From Fractional Charge to Confinement: A Scalar-Field Representation of Quarks

This paper is archived as a speculative research work.Quarks pose a distinctive representation problem in the Scalar Fields: electric charge is not primitive SF ontology, yet the physical quark sector requires two fractional charge magnitudes. This paper represents that distinction through two complete composition-defined constituent classes rather than through partial phase exposure or charge-labeled associations. The two-recurrence class Q^(2)=(T, _T) is based on the triangular bounded-support core, while the one-recurrence class Q^(1)=(B_C, _C) uses a four-point constituent organization. Their respective constituent-conditioned recurrence signatures provide the structural distinction required at the interface for 2/3 -type and 1/3 -type charge classes. Because the seam relations _i are constitutive of quark identity rather than external binding relations, confinement follows directly from the architecture: removal of the defining seam does not leave an unchanged free quark. The framework nevertheless preserves identifiable constituent structure inside larger organizations. A working three-quark proton architecture realizes the constituent pattern Q_A^(2)+Q_B^(2)+Q_C^(1) , giving the structural ratio 2:2:1 , while a separately certified eleven-point Q^(1) - Q^(1) construction proves that two confined quark constituents can remain individually identifiable within a valid Composition. The representation thereby links fractional-charge class, composition-defined quark identity, confinement, and partonic persistence while maintaining a strict separation between Scalar-Field structure and physical electric-charge interpretation.