Finite code and decoder

Use the following transverse dictionary:

\begin{array}{c|c@{\qquad}c|c}
\text{labels}&\text{codes}&\text{labels}&\text{codes}\\ \hline
P&0&A_i&1+i\\
D_i&4+i&B_i&7+i\\
C_i&10+i&e_i&13+i\\
c_i&16+i&t_i&19+i\\
o_i&22+i&u_i&25+i\\
v_i&28+i&w_i^-&31+i\\
w_i^+&34+i&V_i&37+i\\
Q_i&40+i&U_i^-&43+i\\
U_i^+&46+i&\text{exterior rays}&49+i\\
\text{exterior faces}&52+i&&
\end{array}

There are 55 labels; six bits suffice. Codes 55–63 are invalid. The dictionary describes transverse cells and their open axial products. It does not purport to list every auxiliary axial-end boundary cell or every physical apparatus port.

For a precision $b\ge 0$, store for each of the 24 finite edge slots

in $b+3$ bits; inactive slots have report zero. All lengths are less than $8\ell$. At dyadic $s$, the floor is determined exactly by rational comparison and squaring of nonnegative algebraic quantities. No arbitrary-real oracle is required.

The geometric and particle word has

bits: mode, permission, signed exact $j$, fixed-family identifier, length reports, and a nine-bit fixed packet. The packet uses six bits for $P$ and three symbolic identifiers for the geometric source, deficit, and rest/worldsheet frame. It does not approximate $\pi /2$ numerically.

A canonical word decodes to the exact family formula, parameter, mode-appropriate cellulation or germ, chart table, packet, and reports. For $j<0$, only $m=0$ is admitted; for $j>0$, only $m=1$ is admitted; at zero either mode denotes its stated germ. Exact formulas are reconstructed from the fixed family identifier and finite parameter, not from rounded lengths.

For $n$ original names, reserve six current location bits and six history bits per name. Axial port coordinates and any additional spectator locations are independently declared. Actual live quantum ports in this paper lie in the regular collar; the abstract singular label is not a quantum wire on $\mathcal{W}$.