Unified Action for the UAT/UCP Framework: Sₜotal = Sbulk + Sboundary + Scoherence — 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 Sₜotal = Sbulk + Sboundary + Scoherence 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══════════════════════════════════════════════════════════════════ ★ Sbulk — UAT Lagrangian (DERIVED): Scalar-tensor theory with non-minimal coupling ξ = -0. 2810. Generates kₑarly = 0. 967 and the modified Friedmann expansion. Predicts Ωₘ = 0. 3133 (0. 55% agreement with Planck), Λ = 2. 49×10⁻¹²² MPl⁴ (0. 92% agreement), and t₀ = 12. 90 Gyr. ★ Sboundary — 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: Mₚ = Mb × κcrit × φ × (1 - 0. 07) = Mb × 7. 49 Explains Ωₘ^ (eff) = Ωb × 7. 49 = 0. 3133 from first principles. THIS IS NOT A PHENOMENOLOGICAL ANSATZ — it emerges rigorously from the boundary term of the gravitational action. ★ Scoherence — Causal Mass Gap (FORMALIZED): The Wilson coefficients cₙ = κcrit^ (1/n) × 2Rgeom couple the UAT scalar field to Standard Model operators. The geometric projection factor 2Rgeom = 0. 558364 converts pure resonances into observable masses. Predictions (ZERO free parameters beyond 7%): • n=4: Mₒbs = 215. 6 MeV — matches ΛQCD ≈ 217 MeV (0. 65% agreement) • n=5: Mₒbs = 1. 71 TeV — NEW PHYSICS at the LHC (falsifiable) • n=6: Mₒbs = 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 2Rgeom 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 (unifiedₐctionUATUCP. tex) • Python verification script (verifyᵤnifiedₐction. 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. 21109424Ωₘ Relation: DOI: 10. 5281/zenodo. 213281877% Thermal Margin: DOI: 10. 5281/zenodo. 21211964Identity η ≡ κcrit: 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)