Published October 26, 2026
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From Fractional Charge to Confinement: A Scalar-Field Representation of Quarks
Description
This paper is archived as a speculative research work.
Quarks exhibit two fractional electric-charge magnitude classes and spin- 12 behavior, while their experimentally accessible states occur within larger hadronic organizations. We examine a structural account of these properties in Entanglement–Algebraic Spacetime (EAS), an abstract algebra of conserved scalar values and phase-indexed reciprocal associations. Two complete quark-constituent architectures are defined by a core together with its constitutive seam: the triangular-core type Q_ T=(T, _T) and the five-edge, four-point-core type Q_ F=(B_C, _C). The rank-three incidence identity | B|=3|B|-2|E_int(B)| shows that the triangular core exposes three associations and the five-edge four-point core exposes two. A constitutive seam occupies one association in either quark, leaving respectively two and one continuation roles. Their F1 exterior incidences, together with admissible composite cyclic-handedness configurations, are consistent with the physical charge magnitudes 2e_*/3 and e_*/3 assigned by the established Charge Paper correspondence. The dependence of quark identity on the seam yields a structural account of confinement compatible with recognizable constituents inside larger compositions. A nine-point two-Q_ F construction satisfies a separately typed relational valid-Composition theorem, conditional on simultaneous cyclic phase placement (H2) and mixed-phase ambient-walk semantics (H4). A reciprocal proton seam ledger and two seven-point meson architectures illustrate further constituent arrangements at their respective admissibility levels. The spinorial physical correspondence established for qualified quark sources admits spin- 12 carriers for both architectures and singlet/triplet sectors for eligible pairs. The results connect quark constituent identity, fractional charge and spin through one specified algebraic architecture and its separately qualified physical interfaces.
Quarks exhibit two fractional electric-charge magnitude classes and spin- 12 behavior, while their experimentally accessible states occur within larger hadronic organizations. We examine a structural account of these properties in Entanglement–Algebraic Spacetime (EAS), an abstract algebra of conserved scalar values and phase-indexed reciprocal associations. Two complete quark-constituent architectures are defined by a core together with its constitutive seam: the triangular-core type Q_ T=(T, _T) and the five-edge, four-point-core type Q_ F=(B_C, _C). The rank-three incidence identity | B|=3|B|-2|E_int(B)| shows that the triangular core exposes three associations and the five-edge four-point core exposes two. A constitutive seam occupies one association in either quark, leaving respectively two and one continuation roles. Their F1 exterior incidences, together with admissible composite cyclic-handedness configurations, are consistent with the physical charge magnitudes 2e_*/3 and e_*/3 assigned by the established Charge Paper correspondence. The dependence of quark identity on the seam yields a structural account of confinement compatible with recognizable constituents inside larger compositions. A nine-point two-Q_ F construction satisfies a separately typed relational valid-Composition theorem, conditional on simultaneous cyclic phase placement (H2) and mixed-phase ambient-walk semantics (H4). A reciprocal proton seam ledger and two seven-point meson architectures illustrate further constituent arrangements at their respective admissibility levels. The spinorial physical correspondence established for qualified quark sources admits spin- 12 carriers for both architectures and singlet/triplet sectors for eligible pairs. The results connect quark constituent identity, fractional charge and spin through one specified algebraic architecture and its separately qualified physical interfaces.