M¨obius Transport Closure with Admissibility Filtering

This paper establishes that observable transport between sectors L ↔ R satisfies \[ h_LR = v_L v_R / Δ_M \], where the canonical normalization denominator is: \[ Δ_M = 2 · |V(Q₅)| · dim(Q₅) = 2 · 32 · 5 = 320 \] This denominator is not chosen; it is forced by the requirement that global transport conservation \[ S_n + S_d = 0 \] is preserved under partial projection Π_Y. The paper separates two categorically distinct operations: \[ 35 →^Θ 8 ↝ Δ_M = 320 \] The first step is admissibility filtering: the Möbius admissibility operator Θ maps the full 35-slot ternary interaction space (T17) to an 8-dimensional admissible subspace corresponding to the 8 cubic cells of Q₄ ⊂ Q₅. The second step is transport normalization scaling: the 8 admissible carriers normalize against the full oriented transport channel count of 320. The oriented counting conventions across the TA chain are unified here explicitly: 80 unoriented distance-2 pairs in Q₅; 160 oriented defect legs (TA11); 320 full oriented transport channels (TA12), each layer introducing an orientation factor of 2. The factor \[ 320 = 32 · 5 · 2 \] decomposes as vertex count × transport directions × Möbius orientation double cover. The key structural result is that projection breaks local closure but not global closure:\[ Π_Y𝒢 ≠ 𝒢Π_Y \], so the observable sector loses phase locally while the full system remains globally conservative. The observable correction \[ ψ_eff = ψ + ηCψ \] exists precisely because of this local/global distinction. Perfectly aligned states satisfy \[ Π_Yψ = ψ, giving Kψ = 0 \]and \[ Cψ = 0 \] : they are unaffected by the leakage correction. The normalization \[ Δ_M = 320 \] is consistent with TA11 (ε = 1/320), the Hamiltonian depth resolution of TA13, and the Möbius round-trip structure.