Finite dictionaries and canonical reports

Fix finite packet tables, parameter grids, controller widths, location dictionaries, and a prescribed finite word. A finite word in a continuum family, without such an encoding, does not by itself define a finite implementation problem.

For particle codes, exact lengths determine canonical reports

Inactive incoming born slots have canonical report zero. At a germ, their limiting reports are zero and germ mode distinguishes the two codes.

Packet index, exact clock, module, and mode reconstruct the exact realization and complete matching data. Reports are redundant consistency data, not independently variable lengths. Exact algebraic comparisons determine their floors, including equality cases. The particle bounds in app:checks show that $b+4$ bits suffice for each of the 24 reports.

Four-face and collar codes use their own installed dictionaries. They are not silently stored in the unrefined hybrid block. Unbounded exterior cells add no finite-edge reports to that block.

Retaining classical input information to make a deterministic update reversible is standard in reversible computation Bennett1973. The following finite synthesis lemma supplies the explicit bound used here.