The exact price of local realism in CHSH experiments: a measurement-dependence-detection trade-off surface, a moiré phase-locking mechanism that saturates it, and an unmeasured fringe in the fourfold coincidence sum

• URL: http://arxiv.org/abs/2608.18886v2
• Date: Fri, 21 Aug 2026 02:09:51 GMT
• Title: The exact price of local realism in CHSH experiments: a measurement-dependence-detection trade-off surface, a moiré phase-locking mechanism that saturates it, and an unmeasured fringe in the fourfold coincidence sum
• Abstract summary: I solve the unique detection profile $D(m)=sqrtm,h(m)$ under which a deterministic sign model reproduces the singlet exactly.<n>Surviving local accounts trade off measurement dependence against a $cos 4(a-b)$ modulation of the fourfold coincidence sum.<n>I exhibit a local mechanism -- moire phase locking -- with deterministic phase evolution and all randomness quenched in frozen offsets and flight times.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: For local hidden-variable accounts of the CHSH experiment that are faithful -- reproducing the observed singles and coincidence rates and unbiased marginals of a polarization singlet with symmetric detector efficiency $η_{\rm eff}$ -- I determine the minimal measurement dependence $M$ (Hall's variational measure) needed to achieve a CHSH value $S$. Linear programming over all local strategies yields, to machine precision at 32 grid points, $M(S,η_{\rm eff})=\max\{0,η_{\rm eff}((S+2)η_{\rm eff}-4)/6\}$, whose edges reproduce Hall's tight bound at $η_{\rm eff}=1$, the Garg-Mermin detection threshold, and the postselection ceiling $S=4/η_{\rm eff}-2$. The quantum point is certified exactly: $M(2\sqrt{2},9/10)=(27\sqrt{2}-33)/100$, with primal and dual certificates in $\mathbb{Q}(\sqrt{2})$ arithmetic. I solve the unique detection profile $D(m)=\sqrt{m}\,h(m)$ under which a deterministic sign model reproduces the singlet exactly, derive the $\sqrt{m}$ edge law, and prove exact quantum correlations and angle-independent coincidence rates jointly impossible for pure-detection models. Surviving local accounts trade off measurement dependence against a $\cos 4(a-b)$ modulation of the fourfold coincidence sum, of relative amplitude up to 12.4%, which vanishes at the CHSH angles and has never been bounded below 1%. A settings-torus protocol reaches $5σ$ sensitivity at 0.1% within hours: a flat result forces $M\gtrsim 95\%$ of Hall's floor; a fringe would contradict the flat-rate prediction of quantum mechanics. Finally I exhibit a local mechanism -- moire phase locking -- with deterministic phase evolution and all randomness quenched in frozen offsets and flight times; with 1024 offsets it attains the certified floor exactly at $η_{\rm eff}=1$ at every tested fidelity, from 10% down to 1%, and its softening of the correlation extremes is a falsifiable fingerprint.

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