A final sample ledger shows how address, capture, and day gates combine. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The first sample record passes every gate

Spacing is 4 m, rows are 4, captures are 12, and days are 2. All three gates accept, so release is 1.

Arows=1,Acap=1,Aday=1,A=1A_{\text{rows}}=1,\quad A_{\text{cap}}=1,\quad A_{\text{day}}=1,\quad A=1
Multimodal ledgerEach displayed ledger value is bound to a source check.spacingrowscapturesdays4 m4 rows12 captures2 days

One extra phase row blocks the release

The second record keeps captures and days unchanged, but row count is 5 instead of 4. The row gate is 0 and release is 0.

Nrows=54,A=0N_{\text{rows}}=5\ne4,\quad A=0
Multimodal ledgerEach displayed ledger value is bound to a source check.spacingrowscapturesdays4 m5 rows12 captures2 days

A late throughput row also blocks the release

The third record restores 4 rows and 12 captures, but the target takes 4 days. The day gate is 0 and release is 0.

D=4>3,A=0D=4>3,\quad A=0
Multimodal ledgerEach displayed ledger value is bound to a source check.spacingrowscapturesdays4 m4 rows12 captures4 days