Mirror-Induced Carrier Structure and Phase Axis Selection

Title: Mirror-Induced Carrier Structure and Phase Axis Selection Author: Craig Edwin Holdway — Independent Researcher, Winnipeg, Manitoba, Canada ORCID: 0009-0003-2945-2852 Description: This Theorem establishes that the branch-exchange involution J acts as an orientation-reversing anti-automorphism on the triadic carrier C_X = span{e₇, e₆, e₂}, possesses a unique invariant axis, and that this axis coincides exactly with the image of the canonical projector Π_A from T21. The basis action J(e₇) = e₇, J(e₆) = e₂, J(e₂) = e₆ is uniquely selected by the combined constraints of the T26–T29 phase extraction plane, the T23 carrier–representation bridge, and the T21 carrier algebra, independently of a first-principles derivation from T17 kernel geometry. The orthogonal complement P⊥ = span{e₆, e₂} is the J-flipped phase-bearing plane. The J-odd subspace E⁻ = span{e₆ − e₂} is the unique J-odd rotational direction, and μ arises as its amplitude. The commutator transport chain produces a unique irreducibly propagating transverse mode with recurrence Y³ = 5Y and discrete propagation law ψₙ₊₃ = 5ψₙ₊₁. Amendment (incorporated): The local fixed-axis and phase-axis selection results are solid as linear-algebraic consequences of the T21/T23 carrier-triplet structure. Any global symmetry interpretation inherits the unresolved T21 double-cover distinction. Until the spinor-lift closure is proved, T46 should be read as an SO(3)-level observable carrier statement, not yet as a forced SU(2)-state-level statement. Status: T46 local matrix result: Solid. Unique invariant axis of orientation-reversing involution on 3D space: Solid (linear algebra). Fix(J) = Im(Π_A) via phase-transport-bridge compatibility: Conditional on ordered-lift role preservation. Basis action J(e₇) = e₇, J(e₆) = e₂, J(e₂) = e₆: Uniquely selected by compatibility argument; T17 derivation open as independent confirmation. Y³ = 5Y: Solid (direct matrix computation on {9,8,24}). μ = −8βh₁: Conditional on kernel support identification from T14/T17. T46 global SU(2) interpretation: Conditional on T21 spinor-lift closure (Theorem 22 open). Dependencies: T17, T18, T20, T21, T23, T26, T27, T29, T31.