Fixed-Level TQFT Transport of Marked Handleslide Coherence: Disjoint Cubes and a Three-Handle Pentagon
Fix an ordinary level $K\geq1$ and a fully specified family of pairwise disjoint positive handleslides on a compression body. The main question is how a literal geometric relation becomes a literal finite-level operator relation. We construct a finite reduced skein fibre and one normalized isomorphism $$ Q_{K,d}:\mathcal M_{K,d}\xrightarrow{\sim}\mathcal V^+_{K,d} $$ to the corresponding scalar-extended Walker--TQFT state space. Reusing this map at every vertex sends the supplied weight-zero slide cylinders to $E_K$-linear automorphisms: geometric squares become operator squares, finite…
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