Theorem 8.1

Theorem 8.1 (Uniform guarded path presentation). Fix a finite alphabet and history length in degree one and distance one. In each final behavioral fibre, all parallel paths generated by endpoint detours, literal absorptions, causal-garbage changes, and temporal slides are presented by the following length-independent guarded cell families:

1. garbage same-coordinate triangles and different-coordinate squares;

2. collapse cells for garbage-trivial D/A/T edges;

3. strong Peiffer squares and the same-row D/A triangle;

4. carrier-cube and inessential temporal Peiffer squares;

5. strict mixed naturality squares; and

6. the bounded A/T hexagon.

The three support captures use vertical cancellation, and D/T is derived.