TECHNICAL REPORT — ZENODO DEPOSIT Author: Miguel Ángel Percudani ORCID: 0009-0007-1748-3212 ══════════════════════════════════════════════════════════════════ SUMMARY ══════════════════════════════════════════════════════════════════ This work presents the Causal Mass Gap equation, derived from the Unified Applicable Time (UAT) and Unified Causal Principle (UCP) framework: E(n) = E_Planck × (κ_crit)^(1/n) where κ_crit = 10⁻⁷⁸ is the causal coherence constant. The integer n determines which physical scale emerges, with ZERO free parameters beyond the independently calibrated κ_crit. ══════════════════════════════════════════════════════════════════ MAIN PREDICTION (Item 3): NEW PHYSICS SCALES ══════════════════════════════════════════════════════════════════ ★ n = 5 → E(5) ≈ 3.07 TeV A new physics scale accessible at the Large Hadron Collider (LHC) and the proposed Future Circular Collider (FCC). Experimental signatures include dijet and dilepton resonances at m ≈ 3.1 TeV, missing transverse energy, and anomalous vector boson scattering. Falsifiable with HL-LHC or FCC-hh data. ★ n = 6 → E(6) ≈ 1.22 PeV A new physics scale relevant to neutrino mass generation via the seesaw mechanism (M_R ~ 10¹⁴-10¹⁵ eV) and ultra-high-energy cosmic rays. Experimental signatures include spectral features in the diffuse neutrino flux (IceCube, KM3NeT, GRAND) and cosmic ray composition changes (Pierre Auger, Telescope Array). Falsifiable with next-generation neutrino and cosmic ray observatories. ══════════════════════════════════════════════════════════════════ SUPPLEMENTARY DEVELOPMENTS ══════════════════════════════════════════════════════════════════ ★ Item 4: QCD Coherence Length — λ_coh ≈ 5.7 fm The Compton wavelength associated with the n = 4 (QCD) scale defines the characteristic length at which the causal membrane operates. The value of 5.7 fm places the membrane at the mesoscopic boundary between hadronic and nuclear physics: larger than a single proton (~0.84 fm) but of the same order as the QCD string breaking scale and light nuclear radii. This is the scale over which the membrane maintains causal coherence among confined quarks. ★ Item 5: Membrane-Gluon Coupling — α_mem ≈ 0.35 Derived from the vacuum exponent α = φ/2 + 3/4 via α_mem = √(α/4π), this coupling constant quantifies the strength with which the causal membrane interacts with the gluon field. The value 0.35 is comparable to the strong coupling α_s(Q² ≈ 1 GeV²) ≈ 0.3-0.4, suggesting the membrane operates at the same scale and with the same intensity as QCD itself — consistent with the interpretation of quark confinement as a membrane-mediated phenomenon. ══════════════════════════════════════════════════════════════════ KEY FEATURES ══════════════════════════════════════════════════════════════════ • All predictions derived from a SINGLE constant: κ_crit = 10⁻⁷⁸ • ZERO free parameters beyond κ_crit • No fitting to experimental data • The same equation generates dark energy (n = 1/α), QCD confinement (n = 4), TeV-scale physics (n = 5), and PeV-scale physics (n = 6) • All predictions are FALSIFIABLE with current or near-future experimental facilities • Includes independent Python calculator script ══════════════════════════════════════════════════════════════════ REFERENCES ══════════════════════════════════════════════════════════════════ UAT Framework: DOI: 10.5281/zenodo.17729221 UCP Framework: DOI: 10.5281/zenodo.18210808 Λ Resolution: DOI: 10.5281/zenodo.21109424 Causal Pillars: Zenodo (UAT/UCP Core Equations) ══════════════════════════════════════════════════════════════════ LICENSE ══════════════════════════════════════════════════════════════════ Creative Commons Attribution 4.0 International (CC BY 4.0)