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. The minimum composite is represented by a six-point double-triangle neutrino-like candidate; the registered electron-like architecture exhibits nested and level-separated compositional information; and the proton-like candidate exhibits three-constituent composite-dependent completion. The central result is that increasing structural complexity is represented by increasingly rich relational organization rather than by progressively larger bounded supports. Formation content, bounded-support classification, recurrence structure, Composition, and interface correspondences are kept separately typed throughout.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-12
DOI
https://doi.org/10.5281/zenodo.22735650
Primary Topic
Algebraic and Geometric Analysis
Type
preprint
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preprint

Structure Building in the Scalar Fields

Michael E. Labhard
Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
preprint

Structure Building in the Scalar Fields

Michael E. Labhard
preprint en

Abstract

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. The minimum composite is represented by a six-point double-triangle neutrino-like candidate; the registered electron-like architecture exhibits nested and level-separated compositional information; and the proton-like candidate exhibits three-constituent composite-dependent completion. The central result is that increasing structural complexity is represented by increasingly rich relational organization rather than by progressively larger bounded supports. Formation content, bounded-support classification, recurrence structure, Composition, and interface correspondences are kept separately typed throughout.

Zenodo (CERN European Organization for Nuclear Research)
Quality Education
Algebraic and Geometric Analysis
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