Study 22 QMA 2 Local Hamiltonian

Study 22 — The ground state is a coordinate, not a vibe

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

Call it today: execute_2local_hamiltonian at https://affine.earth/language-invariant/mcp
Or walk the whole court: clients/math-court-mcp

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The 2-local Hamiltonian is the bedrock QMA-complete problem — quantum k-SAT. IonQ-class machines and every VQE notebook treat it as a continuous energy landscape. They rotate analog qubits with a floating-point gradient and publish a statistical ground energy. The rotation drifts. The answer is an average. There is no coordinate you can replay tomorrow and get the same bits.

Affine.Earth does not anneal that landscape. A 2-qubit projector is a spatial exclusion zone on the Eisenstein lattice. The presented spin string either sits outside every exclusion or it is blocked. The energy is an exact rational num/den.

The public example locked it. The Glama client posted constraints=0,1,1,1 and config=0,1 as decimal strings. The nine cells returned energy −1/1 and AFFINE_QMA_2LOCAL. Same payload through math_court domain qma_2local. A JSON float on that wire is refused — VQE’s native language cannot enter the court.

The presented configuration is verified. Unknown grounds are not searched. That is still the shear: the adversary is the continuous (e^{-iHt}) story, and it has no string to show.

Frozen law

Symbol	Rule
z = 1−2s	computational bit → discrete direction
E = Σ (J_num/J_den) z_i z_j	exact rational
WIN	fixture energy −1/1 and no exclusion
MISS	aligned config, or energy ≠ sealed ground
REFUSED	IEEE token (. or e) on the wire

Falsifiers

Falsifier	Effect
Fixture config energy ≠ −1/1	Primary MISS
Float payload admitted	Court is broken