Coherence Boundary Depth Scans

readout-overlap-boundary-three-row-scan

A readout overlap boundary scan checks whether the signal interval overlaps the detection window by at least the minimum amount, with endpoint touch counting as no overlap. The rows give overlaps 3, 1, and 0 against minimum 1, yielding margins 2, 0, and -1 (pass, pass, fail) exactly for the stated toy interval ledger; real readout has timing jitter, window calibration, detector efficiency, and overlap-resolution uncertainty.

Positive overlap has a boundary before endpoint touch fails. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Readout needs positive overlap with the window

The window is fixed, and the signal interval moves toward the edge.

m=Δtoverlap−Δtmin⁡m=\Delta t_{\text{overlap}}-\Delta t_{\min}
Positive overlapThe signal overlaps the window by more than the minimum.windowsignaloverlapsignal accepted

Three signal intervals show the positive-overlap boundary

A one-unit overlap is the boundary; endpoint touch has zero overlap and fails.

tstarttendΔtm583210111011130−1\begin{array}{c|c|c|c}t_{\text{start}}&t_{\text{end}}&\Delta t&m\\5&8&3&2\\10&11&1&0\\11&13&0&-1\\\end{array}
Overlap boundaryOne positive unit is still accepted.windowsignaloverlapsignal accepted

Endpoint touch fails because overlap is zero

The interval check treats endpoint touch as no positive overlap.

m=−1failm=-1\quad \text{fail}
Endpoint touch rejectedThe overlap duration is zero.windowsignalno overlapsignal rejected