Study 24 QMA N Representability

Study 24 — A molecule is consistent, or it is not

Status: LIVE ON GLAMA — fixture locked 2026-08-26
Program: Shear Studies Index · Math Court on Glama

Call it today: verify_n_representability at https://affine.earth/language-invariant/mcp
Or walk the whole court: clients/math-court-mcp

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N-representability is the quiet QMA-complete problem behind quantum chemistry. Given local 2-particle density matrices, do they belong to a real N-particle state? Classical groups spend days in floating-point semidefinite programs. Quantum groups try to measure continuous amplitudes. Trailing-bit drift invents geometries that never lived — false-positive molecules with a pretty picture.

Affine.Earth maps the 2-RDM as a rational matrix. Trace, symmetry, and positivity are cross-multiplies. Either the local patches intersect on the 8-manifold or the intersection is void. There is no “almost positive.”

The public example locked it. The Glama client posted rho2=1/2,0/1|0/1,1/2 with n=2. The cells returned WIN. The adversary 3/2,0/1|0/1,-1/2 is MISS — a negative eigenvalue, a molecule the float SDP can still smile at. Same lock through math_court domain qma_nrep.

The marketing fact: consistency of a local quantum state is a boolean string match on affine.earth, not a multi-day solver farm. If your chemistry stack needs a float to decide whether a density is legal, the court has already refused your language.

Frozen law

Symbol	Rule
Trace	a11+a22 = N(N−1)/2 exact
Symmetric	a12 = a21 by cross-multiply
Positive	a11 ≥ 0 and det ≥ 0
WIN	all three hold
MISS	any one fails
REFUSED	IEEE token on the wire