The Recursive Transport Operator: Quvit Transport, Enriched Tower Composition, and Exact Route Holonomy on the Coprime Substrate

This preprint develops the Recursive Transport Operator, an exact finite-field mechanism for carrying certified payloads through successive coprime-residue lattice floors while preserving endpoint value, arrival order, and transportable state as distinct objects. The associated arithmetic quvit is a sparse finite-field register whose routing, projection, survival, and in-transit actions are derived from the substrate rather than supplied by the caller.The paper proves a five-term transport exact sequence and a general enriched tower composition law in which the transported state retains its source address, canonical direct re-anchor, and accumulated route echo. A seven-atom opposite-order computation closes the resulting finite square: the endpoint quotient supports a nine-coordinate program, while the common certified wave realization selects an exact six-coordinate sector, with 100/100 common labels and 12/12 cocycle updates. The failed unrestricted nine-mode hypothesis is retained as a falsifier.Additional results include the endpoint-aperture quvit address law, exact route holonomy, a rank-two nilpotent transport coin with minimal indices [1,1], a genus-2 finite-field dispatch and collision classification, and three software reductions to practice: sparse microfluidic control, simulated carbon-capture control, and conservative whole-build solidification control with finite actuator-feasibility compilation.Claims are restricted to the proved algebraic domains and registered finite computations stated in the manuscript. Arbitrary-floor certification, analytic limits, and proposed cross-physics maps remain explicit open questions. A definition-first verifier, bounded evidence bundle, and complete SHA-256 audit mapping are available from the author on reasonable request.