Weak-Representation Soldering of the Axis Common Matter Carrier: Common-Body Lepton Architecture, Higgs-Resolved Components, and the Physicalization Boundary
Andrew Morton · Public preprint · Conditional representation construction
Builds a conditional weak and chiral lepton representation on the common classical body and identifies the requirements for physical electron and neutrino sectors.
Abstract
We construct a common-body lepton architecture from the established Axis matter-sector results and identify the boundary between the classically localized common carrier and physical electron and neutrino sectors. The charged-cell, multi-cell, and exact charge-three common-envelope constructions supply a projector-resolved internal carrier and a linearly stable classical body. A finite-fiber partial-isometry construction gives an exact conditional 𝔰𝔲(2)_L action, while Abelian equivariance requires equal restricted Parent U(1)_G charge across the weak doublet. Within the declared direct-product gauge structure, this selects the common-carrier realization without an additional dressing representation or enlarged gauge completion. Covariant Higgs-ray projectors resolve charged and neutral components and give the exact longitudinal-response identity P_ν R_z P_ν = 0. The full frame-U(2) lift yields the conditional exterior module Λ^• Ê_W* ≃ 𝟏 ⊕ 𝟐 ⊕ 𝟏; after tensoring with the Lorentz spinor bundle and selecting one total-Weyl sector, this realizes L_L ⊕ ν_R ⊕ e_R together with the corresponding relative central characters and canonical Dirac Yukawa morphisms. The construction remains a representation and stability result rather than a physical lepton theorem. We therefore formulate a graded physicalization certificate separating the bosonic common-body response from fermionic population and propagation, and requiring common-body spectral overlap, covariance and stability, a controlled neutral one-particle sector, and an infrared-complete dressed charged asymptotic sector. Numerical charge, masses, generation selection, flavor normalization, and the physical central-U(1)_Y connection remain open.
Scope
The paper constructs a conditional weak and chiral representation on a classical common body. Physical population, fermionic propagation, neutral one-particle support and a dressed charged asymptotic sector still require further construction and verification; numerical charge, masses and flavor are not derived.
Paper and supporting files
The record includes separate manuscript and bibliography sources plus a reproducibility archive for finite algebraic checks; those checks do not certify physical particle existence.
Read the current paper and supporting files on Zenodo
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Abstract checked 28 August 2026 · v4 · public release 16 August 2026.