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| Main Author: | |
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| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2026
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| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.19683849 |
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Table of Contents:
- <p><span><em>This paper is archived as a speculative research work.</em></span></p> <div class="markdown markdown-main-panel tutor-markdown-rendering enable-updated-hr-color"> <p>The present paper addresses how genuine interaction, once isolated in the kernel, is represented at the interface. We show that realized residual support is not merely a bookkeeping remainder of admissible comparison, but carries the first genuine interaction fiber: a canonically organized residual slot plane forced by the rank-3 cyclic closure grammar. Genuine interaction then organizes response anisotropically on this carrier and selects a preferred projective ray, interpreted as the local interface representative of directed non-quotientable residual response.</p> <p>We further show that once admissible redescription and canonical equivalence are imposed, the minimal stable representation of the residual carrier is naturally complex rather than merely real. This yields an emergent U(1) transport structure on realized residual support. When the interaction-bearing carrier occurs in persistence-protected higher sectors, the interface representation extends non-abelianly: protected doublets force an SU(2) sector and protected triadic sectors force an SU(3) sector. Accordingly, the minimal compact interaction hierarchy of the framework is U(1), SU(2), SU(3).</p> <p>Using these carriers and transport sectors, we construct a unified interface action combining covariant mismatch, closure-defect penalties, and the closure-forced sign split between continuation-compatible and closure-irreducible comparison classes. From this action we derive the coupled matter and transporter equations, the corresponding closure-balance equations, and the associated Lie-algebra-valued edge currents together with their covariant continuity identities. We then reorganize the matter side explicitly into residual-line, protected-doublet, and protected-triad representations and assemble their equations into a unified block-matrix form.</p> <p>This paper shows that kernel-side genuine interaction admits a structured interface representation as a theory of carriers, transport, currents, symmetry sectors, and variational field equations.</p> </div>