Event germs, guard, transport, and finite code

parameter, approximate reports. If an incoming length is ${\ell }_{-}=v(-s)$, floor quantization with step $h$ reports zero throughout

A zero-length-word guard therefore need not detect the event.

Instead, either an external exact clock supplies $s=0$, or the finite code stores

with $d\ge 0$ and a signed $(d+2)$-bit word. The guard tests $j=0$.

For fractional precision $b\ge 1$, an unsigned $(b+4)$-bit word reports

Every displayed length is less than $16$. Both central report slots are zero at the event. The inactive slot is retained; it is not an erased wire.

The decoder reconstructs exact geometry from the family identifier, rational constants, mode, and exact $s$. Reports are checked auxiliary numerical data. Irrational arm lengths are decoded from eq:arms; on a fixed finite parameter grid their reports are computable by exact comparisons of squared rational numbers.

tables and domains. The fixed table contains the four $C_i$, collar chart, prescribed transition words, exterior translations, and $R(\pi /2)$. All entries have rational coefficients. Arbitrary group closure is not asserted.

The exchange code contains 26 report words, one mode bit, an $r$-bit permission word with $r\ge 1$, the exact parameter word, and fixed identifiers. The square code has five reports, mode, permission, and fixed identifiers.

For a fixed named interface of size $n$, encode every location in an $\ell$-bit word covering the finite union of input and output labels. Add an initially zero $\ell$-bit history word per name. Invalid labels and inconsistent reports lie outside the forward decoder domain.