What question did this study set out to answer?

The research aims to establish the behavior of the branch-exchange involution in relation to carrier structures.

May 6, 2026Open Access

Mirror-Induced Carrier Structure and Phase Axis Selection

Key Points

The research aims to establish the behavior of the branch-exchange involution in relation to carrier structures.
Theorem formulation to identify spatial behaviors along unique invariant axes.
Analysis of basis actions and phase extraction planes within specific carrier algebras.
Identified orthogonal complement as a significant phase-bearing plane.
Established recurrence relation Y³ = 5Y governing transverse mode propagation.

Abstract

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 CX = spane₇, e₆, e₂, possesses a unique invariant axis, and that this axis coincides exactly with the image of the canonical projector ΠA 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⊥ = spane₆, e₂ is the J-flipped phase-bearing plane. The J-odd subspace E⁻ = spane₆ − 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 ψ₍+₃ = 5ψ₍+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 (ΠA) 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.

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