Bipartite overlap conjugacy

Abstract

Rebracketing a legal alternating path preserves every half-edge and gives an invertible code.

Definition 1.1 (Construct the overlap homeomorphism).

$$\forall U\in Type,V\in Type,I\in Type,J\in Type,d\in \mathrm{Boundary}\left(U,V,I,J\right),topologyU\in \mathrm{TopologicalSpace}\left(U\right),topologyV\in \mathrm{TopologicalSpace}\left(V\right),\mathrm{Homeomorph}\left(\mathrm{LeftPath}\left(d\right),\mathrm{RightPath}\left(d\right)\right)$$

Formalization. D5/S3/ConceptDynamics/Coding/BipartiteOverlapConjugacy.pathHomeomorph (✓ std3).

Source. Repository-derived.

Commentary.

The preceding and current half-edges give an explicit inverse in both directions. Coordinate evaluation proves continuity on the legal-path subspaces.

References

• Truth anchor: D5/S3/ConceptDynamics/Coding/BipartiteOverlapConjugacy.pathHomeomorph