Methods and Mathematical Foundations of the Tau Universe: The Tav Topology
Authors/Creators
Description
This paper details the mathematical and methodological foundations of the Tav (Tau Advanced Version) framework, an extension of the Tau Universe model. We focus on the 5D topological structure R3,1 × S1, multi-scale fractional compactification, Casimir-derived dark energy, partial computability of Kaluza-Klein (KK) towers, and statistical validation using recent datasets like JWST JADES DR3 (data released May 2024) and DESI 2024. The model resolves cosmological tensions (e.g., H0 and S8) with zero free parameters by treating the universe as a computable prefix of an undecidable 5D manifold. We introduce novel Tau Methods, including Yuan 2n3m filtering for harmonic isolation and Prefix Windowing for computability cutoffs. Predictions for Euclid DR1 (expected October 2026) are provided, emphasizing detectable harmonic spikes at kn = n/τ ≈ n × 0.143 h Mpc−1.
Other
Supplementary Material: Robustness testing of Yuan 2ⁿ3ᵐ filter (Significance Matrix + synthetic power spectrum plots at 8% noise). Demonstrates 3.5–3.8× clarity gain and >5σ recovery in JADES-like noise.
Files
Tau_Methods_and_Mathematical_Foundations_of_Tau_Universe_Final_v1.pdf
Additional details
Dates
- Issued
-
2026-01-16
Software
- Repository URL
- https://github.com/claygatlin/tau-cosmology
- Programming language
- Python
- Development Status
- Active
References
- Theodor Kaluza. "Zum Unit¨atsproblem der Physik". In: Sitzungsberichte der Preußischen Akademie der Wissenschaften (Berlin) (1921). English translation available at arXiv:1803.08616, pp. 966–972.
- Oskar Klein. "Quantentheorie und f¨unfdimensionale Relativit¨atstheorie". In: Zeitschrift f¨ur Physik 37.12 (1926), pp. 895–906. doi: 10.1007/BF01397481.
- Thomas Appelquist and Alan Chodos. "Quantum Dynamics of Kaluza-Klein Theories". In: Physical Review D 28.4 (1983), pp. 772–788. doi: 10.1103/PhysRevD.28.772.
- Robert I. Soare. Recursively Enumerable Sets and Degrees. Springer-Verlag, 1987. isbn: 978-3-540- 15299-6. doi: 10.1007/978-3-642-05725-0.
- Juan Martin Maldacena. "The Large N limit of superconformal field theories and supergravity". In: International Journal of Theoretical Physics 38.4 (1999), pp. 1113–1133. doi: 10.1023/A:1026654312961. arXiv: hep-th/9711200.
- Lisa Randall and Raman Sundrum. "An Alternative to Compactification". In: Physical Review Letters 83.23 (1999), pp. 4690–4693. doi: 10.1103/PhysRevLett.83.4690. arXiv: hep-th/9906064.
- Lisa Randall and Raman Sundrum. "Large Mass Hierarchy from a Small Extra Dimension". In: Physical Review Letters 83.17 (1999), pp. 3370–3373. doi: 10 . 1103 / PhysRevLett . 83 . 3370. arXiv: hep - ph/9905221.
- James R. van Meter. "Undecidability in 5D Spin Foam Models". In: arXiv:gr-qc/0506019 (2005). arXiv: 0506019 [gr-qc].
- Gregory J. Chaitin. Thinking about G¨odel and Turing: Essays on Complexity, 1970–2007. World Scientific, 2007. isbn: 978-981-270-895-3.
- Planck Collaboration. "Planck 2018 results. VI. Cosmological parameters". In: Astronomy & Astrophysics 641 (2020), A6. doi: 10.1051/0004-6361/201833910. arXiv: 1807.06209 [astro-ph.CO].
- Adam G. Riess et al. "A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team". In: The Astrophysical Journal Letters 934.1 (2022), p. L7. doi: 10.3847/2041- 8213/ac5c5b. arXiv: 2112.04510 [astro-ph.CO].
- DESI Collaboration. "DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations". In: arXiv:2404.03002 (2024). arXiv: 2404.03002 [astro-ph.CO].
- Francesco D'Eugenio et al. "JADES Data Release 3: NIRSpec/Microshutter Assembly Spectroscopy for Thousands of Galaxies in GOODS-N and GOODS-S". In: The Astrophysical Journal Supplement Series 277.1 (2025), p. 4. doi: 10.3847/1538-4365/ada148. arXiv: 2404.06531 [astro-ph.GA].