Prime Transport Is a Chain Map for the Complete-Graph Seam Incidence
Prime multiplication is an injective relabelling. Its common Mellin and
half-density scalar lifts to edges, giving the exact chain identity
delta T_p = T_p^(1) delta.
Distinct prime transports commute on vertices and edges, so their braid residual vanishes at label collisions. Primitive and prime-square scale transport therefore preserve the canonical finite-seam incidence before aggregation.
The remaining chain-map obstruction is confined to Fourier–Poisson sewing, which genuinely mixes labels. Its finite primal–dual matrix must preserve the augmentation line before its exterior lift can represent the same seam incidence.
Research packet:
research/grothendieck/prime-transport-is-a-chain-map-for-the-complete-graph-seam-incidence.md
Exact checker:
research/grothendieck/checkers/check_prime_transport_seam_chain_map.py
The checker passes 5/5 gates.