Finite QED Spectral Skeleton from EAS Scalar Fields: Internal Spectral Package, Charge-Class Representation, and NCG Input
This paper is archived as a speculative research work. This paper derives the finite internal spectral skeleton required for the noncommutative-geometric derivation of QED from EAS scalar-field structure. The construction begins with scalar points, rank-3 association records, scalar values/signs, phase-specific reports, and a corrected lepton support package consisting of phase-isomorphic A/B sheets completed by scalar junction points j_0, j_1, j_2. From this scalar-field data we construct the finite QED-sector package S_F^phi = (A_Q^phi, H_F^phi, D_F^phi, J_F^phi, gamma_F^phi, rho_Q^phi). The common-mode phase algebra is A_Q^phi ~= C. The finite carrier is the report space H_F^phi = V_F^phi (+) E_F^phi, where V_F^phi records scalar points and E_F^phi records phase-exposed rank-3 association reports. The finite first-order operator D_F^phi = [ 0, (partial_F^phi)* ; partial_F^phi, 0 ] is built from phase-specific scalar association differences, while its square packages the corresponding finite stiffness/readout form. The protected A/B carrier supplies a real-structure component satisfying (J_F^phi)^2 = -I, and the scalar-point/association-report decomposition supplies the grading gamma_F^phi. The QED phase representation acts through finite charge classes Q_hat in {-1, 0, +1}. In the corrected charge-source account, these charge classes are not sourced by scalar-value signs on the A/B sheets. They are source-compressed from the handedness-induced exterior SOO report rho_H = (rho_{H,0}, rho_{H,1}, rho_{H,2}) by Q_hat = C_Q(rho_H) = (rho_{H,0} + rho_{H,1} + rho_{H,2}) / 3. The same-sign and opposite-sign A/B presentations used below are therefore finite carrier-level encodings of nonzero charge classes and neutral contrast, not the scalar-field origin of charge. The result is a finite internal spectral skeleton derived from scalar-field data rather than postulated, with its NCG role understood against the standard spectral-action framework (Connes 1994, Chamseddine & Connes 1997). This paper supplies the finite input for the subsequent NCG construction in which S_F^phi is paired with the standard spacetime spectral triple to obtain QED by inner fluctuation and spectral action.
Authors
- Michael E. Labhard (ORCID: https://orcid.org/0009-0008-0231-7067)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-05-30
- DOI
- https://doi.org/10.5281/zenodo.20385524
- Primary Topic
- Noncommutative and Quantum Gravity Theories
- Type
- preprint