What question did this study set out to answer?

This research aims to validate the Unified Applicable Time (UAT) framework across multiple lines of empirical evidence in cosmology and stellar astrophysics.

June 29, 2026Open Access

Consolidated Empirical Validation of the Unified Applicable Time (UAT) Framework: Seven Independent Lines of Evidence from Cosmology, Stellar Astrophysics, and Cosmic Microwave Background

Key Points

This research aims to validate the Unified Applicable Time (UAT) framework across multiple lines of empirical evidence in cosmology and stellar astrophysics.
Consolidated validation of UAT using observational data across seven independent datasets.
Direct numerical integration of the UAT Friedmann equation without synthetic data.
Utilization of advanced photometric analysis methods like Welch PSD and Dimensional Phase Entropy Scanning.
UAT demonstrates a 5.9% improvement over ΛCDM in cosmic chronometer fitting.
Observed ω in Kepler and TESS with high significance (Δ = 3.1% and Δ = 3.3% respectively).
CMB analysis reveals φ² relationships in acoustic peaks supporting UAT predictions.

Abstract

We present the consolidated results of seven independent empirical validations of the Unified Applicable Time (UAT) framework and its corollaries — the Unified Causal Principle (UCP) and the Unified Percudani Constant (UPC). All validations use exclusively real observational data with zero synthetic data employed in any external analysis. COSMOLOGICAL VALIDATIONS (3 lines): 1. COSMIC CHRONOMETERS H (z): The UAT Friedmann equation with quantum brake parameter kₑarly = 0. 96734 and H₀ = 73. 00 km/s/Mpc fits cosmic chronometer data with χ² = 7. 38, outperforming ΛCDM (χ² = 7. 84, H₀ = 67. 40) by 5. 9%. The UAT universe age is 13. 06 Gyr. 2. PANTHEON+ TYPE Ia SUPERNOVAE: UAT fits 1701 spectroscopically confirmed supernovae (z = 0. 001-2. 261) with χ² = 787. 3, a 63. 3% improvement over ΛCDM (χ² = 2143. 5). Column mapping: zHD, MUSH0ES, MUSH0ESERRDIAG. H₀ = 73. 00 resolves the Hubble tension. 3. DESI DR1 BARYON ACOUSTIC OSCILLATIONS: UAT fits the seven DESI BAO redshift bins (z = 0. 295-1. 490) with χ² = 6379. 5 vs. ΛCDM χ² = 6489. 2. The angular diameter distance DA/rd shows 40% improvement (χ² 163. 5 vs. 273. 0). UAT outperforms ΛCDM in all three independent cosmological datasets. STELLAR ASTROPHYSICS (3 lines): 4. KEPLER PHOTOMETRY — ω MODULATION: The UAT phase invariant ω = 0. 278 is detected as envelope modulation in 3/3 Kepler variable stars (KIC 10661783, 4851217, 7907119) with mean ω = 0. 2868 (Δ = 3. 1%) at 99× significance over four control bands. 5. TESS PHOTOMETRY — ω VIA PHASE ENTROPY: Dimensional Phase Entropy Scanning (Resonant Hunter v6. 0) detects ω in 7/9 TESS stars with mean ω = 0. 2687 (Δ = 3. 3%). The entropy method proves superior to power spectral density (2. 9× vs. 1. 4× significance). Cross-mission convergence of ω across Kepler and TESS with near-identical calibration margins (~3%) rules out instrumental artifacts. 6. TESS PHOTOMETRY — φ RELATIONSHIPS: The golden ratio φ = 1. 618 structures stellar period ratios in 5/9 TESS stars, yielding 7 independent φ-relationships. TIC 283722336 exhibits φ, φ², and √φ simultaneously. COSMIC MICROWAVE BACKGROUND (1 line): 7. PLANCK CMB — φ² IN ACOUSTIC PEAKS: Analysis of the Planck SMICA 2048 full-sky map (50, 331, 648 pixels) with D_ℓ = ℓ (ℓ+1) C_ℓ/ (2π) scaling reveals two φ² relations in acoustic peak ratios: ℓ₂₀₃/ℓ₅₂₂ = 2. 5714 ≈ φ² (Δ = 1. 8%) and ℓ₄₀/ℓ₁₀₄ = 2. 6000 ≈ φ² (Δ = 0. 7%). 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 in all external validations. CONSTANTS VERIFIED: kₑarly = 0. 967 (H (z) + Pantheon+ + DESI) ω = 0. 278 (Kepler: Δ=3. 1%, TESS: Δ=3. 3%) φ = 1. 618 (CMB: φ², TESS: 7 φ-relations) κcrit = 4. 978 (UCP theoretical framework) Rgeom = 0. 2791 (Internal calibration) 7 out of 7 validation lines confirmed. RELATED DOIs: - UAT Framework: 10. 5281/zenodo. 17729221 - UCP Framework: 10. 5281/zenodo. 17718670 - UPC Framework: 10. 5281/zenodo. 18210808 - Resonant Hunter: 10. 5281/zenodo. 18446712 - Atemporal Antifrequency: 10. 5281/zenodo. 18809178 ---- RELATED DOIs: - UAT Framework: 10. 5281/zenodo. 17729221 - UCP Framework: 10. 5281/zenodo. 17718670 - UPC Framework: 10. 5281/zenodo. 18210808 - Resonant Hunter: 10. 5281/zenodo. 18446712 - Atemporal Antifrequency: 10. 5281/zenodo. 18809178

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