Bell Parameter Dependence on Quantizer Resolution: Evidence from Photonic and Superconducting Systems and Implications for Einstein's Local Realism

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) = 2√2π · 2N · sin(π/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=2√2 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: Sclassical(N → ∞) = Squantum(j = 1/2) = 2√2 suggesting that 2√2 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 CHₙₒᵣₘ by adjusting the temporal resolution window across two independent runs IBM ibm_torino 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.