Manuscript VII-F@1 · VII-F.tex · section · 2d81c03f

A finite cell dictionary

Exact finite decoder and reversible implementation › A finite cell dictionary · lines 1407–1445

There are $25$ cells in the incoming compact patch and $49$ in the outgoing compact patch. The fixed exterior adds three unbounded rays and three faces. Thus the global dictionary contains $55$ labels, and six bits suffice for a cell location.

One explicit dictionary is:

integer codes 0 1 - 3 4 - 6 7 - 9 10 - 12 13 - 15 16 - 18 19 - 21 22 - 24 25 - 27 28 - 30 31 - 33 34 - 36 37 - 39 40 - 42 43 - 45 46 - 48 49 - 51 52 - 54 labels P A_{i} D_{i} e_{i} c_{i} t_{i} o_{i} V_{i} Q_{i} B_{i} C_{i} u_{i} v_{i}^{edge} w_{i}^{-} w_{i}^{+} U_{i}^{-} U_{i}^{+} exterior rays Z_{i} .

Codes $55, \dots, 63$ are invalid.

At $s = 0$ , codes $25, \dots, 48$ are germ metadata and are not valid regular locations. All incoming location labels remain valid outgoing locations at the event. In particular, $τ$ is injective.

Displayed formulas in this passage

unlabeled · line 1415
$integer codes 0 1 - 3 4 - 6 7 - 9 10 - 12 13 - 15 16 - 18 19 - 21 22 - 24 25 - 27 28 - 30 31 - 33 34 - 36 37 - 39 40 - 42 43 - 45 46 - 48 49 - 51 52 - 54 labels P A_{i} D_{i} e_{i} c_{i} t_{i} o_{i} V_{i} Q_{i} B_{i} C_{i} u_{i} v_{i}^{edge} w_{i}^{-} w_{i}^{+} U_{i}^{-} U_{i}^{+} exterior rays Z_{i} .$