Manuscript VIII-B@3 · VIII-B-v3.tex · definition · 3aa6baa1

Definition: Fixed developed presentation

Spinless packets and the matching contract › Fixed presentations and complete acceptance · lines 428–446

VIII-B@3#def:presentation, VIII-B@3#eq:ambient-matching

A developed presentation fixes:

the developed realization and all face, edge, and vertex labels;
every oriented overlap component;
the affine extension $A_{f}$ of each face-coordinate map;
its prescribed developed ambient identification $S_{g f}$ , including the seam identification;
a frame and topological winding convention.

An accepted transition on that component must satisfy the ambient affine-map equality

t_{g \leftarrow f} A_{f} = A_{g} S_{g f} .

Its restriction must also match the realized shared segment.

Displayed formulas in this passage

VIII-B@3#eq:ambient-matching · line 441
$t_{g \leftarrow f} A_{f} = A_{g} S_{g f} .$