Definition: Complete matching output

For a realized description $g$, write

An accepted output supplies the finite tables, exact equalities, and topological evidence for all of the following obligations:

1. {Vertex and overlap matching $\mathcal{V}$.} Every proposed transition equals its prescribed affine map on the declared overlap component. Reverse maps are inverses; paired endpoints and shared segments match; face boundaries close; regular small vertex words are affine identities.

2. {Particle matching $\mathcal{P}$.} The declared deficit, oriented rest frame, affine worldline, and peripheral map agree with the installed packet.

3. {Ordered holonomy evidence $\mathcal{H}$.} The ordered words, overlap-component indices, and winding classes are supplied. A positive primitive particle meridian has winding one, not merely a nonidentity matrix.

4. {Core–collar matching $\mathcal{K}$.} The core and collar share their prescribed boundary realization and transported framing. Their primitive words give the same installed peripheral map.

5. {Worldline data $\mathcal{W}$.} All charts describe the same singular worldline. Its holonomy fixes that worldline pointwise, rest vectors are transported consistently, and the declared slice intersection lies on it.

Embedding, spacelikeness, and nondegeneracy of active cells are separate realization requirements. A germ is accepted as a specified one-sided limiting object, not as a regular cellulation with extra active zero-size cells.