Prescale Recorded Floor Three-Row Scan - Detector Physics: Timing and Spatial Reconstruction Step by Step

A prescale recorded floor scan divides accepted events by the prescale divisor to get recorded events, then checks that count against a minimum floor. With prescale 3, accepted events 6, 12, and 18 give recorded counts 2, 4, and 6 against floor 4, yielding margins -2, 0, and 2 (fail, pass, pass) exactly for the stated toy event ledger; real detectors have trigger efficiency, dead time, prescale jitter, backgrounds, and finite-count uncertainty.

Prescale division turns accepted events into recorded events. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Six accepted events record too few readout rows

Accepted events 6 divided by prescale divisor 3 record 2 events.

m=N_{\text{rec}}\mathbin{-}N_{\min}=2\mathbin{-}4=-2,\quad\text{fail}

Twelve accepted events land on the floor

Accepted events 12 divided by prescale divisor 3 record 4 events.

m=N_{\text{rec}}\mathbin{-}N_{\min}=4\mathbin{-}4=0,\quad\text{pass}

Eighteen accepted events clear the floor

Accepted events 18 divided by prescale divisor 3 record 6 events.

m=N_{\text{rec}}\mathbin{-}N_{\min}=6\mathbin{-}4=2,\quad\text{pass}