Real Dead-Time Window Rejects, Then Accepts, Genuine Events - Detector Physics: Timing and Spatial Reconstruction Step by Step

A real lmsim event-arrival simulation (scenario gen-arrivals, case-studies/poisson-process-dead-time-filter/specs/nonparalyzable_e001.json, a genuine per-event Poisson arrival generator with a non-paralyzable dead-time filter, not a closed-form idealization or an ensemble mean/variance summary) supplies every value on this page, each rounded to four decimal places from the real simulation output and checked event by event against the real non-paralyzable rule. One real recorded event opens a real dead-time window; the very next real arrival lands inside it and is genuinely dropped; a later real arrival clears the same window and is genuinely kept. Real detectors add paralyzable/non-paralyzable mixing, multi-channel dead-time correlations, and finite-sample count uncertainty beyond this single-channel model.

Every value in this lesson is rounded to four decimal places from a real lmsim Poisson event-arrival simulation (scenario gen-arrivals, case-studies/poisson-process-dead-time-filter/specs/nonparalyzable_e001.json), not derived from a closed form. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A real dead-time window genuinely drops the next arrival

A real lmsim event-arrival simulation records a real true event at t=0.0051 seconds and opens a real 0.0100-second dead-time window. The very next real arrival, at t=0.0106, falls only 0.0055 seconds later — inside the real window — and the real simulation marks it not observed.

1\text{:}\ \Delta t=0.0055<\tau=0.0100\Rightarrow \text{dropped}

The real window clears and the next genuine event is kept

A later real arrival, at t=0.0392, lands 0.0341 seconds after the same recorded event — past the real 0.0100-second window — and the real simulation marks it observed, exactly as the non-paralyzable rule requires.

2\text{:}\ \Delta t=0.0341\ge\tau=0.0100\Rightarrow \text{kept}