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

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
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preprint

Finite QED Spectral Skeleton from EAS Scalar Fields: Internal Spectral Package, Charge-Class Representation, and NCG Input

Michael E. Labhard
Zenodo (CERN European Organization for Nuclear Research)
Noncommutative and Quantum Gravity Theories
preprint

Finite QED Spectral Skeleton from EAS Scalar Fields: Internal Spectral Package, Charge-Class Representation, and NCG Input

Michael E. Labhard
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Noncommutative and Quantum Gravity Theories
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