Equal-looking copied spots are rejected unless the checked source matches. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Duplicate spots are not evidence
The helper rejects duplicate reciprocal addresses before a lesson can render.
(2,2) cannot appear twice in one checked map
A stale projected address fails the ledger
If the displayed family is 2,2,1, the cited projected address must stay 2,2.