φ-Lattice of Elementary Particle Masses: A Precise Formula for the Muon Mass from 9 Baryon Sectors

This is version 2 of the φ-lattice study, extended with new experimental tests and theoretical foundations. ═══════════════════════════════════════════════════════════════UPDATE (Version v2, 16 September 2026)═══════════════════════════════════════════════════════════════ NEW EXPERIMENTAL RESULTS — Tests on 19 exotic hadrons (PDG 2024/2025, data from LHCb, BESIII, Belle II): • Pentaquarks: 6/6 hits (100%) Pc(4312), Pc(4330), Pc(4440), Pc(4457), Pcs(4338), Pcs(4459) • Tetraquarks: 6/7 hits (85.7%) X(6900), X(7200), Zcs(3985), Zc(3900), Zb(10610), Zb(10650) • New baryons: 4/5 hits (80%) Xi_cc(++), Xi_bc(0), and others Total: 17/19 hits = 89.5% Statistical significance: P(17/19 by chance) < 10^-15 (≈ 7σ) Notable exact matches:• Zcs(3985) → N_low sector (d = 0.0038)• Pcs(4338) → Omega sector (d = 0.0100)• Pc(4330) → Omega sector (d = 0.0133)• Xi_bc(0) → Sigma* sector (d = 0.0182) The previously reported fermion-boson asymmetry (v47) is NOT confirmed on the extended dataset — the φ-lattice appears universal for all exotic hadrons. ═══════════════════════════════════════════════════════════════NEW THEORETICAL RESULTS — Connection to SU(5) via the Coxeter matrix A₄═══════════════════════════════════════════════════════════════ We discover that 7 of the 9 φ-lattice sectors are exact algebraic combinations of the eigenvalues λ_k of the Coxeter matrix A₄ (the Cartan matrix of SU(5)): λ_k = 2 - 2·cos(kπ/5), k = 1, 2, 3, 4 λ_1 = X² = 0.3819660113 (exact) λ_2 = 1 + X² = 1.3819660113 λ_3 = φ² = 2.6180339887 λ_4 = 2 + φ = 3.6180339887 Exact sector identifications:• N_low = -λ_1• Sigma* = +λ_1• Xi_3/2 = -λ_1• Omega = -λ_1 / 2• Delta = 2·λ_2 - λ_3• N_heavy = -X·λ_1 / 2• Sigma = +X·λ_1 / 2 Only Ξ_1/2 (0.321175) remains open — likely involving an SU(3) factor of 1/3. ═══════════════════════════════════════════════════════════════CONTENTS OF THIS VERSION═══════════════════════════════════════════════════════════════ • v50_archive.pdf — full archive (49 versions, Russian)• v52_publication.pdf — Russian publication version• v53_english.pdf — English full paper• v54_beamer.pdf — English Beamer presentation• v56_chinese.pdf — Chinese full paper• v57_beamer_chinese.pdf — Chinese Beamer presentation• v58_new_tests.pdf — NEW: Tests on exotic hadrons (v2)• v63_theory_summary.pdf — NEW: Theoretical foundation (v2) ═══════════════════════════════════════════════════════════════ORIGINAL ABSTRACT (Version v1, 16 September 2026)═══════════════════════════════════════════════════════════════ We report the discovery of a φ-lattice structure in elementary particle masses. All 21 known baryons group into 9 sectors of the form a + b·cos(72°) with precision 10^-16. For the muon we find the exact formula n(μ⁻) = 11 + X⁵(1 − X³/2) where n(m) = log_φ(m/m_e), X = 1/φ, with relative accuracy 5.6 × 10^-7 — three orders of magnitude better than the PDG experimental precision. All 6 known pentaquarks also fall into sectors of the same lattice. We establish exact algebraic identities relating powers of X to Fibonacci numbers through cos(72°): X^n = (−1)^n F_(n−1) + (−1)^(n+1) · 2 F_n · cos(72°) X^5 − X^4 = −X^6 The lepton bases correspond to Lucas numbers: e⁻: 0, μ⁻: 11 = L_5, τ⁻: 17 = 2L_5 − F_5 SU(3) structure is confirmed: octet 8/8, decuplet 10/10 = 18/18. The result suggests a deep connection between the golden ratio, the Fibonacci sequence, and the structure of strongly-interacting particles. ═══════════════════════════════════════════════════════════════KEYWORDS═══════════════════════════════════════════════════════════════ golden ratio, Fibonacci numbers, muon mass, baryon sectors, pentaquarks, tetraquarks, SU(3) symmetry, SU(5), Coxeter matrix, φ-lattice, Q(√5), exotic hadrons, PDG 2024/2025 ═══════════════════════════════════════════════════════════════CITATION═══════════════════════════════════════════════════════════════ MOBIDUR (2026). φ-Lattice of Elementary Particle Masses: A Precise Formula for the Muon Mass from 9 Baryon Sectors. Zenodo. https://doi.org/10.5281/zenodo.22801092 ═══════════════════════════════════════════════════════════════