Fixed presentations and complete acceptance

The ambient equality is important. Agreement on the endpoints of one segment does not generally determine a Lorentz-affine map: a nontrivial boost can fix a spacelike line pointwise.

Write the certificate as

Its components contain the following five checks:

1. Realized local matching: endpoints, shared segments, polygon closure, overlap components, canonical ambient transitions (eq:ambient-matching), and regular local vertex words.

2. Packet matching: deficit, oriented rotation, and spinless peripheral affine map.

3. Marked ordered words: affine products with their overlap data and integer winding marks.

4. Peripheral agreement: core and collar primitive maps in the declared transported frame.

5. Particle data: worldline, rest vectors, slice intersection, and pointwise fixation of the worldline.

Embedding, spacelikeness, and active-cell nondegeneracy are separate geometric preconditions. Matrix matching alone proves none of them.