Structure Building in the Scalar Fields

This paper is archived as a speculative research work.We develop a structural hierarchy for EAS Scalar Fields using only the relational mathematics admitted at the SF level. The hierarchy begins with the symmetric binary bit (SBB) as the first relational unit considered here, proceeds to the unique three-point bounded-support type, and then passes to separately typed Compositions. Within the compositional domain we distinguish generic Composition from a stronger valid-Composition class specified by six explicit conditions: a triangle root, rank–3 completion, phase-distinct triangle-to-exterior roles, all-point phase-specific triangle-to-exterior chain admissibility, inclusion of each phase-active association in such a chain, and exactly one associated partner per point in each phase. From ordered rank–3 association, bilateral phase-specific reciprocity, and these six conditions we prove the Composite Handedness Uniformity theorem: every valid Composition has one common point-level SF-to-slot handedness. The six-point double-triangle neutrino-like candidate satisfies the six validity conditions; the registered electron-like architecture exhibits separately typed nested and level-separated recurrence information; and the proton-like candidate exhibits composite-dependent completion whose local same/opposite-handed classification must be kept distinct from valid-Composition status. Increasing structural complexity is thereby represented by increasingly rich relational organization rather than by progressively larger bounded supports, while formation content, recurrence orientation, point-level handedness, Composition, and interface correspondences remain separately typed.