Theorem: Unique transverse incidence-event parameter

The declared family has exactly one incidence-event parameter, $s=0$. Across it:

1. the six vertices $B_i,C_i$ emerge from $P$;

2. twelve edges and six faces emerge with the laws above;

3. the transverse link at the singular intersection changes from three incident faces to six.

There is no other collision, vanishing active cell, or contact with the crest in the parameter window.

Proof. The incoming cyclic link is

The outgoing cyclic link is

The bisectors are genuine creases because the adjacent gradients are $(3/5,0)$ and $(0,3/5)$. Across a cone ray, unfolding changes the sign of the transverse gradient, so those creases are also genuine.

For each open epoch, the combinatorics is fixed. Positivity follows from Propositions prop:lengths and prop:areas; separation and complete coverage follow from Lemma lem:decomposition. All born coordinates tend to the apex at zero, while the persistent cells have their incoming nondegenerate limits. The different link valences exclude a mere relabeling.