Manuscript VIII-A@3 · VIII-A-v3.tex · theorem · 2398a747
Theorem: Fixed-presentation completeness
Completeness and observation invariance › A1: uniqueness in the fixed presentation · lines 907–924 · proof included or linked
VIII-A@3#A:thm:A1
Fix a realized description, its adapted charts, packet, reference framing, overlap components, and seam maps. Two proposals agreeing on these data but differing on one prescribed transition cannot both be certified. The same conclusion holds if several transitions differ.
Proof. The fixed data prescribe the unique affine map
Condition (E1) requires the proposed transition to equal this map. Two different affine maps cannot both equal it. Apply this argument to any differing component.
Displayed formulas in this passage
unlabeled · line 918