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This research explores a SO(10)/Pati-Salam grand unified theory (GUT) candidate focusing on its Lagrangian and predictions.

May 25, 2026Open Access

Triptych-GUT V3 — An algebraically constrained SO(10)/Pati-Salam candidate: Lagrangian, thresholds, fermion spectrum and falsifiable predictions

Key Points

This research explores a SO(10)/Pati-Salam grand unified theory (GUT) candidate focusing on its Lagrangian and predictions.
Developed a standalone GUT candidate based on the Triptych Conceptual framework with a dimensional input of 246.220 GeV.
Formulated the breaking chain SO(10) → SU(4)C × SU(2)L × SU(2)R and evaluated scalar sector contributions.
Derived exact values for parameters including Cabibbo angle and bottom-quark mass through algebraic constraints.
Proton decay predicted via p → e⁺π⁰ with a falsifiable lifetime band of τ_p ∈ [2×10^41, 3×10^45] years, consistent with experimental limits.
B-L threshold measured with a Haar measure constraint f_B-L = 3/4, yielding critical insights for GUTs.
Calculated relation for sin²θ13^PMNS = m_s/m_b, supporting the minimal model for fermion masses.

Abstract

DESCRIPTION EN We present a standalone SO (10) /Pati-Salam GUT candidate derived from the Triptych Conceptual framework with a single dimensional input v = 246. 220 GeV and four axioms A1, A2, A3, A7. The breaking chain SO (10) → SU (4) C × SU (2) L × SU (2) R → SM is completed by a LR-symmetric scalar sector (Σ, ΩL, ΩR, Φ), yielding b₄C = −20/3 and b₂L = b₂R = −8/3 exact. The B-L threshold is fixed by a Haar measure constraint fB-L = 3/4 exact. In the fermion sector: Cabibbo angle sin θ12 = λ = (√6−2) /2 exact; bottom-quark mass mb = uₘin · m_τ · exp (−Vₘin/16) at 0. 006% of PDG exact, SymPy; quark-lepton relation sin²θ13PMNS = mₛ/mb estab. ; Koide relation K = 2/3 exact. The CKM unitarity-triangle backbone is fixed by σgold · σ_* = 1/2 exact. Proton decay via p → e⁺π⁰ gives a falsifiable lifetime band τₚ ∈ 2×10⁴1, 3×10⁴5 yr, compatible with Super-Kamiokande and above Hyper-Kamiokande sensitivity. Four residual dynamical locks define the programme for V4. Description FR Nous présentons un candidat GUT SO (10) /Pati-Salam autonome dérivé du cadre du Triptyque Conceptuel avec une unique entrée dimensionnelle v = 246, 220 GeV et quatre axiomes A1, A2, A3, A7. La chaîne de brisure SO (10) → SU (4) C × SU (2) L × SU (2) R → MS est complétée par un secteur scalaire LR-symétrique (Σ, ΩL, ΩR, Φ), donnant b₄C = −20/3 et b₂L = b₂R = −8/3 exact. Le seuil B-L est fixé par une contrainte de mesure de Haar fB-L = 3/4 exact. Dans le secteur fermionique: angle de Cabibbo sin θ12 = λ = (√6−2) /2 exact ; masse du quark bottom mb = uₘin · m_τ · exp (−Vₘin/16) à 0, 006 % du PDG exact, SymPy ; relation quark-lepton sin²θ13PMNS = mₛ/mb établi ; relation de Koide K = 2/3 exact. Le squelette algébrique du triangle d’unitarité CKM est fixé par σgold · σ_* = 1/2 exact. La désintégration du proton via p → e⁺π⁰ donne une bande de durée de vie falsifiable τₚ ∈ 2×10⁴1, 3×10⁴5 ans, compatible avec Super-Kamiokande et au-delà de la sensibilité de Hyper-Kamiokande. Quatre verrous dynamiques résiduels définissent le programme pour V4.

Triptych-GUT V3 — An algebraically constrained SO(10)/Pati-Salam candidate: Lagrangian, thresholds, fermion spectrum and falsifiable predictions

Key Points

Abstract

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