Manuscript VIII-B@3 · VIII-B-v3.tex · section · 3aa6baa1

Cell dictionary and encoding

Cell dictionary and encoding · lines 2698–2752

Code	Cell slot
Code	Cell slot
0	$P$
1–3	$A_{i}$
4–6	$D_{i}$
7–9	$r_{i}^{rad}$
10–12	$[A_{i}, A_{i + 1}]$
13–15	$[A_{i}, D_{i}]$
16–18	$[D_{i}, D_{i + 1}]$
19–21	$V_{i}$
22–24	$Q_{i}$
25–27	$B_{i}$
28–30	$C_{i}$
31–33	$u_{i}$
34–36	$v_{i}$
37–39	$w_{i}^{-}$
40–42	$w_{i}^{+}$
43–45	$U_{i}^{-}$
46–48	$U_{i}^{+}$
49–51	Exterior rays
52–54	Unbounded exterior faces

At the incoming source slice, slots 25–48 are invalid locations. Other listed slots have their incoming meanings. The radial slot is epoch dependent, but source replacement does not cross epochs.

This dictionary abstracts location to a cell label. It does not encode a continuously variable point within a cell. Source replacement preserves labels, not old developed coordinates.

One possible index encoding stores $m + K_{q}$ in $q + 2$ bits; one possible clock encoding stores $j + 2^{p_{clk}}$ in $p_{clk} + 2$ bits. Unused strings are invalid. Field order, valid metadata, and encodings are fixed before constructing $P_{geo}$ .

Invalid strings need no geometric interpretation. They complete the update to a permutation. Likewise, no geometric decoding is asserted for nonzero-work inputs or intermediate circuit words.