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April 19, 2026Open Access

Extended Triptych V3 — Consolidated Synthesis: U(1)×SU(2)×SU(3) gauge structure, foundations, algebraic identities and running

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Authors

YNYann Nédélec

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Overview

Working document consolidates gauge structure insights in the Standard Model, suggesting structural identities and key results.

Key Points

  • This document aims to synthesize and structure the results related to the U(1)×SU(2)×SU(3) gauge structure.
  • Developed from the master equation (□_g + R/6)ψ + ∂V/∂ψ* = 0.
  • Utilized minimal coupling and non-abelian Madelung decomposition.
  • Identified key algebraic and structural identities within the Standard Model.
  • Established Theorem G focusing on structural protection of G_N.
  • Algebraically identified sin²θ_W = (2−√2)/4.
  • Showed tan θ_W = V_min reflects in integers.
  • Concluded m_Z = m_H = v/2 at the UV fixed point.
  • Reconstructed the CKM sector with high precision.

Cite This Study

Yann Nédélec (2026) studied this question.

synapsesocial.com/papers/69e472d8010ef96374d8eb8chttps://doi.org/10.5281/zenodo.19626511
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Also Consider

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  1. 1Extended Triptych V4 — Madelung decomposition, gauge structure U(1)×SU(2)×SU(3), fermionic spectrum and fine-structure constant in the fields ℤ[√2], Q(√5) and Q(√6)2026
  2. 2Extended Triptych V5 — Madelung decomposition, gauge structure and fermionic spectrum in ℤ[√2], ℚ(√5), ℚ(√6)2026
  3. 3Triptych-GUT V2.1 — A candidate framework for dynamical, algebraic and spectral grand unification2026
  4. 4Triptych-GUT V13: Algebraic, Spectral and Dynamical Framework for Grand Unification with a Single Dimensional Calibration2026
  5. 5The Triptych — A Candidate Dynamical Grand Unification Framework, Algebraic and Spectral, Structured by Fixed Points, with a Single Dimensional Calibration Scale and No Continuous Free Parameter2026