Spatial Boundary Depth Scans

Trigger Enabled Floor Three-Row Scan

A trigger enabled floor scan checks whether the number of enabled triggers meets a minimum count, so too few enabled channels fails the gate. The three rows give enabled counts 3, 4, and 5 against floor 4, yielding margins -1, 0, and 1 (fail, pass, pass) exactly for the stated toy trigger ledger; real detectors have threshold calibration, dead time, trigger efficiency, pileup, and finite-count uncertainty.

A policy floor on enabled channels is separate from the trigger bit. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Accepted candidate still lacks enabled-channel margin

Candidate channel 2 is accepted by the trigger bit 1. Enabled channel count is 3.

m=E−Emin⁡=3−4=−1,failm=E\mathbin{-}E_{\min}=3\mathbin{-}4=-1,\quad\text{fail}
Trigger maskEnabled channels and veto bits decide acceptance.onononoffoffoffoffoffhittotalChannels=8 countenabledChannels=3 countcandidateChannel=2 countcandidateEnabled=trueveto=falseaccepted=true

Four enabled channels exactly meet the policy floor

Candidate channel 2 is accepted by the trigger bit 1. Enabled channel count is 4.

m=E−Emin⁡=4−4=0,passm=E\mathbin{-}E_{\min}=4\mathbin{-}4=0,\quad\text{pass}
Trigger maskEnabled channels and veto bits decide acceptance.ononononoffoffoffoffhittotalChannels=8 countenabledChannels=4 countcandidateChannel=2 countcandidateEnabled=trueveto=falseaccepted=true

Five enabled channels clear the policy floor

Candidate channel 2 is accepted by the trigger bit 1. Enabled channel count is 5.

m=E−Emin⁡=5−4=1,passm=E\mathbin{-}E_{\min}=5\mathbin{-}4=1,\quad\text{pass}
Trigger maskEnabled channels and veto bits decide acceptance.onononononoffoffoffhittotalChannels=8 countenabledChannels=5 countcandidateChannel=2 countcandidateEnabled=trueveto=falseaccepted=true