Microscopic Parent Reconstruction in the Axis Model: Charged Simplicity-Defect Response, Determinant Soldering, and Infrared Compatibility
Andrew Morton · Public preprint · Conditional microscopic compatibility
Builds a microscopic route to the charged-field content of the localized-cell theory and establishes conditional infrared compatibility.
Abstract
The constructive charged-cell theory of the Axis Model establishes a finite-energy localized classical solution in a scalar–charged-field–Proca sector, while the primitive complex charged field enters that construction as Parent data rather than as a reduction of the earlier pre-geometric architecture. We construct a microscopic route from a local SU(2)_UV BF/coherence sector to the required infrared charged-field content. Direct local descent of a fundamental V_(1/2) block from the integer-spin local field algebra is excluded by center parity and by the Lorentz type of the available off-Cartan modes. A unique minimal residual-charge scalar composite nevertheless exists before exact simplicity reduction: the weight-one component of the symmetric-traceless simplicity defect, 𝒪_C⁺ = ∗_B(B⁺ ∧ B⁰). Exact simplicity removes this channel. Selective relaxation together with a positive kinetic response produces one real two-dimensional charged response fiber. Its nonlinear regular domain is an open disk, and determinant normalization gives a natural positive Gram sigma-model metric whose degeneracy boundary lies at infinite field distance. Physical U(1)_G charge requires a distinct compact charge line and a bifundamental soldering map. A minimal global realization is supplied by a split rank-two Hermitian link bundle with a unit section and determinant-line soldering. A polynomial linear-link completion then reduces to a controlled localized charged-cell infrared action with explicit ancestor power counting and remainder parameters. The resulting renormalizable microscopic family is broader than the localized-cell truncation, and the microscopic coefficients are not uniquely selected. Separately, the exact localized-cell theorem persists on a nonzero open operator neighborhood. A nonzero tree-level descendant intersects a conservative core persistence domain, establishing structural microscopic-to-infrared compatibility. Complete core-tail inheritance, independent microscopic parameter selection, and quantum-particle physicalization remain open.
Scope
The construction establishes conditional microscopic compatibility. Selection of a unique microscopic parent, inheritance of the localized-cell theorem with controlled core and tail bounds, and quantum-particle existence remain open.
Paper and supporting files
The Zenodo deposit includes manuscript sources, analytic calculations, verification scripts and numerical outputs for the conditional microscopic construction.
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