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We present the consolidated results of nine objective empirical validations of the Unified Applicable Time (UAT) framework and its corollaries — the Unified Causal Principle (UCP) and the Unified Percudani Constant (UPC) — plus one subjective observation and three documented exclusions. All validations use exclusively real observational data with zero synthetic data employed in any external analysis. ═══════════════════════════════════════════════════════════════ COSMOLOGICAL VALIDATIONS (5 objective lines) ═══════════════════════════════════════════════════════════════ 1. COSMIC CHRONOMETERS H(z): 12 points, z=0.07-1.75. χ²(UAT)=7.38 vs χ²(ΛCDM)=7.84 → UAT 5.9% better. H₀=73.00 km/s/Mpc. Universe age: 13.06 Gyr. 2. PANTHEON+ TYPE Ia SUPERNOVAE: 1701 SNe, z=0.001-2.261. χ²(UAT)=787.3 vs χ²(ΛCDM)=2143.5 → UAT 63.3% better. Explicit column mapping: zHD, MU_SH0ES, MU_SH0ES_ERR_DIAG. 3. DESI DR1 BAO: 7 bins, z=0.295-1.490. χ²(UAT)=6379.5 vs χ²(ΛCDM)=6489.2 → UAT 1.7% better. D_A/r_d: χ² 163.5 vs 273.0 (40% improvement). 4. UNION3 SUPERNOVAE: ~2000 SNe, z=0.017-2.299. χ²(UAT)=2508 vs χ²(ΛCDM)=2625 → UAT 4.5% better. Independent confirmation of Pantheon+ result. 5. TIME-DELAY STRONG LENSING (H0LiCOW/TDCOSMO/STRIDES): 11 lenses. H₀=73.49±0.86 km/s/Mpc. UAT at 0.6σ → CONSISTENT. ΛCDM at 7.1σ → EXCLUDED. ΛCDM's H₀=67.4 is catastrophically rejected by lensing data. UAT outperforms ΛCDM in ALL FIVE cosmological datasets. UAT: H₀=73.00 km/s/Mpc — consistent with local, lensing, and CMB. ΛCDM: H₀=67.40 km/s/Mpc — excluded at 7.1σ by lensing alone. ═══════════════════════════════════════════════════════════════ STELLAR ASTROPHYSICS (3 objective lines) ═══════════════════════════════════════════════════════════════ 6. KEPLER PHOTOMETRY — ω MODULATION: ω=0.2868 (Δ=3.1%) in 3/3 stars at 99× significance over four control bands. KIC 10661783, 4851217, 7907119. 7. TESS PHOTOMETRY — ω VIA PHASE ENTROPY: Dimensional Phase Entropy Scanning (Resonant Hunter v6.0). 1.5-day physical window, dynamic Welch scaling (Δf<0.01), Hilbert phase entropy. ω=0.2687 (Δ=3.3%) in 7/9 TESS stars. 2.9× over power method. Cross-mission convergence with Kepler at ~3% calibration margin. 8. TESS PHOTOMETRY — φ RELATIONSHIPS: Golden ratio φ=1.618 structures stellar period ratios in 5/9 TESS stars (7 independent φ-relationships). TIC 283722336 exhibits φ, φ², √φ simultaneously. ═══════════════════════════════════════════════════════════════ COSMIC MICROWAVE BACKGROUND (1 objective line) ═══════════════════════════════════════════════════════════════ 9. PLANCK CMB — φ² IN ACOUSTIC PEAKS: Planck SMICA 2048 (50,331,648 pixels). D_ℓ=ℓ(ℓ+1)C_ℓ/(2π) scaling. ℓ₂₀₃/ℓ₅₂₂=2.5714≈φ² (Δ=1.8%). ℓ₄₀/ℓ₁₀₄=2.6000≈φ² (Δ=0.7%). Two φ² relations detected with sub-2% precision. ═══════════════════════════════════════════════════════════════ ADDITIONAL ANALYSES ═══════════════════════════════════════════════════════════════ 10. GWTC-3 GRAVITATIONAL WAVES — φ IN BLACK HOLE MASSES (SUBJECTIVE): 44 BBH events. Four φ-like ratios among six peaks in primary mass distribution. Sensitive to binning. Median q=0.717 (1/φ=0.618). Reported for future investigation with larger catalogs (O4, O5). 11. LYMAN-α FOREST BAO (z=2.334): ΛCDM marginally preferred (χ² 1.31 vs 5.09). UAT at 2.2σ — within systematic uncertainties of Lyman-α forest modeling. Reported for completeness. ═══════════════════════════════════════════════════════════════ WHERE ΛCDM FAILS AND UAT RESOLVES ═══════════════════════════════════════════════════════════════ • ΛCDM at 7.1σ tension with time-delay strong lensing H₀ • ΛCDM at 4.9σ tension with local H₀ (SH0ES) • ΛCDM at 3.4σ tension with weak lensing S₈ • UAT resolves ALL THREE tensions simultaneously • UAT outperforms ΛCDM in ALL FIVE cosmological datasets ═══════════════════════════════════════════════════════════════ DISCARDED INVESTIGATIONS ═══════════════════════════════════════════════════════════════ • LIGO Raw Data (O4b): σ=137.4 was calibration anchor artifact. • SDSS DR16: Server returned only local volume (z<0.09). • FRB Dispersion Measure: Host galaxy DM uncertainty too large. ═══════════════════════════════════════════════════════════════ METHODOLOGY ═══════════════════════════════════════════════════════════════ • All cosmological validations use direct numerical integration of the UAT Friedmann equation — independent of CLASS, CAMB, or any ΛCDM infrastructure. • Stellar validations employ Welch PSD, Hilbert phase entropy, and Lomb-Scargle periodograms via the Resonant Hunter protocol. • CMB validation uses healpy.anafast with D_ℓ scaling. • Golden Rule strictly enforced: zero synthetic data. ═══════════════════════════════════════════════════════════════ CONSTANTS VERIFIED ═══════════════════════════════════════════════════════════════ k_early = 0.967 (5 cosmological datasets) ω = 0.278 (Kepler: Δ=3.1%, TESS: Δ=3.3%) φ = 1.618 (CMB: φ², TESS: 7 φ-relations, GWTC-3: subjective) κ_crit = 4.978 (UCP framework) R_geom = 0.2791 (Internal calibration) 9 objective + 1 subjective + 1 marginal = 11 lines of evidence Golden Rule: ✓ | Zero synthetic data: ✓
Percudani M. A. 2026. Consolidated Empirical Validation of the Unified Applicable Time (UAT) Framework: Nine Objective Lines of Evidence from Cosmology, Stellar Astrophysics, Cosmic Microwave Background, and Gravitational Lensing with One Subjective Observation from Gravitational Wave Astrophysics. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115667