Unified Action for the UAT/UCP Framework: S_total = S_bulk + S_boundary + S_coherence — Complete Derivation of the Causal Membrane Mass, the QCD Confinement Scale, and New Physics Predictions at 1.71 TeV and 682 TeV

TECHNICAL REPORT — ZENODO DEPOSITAuthor: Miguel Ángel PercudaniORCID: 0009-0007-1748-3212 ══════════════════════════════════════════════════════════════════SUMMARY══════════════════════════════════════════════════════════════════ We present the complete unified action for the Unified Applicable Time (UAT) and Unified Causal Principle (UCP) framework. The total action S_total = S_bulk + S_boundary + S_coherence unifies three previously independent formulations into a single mathematical structure with exactly ONE free parameter — the 7% thermal calibration margin. Every constant used in this work is explicitly defined, numerically stated, and referenced to its origin in the UAT/UCP literature or in established physical measurements. No quantity is taken for granted. ══════════════════════════════════════════════════════════════════THE THREE SECTORS══════════════════════════════════════════════════════════════════ ★ S_bulk — UAT Lagrangian (DERIVED): Scalar-tensor theory with non-minimal coupling ξ = -0.2810. Generates k_early = 0.967 and the modified Friedmann expansion. Predicts Ω_m = 0.3133 (0.55% agreement with Planck), Λ = 2.49×10⁻¹²² M_Pl⁴ (0.92% agreement), and t₀ = 12.90 Gyr. ★ S_boundary — Causal Membrane Mass (FORMALIZED): The Gibbons-Hawking-York surface term evaluated over the topologically truncated 8-phase cycle (348.12° instead of 360°). The scalar field collapses onto the dominant eigenstate of the 4×4 coherence matrix (the golden ratio φ), degraded by 7% thermal noise. Result: M_p = M_b × κ_crit × φ × (1 - 0.07) = M_b × 7.49 Explains Ω_m^(eff) = Ω_b × 7.49 = 0.3133 from first principles. THIS IS NOT A PHENOMENOLOGICAL ANSATZ — it emerges rigorously from the boundary term of the gravitational action. ★ S_coherence — Causal Mass Gap (FORMALIZED): The Wilson coefficients c_n = κ_crit^(1/n) × 2R_geom couple the UAT scalar field to Standard Model operators. The geometric projection factor 2R_geom = 0.558364 converts pure resonances into observable masses. Predictions (ZERO free parameters beyond 7%): • n=4: M_obs = 215.6 MeV — matches Λ_QCD ≈ 217 MeV (0.65% agreement) • n=5: M_obs = 1.71 TeV — NEW PHYSICS at the LHC (falsifiable) • n=6: M_obs = 682 TeV — NEUTRINO SEESAW SCALE (IceCube-Gen2 testable) ══════════════════════════════════════════════════════════════════KEY FEATURES══════════════════════════════════════════════════════════════════ • All constants explicitly defined in Tables 1-2 with values, units, and references• 8-phase coherence matrix constructed and diagonalized• GHY boundary term adapted to truncated 8-phase geometry• Geometric projection factor 2R_geom derived from interference residue• Complete numerical verification via accompanying Python script• Three falsifiable predictions with zero additional free parameters• Corrections to previous Causal Mass Gap predictions (pure resonances → observable masses) ══════════════════════════════════════════════════════════════════CONTENTS══════════════════════════════════════════════════════════════════ • LaTeX manuscript (unified_action_UAT_UCP.tex)• Python verification script (verify_unified_action.py) - Runs in any Colab environment - Requires only NumPy and SciPy - Does not depend on the UAT/UCP digital twin ══════════════════════════════════════════════════════════════════REFERENCES══════════════════════════════════════════════════════════════════ UAT Framework: DOI: 10.5281/zenodo.17729221UCP Framework: DOI: 10.5281/zenodo.18210808UAT Lagrangian: DOI: 10.5281/zenodo.20500431Λ Resolution: DOI: 10.5281/zenodo.21109424Ω_m Relation: DOI: 10.5281/zenodo.213281877% Thermal Margin: DOI: 10.5281/zenodo.21211964Identity η ≡ κ_crit: Zenodo (2026)Age of the Universe: Zenodo (2026)Causal Mass Gap: Zenodo (2026)Membrane Dynamics: Zenodo (2026)Gibbons-Hawking (GHY): Phys. Rev. D 15, 2752 (1977)York (boundary term): Phys. Rev. Lett. 28, 1082 (1972) ══════════════════════════════════════════════════════════════════LICENSE══════════════════════════════════════════════════════════════════ Creative Commons Attribution 4.0 International (CC BY 4.0)