Classical Common-Envelope U(1)_G Charge-Three Body Factor in the Axis Model: Continuum Existence, Hamiltonian Stability, and Branch-Resolved Fragmentation

Andrew Morton · Public preprint · Classical existence, stability and fragmentation bounds

Establishes a linearly stable classical charge-three body and bounds its energy relative to specified fragmentation branches.

Current program context

The later weak-representation paper develops the conditional weak exterior module and separates its representation algebra from the additional requirements for physical electron and neutrino sectors.

Abstract

We establish an exact classical common-envelope charge-three body factor in a scalar–charged-field–Proca parent theory with conserved U(1)_G charge. A computer-assisted core–tail construction proves the existence of a locally unique, finite-energy, spherically symmetric solution with N_cell = 3, componentwise exponential decay, and certified rest energy 12.6333236079 ≤ E₃ ≤ 12.9933308143. A constrained continuum Hessian certificate gives Morse index one, with kernel generated exactly by the global phase mode and three spatial translations. The charge–frequency slope is strictly negative, and the quadratic form is strictly coercive on the fixed-charge, fixed-momentum quotient. The associated reduced Hamiltonian generator is maximal skew-adjoint in the quotient energy inner product and generates bounded unitary linear evolution. Lorentz covariance therefore places the stable rest solution on an exact classical Poincaré mass hyperboloid. A separately certified charge-two branch satisfies 9.7252796546 ≤ E₂ ≤ 10.0632863096. Together with the certified charge-one branch, outward-rounded interval comparison gives E₃ < E₁ + E₂, E₃ < 3E₁, with lower separation margins 1.8304908512 and 2.3022952182 in parent energy units. These inequalities establish energetic separation from the declared localized 1 + 2 and 1 + 1 + 1 fragmentation channels. Within the Axis Model matter construction, the exact charge-three solution provides the common spatial factor for the conditional neutral degree-three frame singlet. Their tensor product defines an exact linearly stable conditional classical common-envelope body factor. A spectator-fiber inheritance result shows that adjoining a passive two-dimensional weak fiber preserves the localization, classical stability, Poincaré orbit, and branch-resolved fragmentation certificate for each fixed weak component. The result therefore supplies the classical body layer connecting localized charged-cell dynamics to the downstream fermion construction. Controlled quantum-particle existence, spin and exchange statistics, electroweak component resolution, and electromagnetic identity define the subsequent interfaces.

Scope

The result is an exact, linearly stable classical body, with fragmentation bounds for the specified branches rather than a proof of a global minimum. Charge-three refers to screened Parent U(1)_G charge, not three electromagnetic charges; quantum-particle existence, physical electroweak identity, and spin and exchange statistics remain unestablished.

Paper and supporting files

The Zenodo record includes the manuscript PDF and the Axis Common Envelope Body Reproducibility archive.

Read the current paper and supporting files on Zenodo

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Abstract checked 28 August 2026 · v1 · public release 11 August 2026.