COMPLETE RESEARCH RECORD — ZENODO DEPOSITAuthor: Miguel Ángel PercudaniORCID: 0009-0007-1748-3212 ═══════════════════════════════════════════════════════════════ABSTRACT═══════════════════════════════════════════════════════════════ This work presents a first-principles resolution of the cosmological constant problem within the Unified Applicable Time (UAT) framework. The vacuum energy density is derived from three independent physical inputs, each constrained by distinct principles: PILLAR 1 — INFORMATIONAL: κcrit = 10⁻⁷⁸ Explicit calculation from the Bekenstein bound on the particle horizon (R ≈ 46. 5 Gly) yields Nₐccessible ≈ 10⁷⁸ accessible bits, giving κcrit = 1/Nₐccessible = 10⁻⁷⁸. Uncertainty: ±0. 5 in exponent. PILLAR 2 — GEOMETRIC-DIMENSIONAL: φ/2 = 0. 809017 The complex 4×4 coherence matrix of the 8-phase causal array (kₑarly = 0. 96734 from UAT Lagrangian) yields λₘax ∝ φ = 1. 618034. Combined with LQG spectral dimension flow (dS: 4 → 2): dₑff = dS (UV) × φ / dS (IR) = 2φ/4 = φ/2. PILLAR 3 — THERMODYNAMIC: 3/4 = 0. 750000 Quadratic scaling of the double-well potential V ∝ δ² near its minimum yields equipartition at half-phase: 1 − (1/2) ² = 3/4. (Heuristic derivation; full rigor under investigation. ) These combine to give α = φ/2 + 3/4 = 1. 559017, yielding: V₀ = EPlanck × κcrit^α = 2. 50 × 10⁻¹²² MPl⁴ ρ_Λ ≈ 6. 90 × 10⁻²⁷ J/m³ Matching Planck 2018 (6. 83 ± 0. 08 × 10⁻²⁷ J/m³) with ~1% agreement. No parameters were fitted to the cosmological constant itself. ═══════════════════════════════════════════════════════════════FALSIFIABLE PREDICTIONS═══════════════════════════════════════════════════════════════ • Black hole entropy correction: S = A/ (4ℓ²) − (φ/2) ·ln (A/ (4ℓ²) ) • Hawking radiation suppression: PUAT = (3/4) × PHawking• Golden Dirac comb in gravitational wave ringdown (LISA, 2035) • Testable with: LISA, CTA/LHAASO, Fermi-LAT/HAWC, Euclid/Roman ═══════════════════════════════════════════════════════════════METHODOLOGICAL LESSONS (Documented in Section 5) ═══════════════════════════════════════════════════════════════ This investigation included an extensive exploratory phase whose results were discarded following rigorous statistical calibration: • LIGO/Virgo ringdown search: Null result after Monte Carlo PAR protocol (500 iterations). Signal indistinguishable from noise at ±1% tolerance. • Fibonacci ratio detection in 8 astronomical catalogs (Kepler, Chandra, Fermi, JWST, HST, LISA Pathfinder, Planck, DESI): All results invalidated after Monte Carlo test revealed true false-positive rate of 33. 7% (not the assumed 5%). These methodological lessons are documented as contributions to best practices in astrophysical pattern detection. ═══════════════════════════════════════════════════════════════CONTENTS═══════════════════════════════════════════════════════════════ • FinalReport. pdf — Complete manuscript (15 pages, 2 figures, 2 tables) • FinalReport. tex — LaTeX source• deepᵣesolutionccp. py — Analytical derivation script with: - 4×4 complex coherence matrix diagonalization - kₑarly derivation from Lagrangian constraints - Nₐccessible calculation from Bekenstein bound - Numerical verification of all constants ═══════════════════════════════════════════════════════════════KEYWORDS═══════════════════════════════════════════════════════════════ cosmological constant, dark energy, vacuum energy density, golden ratio, causal coherence, Bekenstein bound, Loop Quantum Gravity, spectral dimension, 8-phase coherence matrix, black hole thermodynamics, Hawking radiation, primordial black holes, gravitational waves, LISA, falsifiable predictions, look-elsewhere effect, Monte Carlo calibration, Unified Applicable Time, UAT framework ═══════════════════════════════════════════════════════════════REFERENCES═══════════════════════════════════════════════════════════════ UAT Framework: DOI: 10. 5281/zenodo. 17729221UCP Constant: DOI: 10. 5281/zenodo. 17718670 ═══════════════════════════════════════════════════════════════LICENSE═══════════════════════════════════════════════════════════════ Creative Commons Attribution 4. 0 International (CC BY 4. 0)
Miguel Percudani (Wed,) studied this question.