Signed Longitudinal Displacement Occupancy in the Axis Parent: Exact-Source Closure, a Constructive Charged-Cell Parent, Continuum Radial Localization, and the Three-Axis Composition Interface

Andrew Morton · Public preprint · Classical continuum existence

Constructs and validates an exact localized classical charged cell that provides the starting point for the Axis matter program.

Abstract

We construct a coherent-domain parent theory for a localized charged cell whose internal geometry consists of one signed longitudinal line and a complementary rank-two transverse plane. The signed source is carried by the existing Stueckelberg-completed U(1)_G sector. In component-canonical normalization the cell has charge weight q_G^σ = σ/√2, the retained interaction algebra is neutral, the Ward current is conserved, and the neutral-vector quadratic operator contains one electromagnetic null direction and one massive G_μ direction. The constructive parent is analytic on the scalar interval 0 ≤ ρ ≤ 6/5. Its charged Nambu cluster is uniformly isolated from the neutral heavy block by a gap of at least 5.98, its spectral projector is constant, and its band metric vanishes. Elimination of the neutral source-dual block gives K_G = 50, e_G = 0.1, and m_G = 0.8, and reduces the parent exactly to a frozen scalar–charged-field–Proca action with no downstream electroweak, gravitational, or fermion input. For the associated spherically symmetric unit-charge sector, interval arithmetic first certifies a Gauss-compatible trial configuration below the exact free charged threshold and encloses a unique finite Chebyshev–Lobatto collocation root. A subsequent function-space validation combines an exact half-line stable-tail graph with a bordered Chebyshev core operator. Directed interval bounds control the resolved finite block, every unresolved mode, both finite/high coupling directions, and the nonlinear derivative variation in one scaled product space. At the common radius r_⋆ = 0.0029, all ten radii polynomials are negative and the largest contraction row is 0.490268 < 1. The resulting solution exists on [0, ∞), has exact charge Q = 1, is locally unique in the certified Banach ball, and obeys componentwise exponential tail bounds with 0 < ρ < 6/5, f(0) > 0, W > 0, and κ > 9. Its total energy satisfies E_⋆ ≤ 7.451726 < 10.000999950004999 = m_∞, so the exact continuum solution is strictly subthreshold. Together, these results establish an exact localized one-cell sector and a typed composition export. Conditional on an ordinary one-cell-per-frame-line embedding and an isotropic selector, three equal-sign cells define the unique nonzero frame-scalar candidate sector with ledger (3z^σ, 6x). The postparent matter-carrier theory begins with the ordinary-slot embedding and physical-body selector; spacetime spin enters through an independent downstream factor.

Scope

The theorem constructs a localized classical solution for a specified parent action; its coefficients are constructive inputs. Its screened U(1)_G charge is distinct from electromagnetic charge, and quantum-particle existence, spin and exchange statistics, and physical multi-cell composition remain separate requirements.

Paper and supporting files

The Zenodo record includes the manuscript PDF and the Parent Reproducibility and Source archive.

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Signed Longitudinal Displacement Occupancy in the Axis Parent: Exact-Source Closure, a Constructive Charged-Cell Parent, Continuum Radial Localization, and the Three-Axis Composition Interface

Abstract

Scope

Paper and supporting files

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