Manuscript En03-A@1 · En03-A.tex · section · 5398614e

Compact collar and frozen exterior

External conical geometry and certified local moves › Compact collar and frozen exterior · lines 1940–2003

En03-A@1#tab:certificate, En03-A@1#tab:snapshots

Field	Incoming	Event	Outgoing
Core faces	$E, W, N, S$	same	same
Collar faces	four hexagons	same	same
Central adjacency	$E W$	four-face point	$N S$
Central triples	$E W N, E W S$	common junction	$N S E, N S W$
Central length	$16 (- s) /25$	$0$	$16 s /39$
Four arms	$\frac{10 + s}{75} 1921$	$\frac{2}{15} 1921$	$\frac{26 + s}{195} 1921$
Four horizontal cap segments	$X_{s}$	$10/3$	$X_{s}$
Four vertical cap segments	$Y_{s}$	$26/5$	$Y_{s}$
Two horizontal collar joins	$(4 - s) /3$	$4/3$	$(4 - s) /3$
Two vertical collar joins	$(4 - s) /5$	$4/5$	$(4 - s) /5$
Four outer horizontal segments	$14/3$	$14/3$	$14/3$
Four outer vertical segments	$6$	$6$	$6$
Core charts	eq:boosts	unchanged	unchanged
Core transitions	$C_{i} C_{j}^{- 1}$	same table	new incidence
Collar transitions	$A_{i} A_{j}^{- 1}$	unchanged	unchanged
Boundary transitions	fixed	fixed	fixed
Particle labels	$(π /2, e_{0})$	unchanged	unchanged
Mode	$0$	$0 \to 1$	$1$
Permission	$k \geq 1$	$k \to k - 1$	$k - 1$

affected bounded data; the fixed exterior completes the configuration. A regular patch has 18 vertices, 25 edges, and 8 faces. The event realization has 17 vertices and 24 edges. Two stored central slots give 26 length reports.

Length	$- 1$	$- 1/2$	$0$	$1/2$	$1$
Active central	$16/25$	$8/25$	$0$	$8/39$	$16/39$
Arm/ $1921$	$3/25$	$19/150$	$2/15$	$53/390$	$9/65$
$X_{s}$	$3$	$19/6$	$10/3$	$7/2$	$11/3$
$Y_{s}$	$5$	$51/10$	$26/5$	$53/10$	$27/5$
$(4 - s) /3$	$5/3$	$3/2$	$4/3$	$7/6$	$1$
$(4 - s) /5$	$1$	$9/10$	$4/5$	$7/10$	$3/5$
Outer horizontal	$14/3$	$14/3$	$14/3$	$14/3$	$14/3$
Outer vertical	$6$	$6$	$6$	$6$	$6$

reference snapshots. Report words are derived from these laws, not independent exact geometric labels.

Compact collar and frozen exterior

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