All Bell experiments to date share a fundamental design feature: the binarization of continuous detector signals into discrete outcomes \-1, +1\. This paper presents a local deterministic model that demonstrates how this binarization process affects the observed Bell parameter S. We derive an exact geometric function: S (N) = 22 2N (2N) where S depends strictly on the detector's quantization resolution N, growing monotonically from S=1. 8006 at N=1 to the Tsirelson bound S=22 as N, without postulating nonlocality at any point. This curve is of purely geometric origin — computable before any experiment. A key result is the convergence identity, verified numerically from first principles: S₂₋₀ₒₒ₈₂₀₋ (N) = Sₐₔ₀₍ₓₔ₌ (j = 1/2) = 22 suggesting that 22 is not an exclusive frontier of quantum mechanics but a geometric limit reached by both classical and quantum systems at maximum information resolution. This theoretical framework is empirically validated using: NIST 2015 Public Data: showing a +0. 53\% increase in CH₍₎ₑ₌ by adjusting the temporal resolution window across two independent runs IBM ibmₜorino Quantum Hardware (2026): showing a +0. 84\% increase in S using multi-threshold superconducting detectors with M=2N real thresholds. These results imply that the domain of validity of Bell's theorem is the binary measurement regime. In the continuous regime, Einstein's question about local realism remains open as a falsifiable hypothesis with exact quantitative prediction: S must grow with N at an approximate geometric rate of 1/4 per additional bit, verifiable with 330, 000 shots on high-fidelity hardware. Keywords: Bell's Theorem, Local Realism, Quantization Resolution, CHSH Inequality, NIST 2015, IBM Quantum, Fine's Theorem, Tsirelson Bound, Signal Processing.
Jonathan Federico Castro Rouanet (Thu,) studied this question.