M¨obius Transport Closure with Admissibility Filtering

This paper establishes that observable transport between sectors L ↔ R satisfies \ hLR = vL vR / ΔM \, where the canonical normalization denominator is: \ ΔM = 2 · |V (Q₅) | · dim (Q₅) = 2 · 32 · 5 = 320 \ This denominator is not chosen; it is forced by the requirement that global transport conservation \ Sₙ + Sd = 0 \ is preserved under partial projection ΠY. The paper separates two categorically distinct operations: \ 35 →^Θ 8 ↝ ΔM = 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: \ ΠY𝒢 ≠ 𝒢ΠY \, so the observable sector loses phase locally while the full system remains globally conservative. The observable correction \ ψₑff = ψ + ηCψ \ exists precisely because of this local/global distinction. Perfectly aligned states satisfy \ ΠYψ = ψ, giving Kψ = 0 \ Cψ = 0 \: they are unaffected by the leakage correction. The normalization \ ΔM = 320 \ is consistent with TA11 (ε = 1/320), the Hamiltonian depth resolution of TA13, and the Möbius round-trip structure.