Demonstrates distinct scalar outputs from rearranged transport segments, indicating nuanced transport behavior.
Within the T17 - T30 kernel transport framework, two realizations of a triadic kernel sharing the same spectral carrier and commutator source are shown to produce distinct scalar outputs when their transport segments are rearranged. The native kernel K = [A, T, B] and its mirrored anti-automorphic realization J(K) = [B, T^rev, A] share the common carrier χ₀(η,p) = (1/p)sin(ηp) − η·cos(ηp) and the same commutator source. The mirrored scalar branch satisfies: Ξ_J(η,p,a) = −β(a)·χ₀(η,p) where β(a) is the scalar-channel coefficient of the round-trip transport closure Xd→nXn→d = α(a)P⊥ + β(a)P_sc. Three further results are established: the scalar-visible transport residue is β(a) − α(a); the complementary-sector closure defect is Δ⊥(a) = (α(a) − 1)P⊥; and this defect is generically nonzero whenever transport-realization change is not confined to the scalar channel. The theorem is purely internal. No physical or Hilbert-space identification is asserted. The interpretive remark notes structural analogy to path-dependent amplitude formation in quantum systems: analogy only. Status: Carrier invariance, transport coefficient isolation, round-trip closure readout, and complementary-sector defect formula are solid by direct algebraic argument. Conditional on assumption (iv), the decomposition of the round-trip transport operator is assumed, not derived; explicit computation of α(a) and β(a) from the T17 kernel architecture remains open. Conditional on assumption (iii), transport non-neutrality assumed; structural derivation from T17 geometry is open. All results inherit T16/T17/T20 conditionality. Dependencies: T14, T15, T16, T17, T18, T19, T20, T26, T27, T28, T29, T30.
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Craig Edwin Holdway (2026) studied this question.
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