Interface contract: Four-face realization and exchange

For $\sigma \in [-1,1]$, the installed profile-$\mathsf{A}$ constructor supplies:

1. an embedded spacelike capped graph, with slope bound $3/5$, the displayed patch dictionary, and a complete declared ambient finite dictionary with affine within-epoch length laws;

2. exactly one four-face adjacency exchange, at $\sigma =0$, with positive noncentral cells;

3. adapted affine charts, identity contractible patch words, and complete accepted ambient (E1)–(E5);

4. a certified boundary interface with its resting exterior, with particle and seam outside the moving incidence patch;

5. fixed ambient packet ${\Pi }_{{\mu }_0}$, fixed exterior particle incidence, and certified original-name transport through the exchange.

The transport may identify junction labels. A finite implementation must retain enough input information to reverse that identification. No source command is admitted in this profile.