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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19800512 |
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Table of Contents:
- <p>Geometric Unity from First Principles I develops a classical, semidirect-covariant formulation of Geometric Unity on an ambient manifold Y with a four-dimensional observation slice X. The paper reconstructs several central GU ideas from explicit geometric data, stated assumptions, and checkable variational claims.</p> <p>The work focuses on three technical gaps in public Geometric Unity presentations. First, it defines the Shiab pairing as the scalar coefficient of a canonical wedge-star density on admissible same-degree bundle-valued forms. Second, it constructs completed semidirect-covariant geometric variables: the affine-invariant gauge connection A − B, its curvature F(A − B) = F − D_A B + B ∧ B, and the augmented torsion T_aug = T(ω̂_B) = T(ω) − Φ(B), where ω̂_B is the completed spin connection. Third, it proves a fixed-embedding Projection–Variation theorem showing that, under admissible boundary and corner hypotheses, variation on the observation slice agrees with the pullback of the Euler–Lagrange system for the corresponding slice density.</p> <p>The paper also distinguishes the completed GR slice from the raw ambient connection. Under the completed slice condition, the completed tangential connection reduces to the Levi–Civita connection of the induced metric on X, while the raw tangential connection requires an additional compatibility condition. This distinction removes a common ambiguity in two-space formulations.</p> <p>As an induced consequence, the quadratic slice theory contains Einstein–Hilbert, Yang–Mills, and Dirac kinetic sectors with the stated sign conventions and no irreducible bilinear graviton–gauge mixing. Eliminating nondynamical axial torsion gives a fixed-sign local axial contact, written in the sign-safe O_55 basis.</p> <p>This paper is the first installment in the “Geometric Unity from First Principles” series. Its purpose is not to claim a completed physical model, but to establish a rigorous classical scaffold for later work on matter embedding, anomaly closure, BRST/BV quantization, renormalization, boundary dynamics, and observable tests.</p>