A predictive time-exclusion system: an O(1) decision architecture with offline Bayesian calibration for active gating in single-photon detection

This work proposes a gating protocol conditioned on the negative outcome of a reference detector: the absence of a click at A probabilistically excludes path A and predicts the arrival time at B from the calibrated geometric delay. For a 15 m fiber with refractive index n=1.5, the delay is approximately 75.05 ns. Path inference is P_inference(B|S_A)=1/(2−η_A), invariant to losses in arm B; the observable yield, however, depends on the end-to-end efficiency of B and is evaluated here by paired comparison against the baseline of opening B's window on every accepted event. Under a heralded source with exactly one photon per accepted event, no false clicks at A, and no gate-command failures, the protocol suppresses a fraction η_A/2 of acquisition windows without rejecting genuine detections available to the baseline, raising the yield per opened window by 2/(2−η_A) — a factor independent of the multiplicative efficiencies common to arm B. For η_A=0.65: 32.6% of windows suppressed, 100% retention, and enrichment of 1.483. With a 1% independent false-click probability at A, retention falls to 99.0% while enrichment is unchanged — which is why savings, retention, and enrichment are always reported jointly. The gain collapses with heralding efficiency r (at r=0.1, enrichment of 1.03) and is exactly null for a fixed-mean coherent source without a herald. The primary decision has O(1) complexity and does not depend on real-time Bayesian inference; a secondary Bayesian layer can run offline for calibration. The protocol is falsifiable and intended for subsequent experimental validation; no bench result is claimed.