Context
The general calculus treats a failed lift as a cocycle, its cohomology class as the obstruction, and a primitive—when one exists—as the receipt that repairs the presentation.
Proof or evidence
A unipotent three-cycle supplies the explicit displacement.
Verification notes
The exact archived proofs were reconstructed, the displayed hypotheses and degree conventions were checked, the original finite controls were replayed, and an independent implementation tested the connecting, graph-transport, staged, and missing-subcomplex boundaries.
Limitations
- The quotient loop alone does not determine its lifted endpoint.