Cross-modal counts need exact agreement before a shared sample ledger is trusted. 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 row has equal address counts

The x-ray bins, phase rows, and optical fields are all 4, so the acceptance bit is 1.

Nbin=4,Nrow=4,Nfield=4,A=1N_{\text{bin}}=4,\quad N_{\text{row}}=4,\quad N_{\text{field}}=4,\quad A=1
Multimodal ledgerEach displayed ledger value is bound to a source check.binsrowsfields4 bins4 rows4 fields

A missing reciprocal bin fails the address audit

The second row has 3 bins but 4 phase rows and 4 optical fields, so the acceptance bit is 0.

(3,4,4)A=0(3,4,4)\Rightarrow A=0
Multimodal ledgerEach displayed ledger value is bound to a source check.binsrowsfields3 bins4 rows4 fields

An extra phase row fails the same audit

The third row has 5 phase rows while bins and fields remain 4. The exact acceptance bit is 0.

(4,5,4)A=0(4,5,4)\Rightarrow A=0
Multimodal ledgerEach displayed ledger value is bound to a source check.binsrowsfields4 bins5 rows4 fields