{"ID":23785146,"CreatedAt":"2026-09-18T12:18:08.888591469Z","UpdatedAt":"2026-09-18T14:54:40.538408265Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2608.18886","arxiv_id":"2608.18886","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":"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 register fidelity, from 10% to 1%, and its softening of the correlation extremes is a falsifiable fingerprint.","short_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) neede...","url_abs":"https://arxiv.org/abs/2608.18886","url_pdf":"https://arxiv.org/pdf/2608.18886v3","authors":"[\"Aaron Alai\"]","published":"2026-08-19T13:14:52Z","proceeding":"quant-ph","tasks":"[\"quant-ph\"]","methods":"[]","has_code":false}