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August 19, 2026Open Access

Closure Rank, Gauge Carriers, and Canonical Representations Reconstruction, Dimensional Compression, and the 1→2→3 Generative Gauge Hierarchy

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Authors

PLPhilip Lilien

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Overview

Theoretical analysis reveals a matroid-based dimensional hierarchy mapping to U(1), SU(2), and SU(3) gauge carriers, suggesting algebraic foundations for fundamental physical symmetries.

Key Points

  • To develop a mathematical reconstruction of the 1 to 2 to 3 closure-carrier hierarchy and investigate how fundamental gauge group symmetries emerge from order-theoretic and matroidal geometries.
  • Constructed a finite reconstruction functional obeying normalization, monotonicity, unit-bounded growth, and submodularity to generate matroidal rank geometry.
  • Applied minimal complex realization on carrier support spaces and analyzed carrier stabilizers using continuous phase freedom and determinant-neutral bundle conditions.
  • Established that minimal complex realizations for ranks one through three yield complex spaces C, C^2, and C^3, bounded strictly at rank three by an exterior algebra support boundary.
  • Demonstrated that preserving complex phase and volume top forms reduces stabilizer groups to U(1), SU(2), and SU(3), generating standard adjoint representations 3 and 8 alongside tensor and exterior power families.

Cite This Study

Philip Lilien (2026) studied this question.

synapsesocial.com/papers/6a8563c403308d306e2d710fhttps://doi.org/10.5281/zenodo.21981354
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