ETCF - Emergent Temporal Coherence Framework

ETCF — Emergent Temporal Coherence Framework Abstract — English Michele Artioli | June 2026 We present the Emergent Temporal Coherence Framework (ETCF), a theoretical framework proposing that the fundamental constants of physics — particle masses, coupling constants, and mixing parameters — are not free parameters of nature but emerge necessarily from the combinatorial geometry of the 600-cell H₄, a regular four-dimensional polytope with 120 vertices whose symmetry structure is governed by the golden ratio φ. The framework operates entirely within ℤ[φ] — the ring generated by 1 and φ — and adopts zero free parameters as the benchmark for a valid derivation. The substrate Ω₀ is defined as a discrete, pre-metric, four-dimensional structure whose geometry is that of the H₄/E₈ lattice. Spacetime, mass, velocity, and time are not primitive: they emerge from phase correlation structures defined on this substrate through a modified Gross-Pitaevskii equation and a Madelung transformation. The 120 vertices of the 600-cell partition into 83 active nodes (local symmetry Z₁/Z₂/Z₃) and 37 inactive nodes (Z₅ + antipole), the latter having identically zero phase sum by algebraic identity. This partition — and the extended structure F₁₂ = H₄ ∪ D₄_extra with cardinality 144 = F₁₂ (twelfth Fibonacci number) — is the primary source from which physical observables are derived. The principal results, classified by epistemic status, are as follows. Proved results (deviation < 0.1%, complete structural derivation): the speed of light as the Bogoliubov sound speed of the condensate (0.0000% deviation); the photon as the zero-winding mode with spin 1, zero mass, and two polarisations; the muon anomalous magnetic moment Δaμ = (83/61) × 183 × 10⁻¹¹ = 249 × 10⁻¹¹ (0.000% from Fermilab/BNL 2023); the fine structure constant α⁻¹ = 248 − 3 × 37 = 137 (0.026%, residual attributed to QED running); the tau-to-muon mass ratio mτ/mμ = 33 − 10φ (0.016%); the coupling ratio αs/αem at the Planck scale 4 + 3φ (0.019%) and at M_Z scale 7 + 5φ (0.031%); the tau absolute mass mτ/m_P = φ⁻⁹⁶ × (33 − 10φ) (0.006%). Near-coincidence results (NC, deviation < 0.15%, algebraic structure identified): the muon absolute mass mμ/m_P = φ⁻⁹⁶ with exponent 96 = dim(𝕆) × |shell₁| = 8 × 12 (0.018%); the dark-to-baryonic matter ratio ΩDM/Ω_b = 12φ − 14 = 5.4164 (0.78%); the electron mass exponent k_e = 107.081 (0.084%, below the 0.1% threshold); six quark masses in the form φ⁻ᵏ with k = k₀ + n/d (all < 0.15%); the four CKM parameters including cos(δ_CP) = (3 + φ)/13 (0.04%); three neutrino observables including θ₂₃ = 45° (structural), sin²θ₁₂ = 37/120 (0.4%), and Δm²_atm/Δm²_sol = 203/6 (0.09%). The effective curvature K_eff = (336 + 72φ)/83, the phase fluctuation δΦ = φ⁻¹/10, and the inter-section coupling ε = (78 − 27φ)/120 form a closed algebraic system of invariants in ℤ[φ], with the exact identity K_eff + ΔK = 6. The E₈ → F₁₂ projection is established as canonical and unique (Theorem E). Emergent gravity yields T_μν from the substrate curvature with closed spacetime topology (Ω_k < 0) as a structural prediction. The cosmological constant problem is reduced from 121 orders of magnitude to an O(1) factor f = 3φ − 4 ∈ ℤ[φ], implying H₀_ETCF = 68.94 km/s/Mpc (0.61% deviation from DESI DR1). The framework makes four primary falsifiable predictions testable in the near term: (1) mτ = 1777.138 MeV/c², currently at 2.32σ tension with PDG 2024, to be resolved by Belle II with σ < 0.05 MeV by 2026–27; (2) Δaμ = 249.0 × 10⁻¹¹, in exact agreement with current Fermilab/BNL data, to be confirmed with σ = ±1.4 × 10⁻¹¹; (3) Δα/α = φ⁻²⁴ = 9.645 × 10⁻⁶ (Webb dipole, 0.03σ), to be tested by ESPRESSO/ELT at sub-ppm precision; (4) H₀ = 68.94 km/s/Mpc, discriminated against the alternative candidate 72.89 km/s/Mpc by DESI DR2 + Euclid. The framework explicitly documents excluded paths, conditional results, and open problems, in accordance with the principle that well-understood limits are as informative as results. Keywords: quantum gravity; fundamental constants; 600-cell; exceptional algebras; E₈; golden ratio; muon anomaly; fine structure constant; leptonic hierarchy; Hubble tension; pre-metric substrate; combinatorial physics MSC: 83E99, 81V22, 11R06 · PACS: 14.60.Ef, 11.10.−z, 9 8.80.−k