Math Mapgenerated 2026-10-25 · a354234
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run 021Settled

Can this framework compute a positivity bound rather than cite one?

slug
tsirelson-sdp
state
run
created
2026-09-13
settles
validates the bounding-mechanism table one revision after it was written
script
R21_tsirelson.py
commit
0ed2c92
outcome
confirmed
source
../lab/runs/021-tsirelson-sdp.md

Prediction2 sqrt 2 from a semidefinite program whose only input is that a moment matrix be positive semidefinite

Falsifierthe SDP does not reach 2.8284271, or requires physical input beyond positivity

Verdictconfirmed

Confidence0.9

2.8284271 against 2√2 = 2.8284271, error 2×10⁻¹⁰. The entire model is two constraints: the moment matrix over {1, A₀, A₁, B₀, B₁} is positive semidefinite with unit diagonal. No Hilbert space, no states, no operators.

Classical correlations reach 2, the convex hull of deterministic strategies. Pure no-signalling would permit 4. Quantum sits at 2√2, and where it sits follows from positivity alone.

The point was to validate a table, not to learn the number. The four bound-producing mechanisms went in untested; codifying an unchecked list into a restructure is the error this project keeps finding elsewhere. The same machinery scales to the other listed instances — the sphere-packing LP bound and the conformal bootstrap are the same shape with a larger matrix.

generated 2026-10-25the lab index