Three distinct numerical roles

Fix integers

They specify report precision, clock precision, and permission width.

The continuous family (eq:family) is used to prove geometry and one-sided laws. The finite decoder represents only its dyadic subfamily. Rounded reports are additional finite data and do not define that subfamily.

For each of the $24$ finite edge slots in Proposition prop:lengths, store

An inactive slot has report zero. All finite lengths are less than $6$, so $b+3$ bits per report suffice.

The canonical report residual satisfies

All reports can be determined exactly from the symbolic length table: the lengths are rational multiples of square roots of fixed integers, and floor comparisons reduce to exact rational or integer comparisons.