Establishes a transport scale and phase axis in the context of oriented transport mechanisms, indicating new structural insights.
TA11 closes the first Transport Architecture block (TA3–TA11) by establishing the primitive one-way transport scale ε = 1/320 and fixing the phase axis A = iσ_y, both from the same oriented two-leg transport mechanism. The oriented distance-2 transport layer E₂(Q₅) contains exactly 160 directed channels (80 unordered pairs × 2 orientations). Normalizing a unit closure defect against this layer gives \[ δ_full = 1/160 \]. The branch-exchange involution Θ, established in T47/T50, splits this defect equally across two oriented legs, fixing ε = 1/320. By TA5, the observable round-trip phase coefficient is \[ μ = 2ε = 1/160 \]. The phase-doubling lemma establishes that the same two-leg mechanism that produces magnitude doubling also forces the phase axis. Each mediated leg contributes π/4, accumulating π/2 total. Purely real symmetric coupling produces no phase residue, \[ Q = Qᵀ ∈ ℝ \] implies \[ Im(Q) = 0 \] implies \[ µ = ½Tr(QR) = 0 \], so nonzero phase requires oriented complex transport contributions. The two-leg accumulation forces the generator \[ A ~ iσ_y \]. The T8–TA11 Bridge Lemma identifies the spectral ratio β/α with the primitive transport scale under three constraints: same defect source \[ (δ_full = 1/160) \], same two-branch splitting \[ (ε = 1/320) \], and same perturbative normalization. This gives \[ β/α = ε_one-way = 1/320 \], structurally derived rather than numerically inserted. The continuous phase closure theorem shows that iterating the one-way transport operator gives \[ T_phase^k = e(k/320)A + O(k/320²) \], with observable readout \[ µ_k = sin(k/320) + O(k/320²) \], controlled for \[ k ≪ 320² \]. The primitive scale 1/320 thereby links the spectral ratio, one-way transport, phase generator, continuous-limit evolution, and observable sine-law readout in a single unified structure. Geometry supplies the defect scale. Transport supplies the phase structure.
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Craig Edwin Holdway (2026) studied this question.
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