A predictive time-exclusion system: a Bayesian O(1)-complexity estimator for active gating in single-photon detection

This work proposes a temporal estimation protocol based on the probabilistic exclusion of an alternative path following a negative outcome at a detector. For a 15 m fiber with refractive index n=1.5, the computed geometric delay is approximately 75.05 ns. The ideal model predicts P(B|SA) = 1/(2 − ηA), giving 74.07% and 90.91% for detection efficiencies of 0.65 and 0.90. A reproducible Monte Carlo simulation (N=200000, seed 20260912) confirms these values within sampling noise (74.28% and 90.92%) and, for a model with realistic losses (ηgeom=0.95, dark count rate 1%, jitter σ=0.08 ns), yields P(B|SA) = 70.6% and 86.4%, with a mean absolute temporal error (MAE) of 0.064 ns computed directly from the simulated error sample. The primary decision has O(1) algorithmic complexity and does not depend on real-time Bayesian inference; a secondary Bayesian layer can be executed offline for calibration. An adversarial analysis shows that, at the pessimistic combination of plausible datasheet extremes (ηA=0.35, ηgeom=0.80), P(B|SA) drops to 48.54%, below chance — delimiting the parameter range in which the protocol is useful. The protocol is falsifiable and intended for subsequent experimental validation; no bench result is claimed.