This Theorem establishes the round-trip transport residual (T − I) ᵣot = (1/160) A from a second independent derivation route (barrier symmetry B = e^ (π/4) AΘ acting on an ordered pair of noncommuting generators), confirming and strengthening the T48 result. The barrier symmetry acts by exchange-and-inversion: BPB¹ = −Q, BQB⁻¹ = −P, consistent with T47. One-leg transport is modeled by X₍→₃ = (I + λP) (I + λQ) ; the return leg by X₃→₍ = (I − λQ) (I − λP). A supporting lemma establishes by explicit second-order expansion that T = X₃→₍X₍→₃ satisfies: T − I = 2λ²A − 2λ²I + O (λ³) where A = ½P, Q is the antisymmetric generator and −2λ²I is an isotropic normalization drift that does not affect relative phase or branch observables. Using P² = Q² = I on the reduced two-state space (supported by T36–T37) and P, Q = 2A. Under the one-leg normalization λ² = 1/320 inherited from T8 via T48: (T − I) ᵣot = (1/160) A That both the T48 near-identity route and the T49 barrier-symmetry route converge on the same residue is structurally significant. Status: First-order cancellation, second-order decomposition, and scalar term analysis solid by direct computation. λ² = 1/320 inherited from T8 via T48, not rederived here. B exchange-and-inversion action on P, Q assumed consistent with T47, explicit derivation from T17 kernel geometry open. P² = Q² = I supported by T36–T37, not independently rederived. Qubit algebra correspondence structural, holds within T36–T37 hypotheses, does not assert the full framework is a quantum theory. Dependencies: T7, T8, T17, T36, T37, T47, T48.
Craig Edwin Holdway (Sun,) studied this question.