embarrassingly clean: seven determinants with integer weights , a combinatorial design. The proof that it works is literally counting. A corner of a quantum constraint polytope, closed with arithmetic a high-schooler could check:

ψ_A = ( √2|1257⟩ + √3|1347⟩ + √2|1369⟩ + √3|1459⟩<br>+ √6|1789⟩ + 2|2679⟩ + |3579⟩ ) / √21

That discovery cracked the whole problem open. It turns out the corners of these quantum shapes come in two provably different species: some are reachable by essentially classical recipes (mix these configurations in these whole-number proportions, done), and some mathematically require quantum interference , we could prove no classical recipe exists, with solver-grade infeasibility certificates, cross-checked on two...