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

The unique event and its germs

The retuned polyhedral slicing family › The unique event and its germs · lines 1162–1187

Possible extra event	Exclusion
Inner cells reach the cap	$ρ \leq s / c < r$
Persistent radial edge collapses	$r - β s = β (2 - s) > 0$
Inner triangle degenerates off $s = 0$	Positive coefficient times $s^{2}$
Outgoing pentagon degenerates	$Area (V_{i}) > S_{α} β^{2} /3$
Collar degenerates	$r < 7/2 < 4$
New vertices coincide off $P$	Distinct ray/interior placement for $s > 0$
Particle-star edge loses its crease	Distinct unfolded gradients

The common limiting slice consists of the regular core triangles, collar, and resting exterior. The labels $P, A_{i}, D_{i}$ , the persistent slots, and the core/collar/exterior face labels persist. The outgoing-only $B_{i}, C_{i}$ , $P B_{i}, P C_{i}$ , $B_{i} C_{i}, C_{i} B_{i + 1}$ , and $U_{i}^{\pm}$ belong to outgoing germ metadata. A zero report in an inactive slot is a coding convention, not an additional geometric cell.

The unique event and its germs

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