The Tau Universe: A Single Compact Fifth Dimension and Tav Topology Unify Cosmology, Flavor, Precision Moments, Higgs Self-Couplings, Strong-CP, Axions, Baryogenesis, Neutrinos (Active + Sterile), and Gravitinos — Consolidated Preprint v2.0

This consolidated preprint presents Version 2. 1 of the Tau Universe Framework, a theoretical construction in which all observable physics arises as the effective 4D theory of 5D Einstein–Kaluza–Klein gravity compactified on a circle S1 of radius τ = 7 h−1 Mpc, augmented by Tav topology. Tav topology is a partially non-computable resonance structure encoding the 142857 cyclic symmetry of the logistic map at r (τ) = 4 − 3/π2, the Berard constant β ≈ 1. 054, and halting-problem embeddings. The framework introduces no free parameters beyond τ (fixed by cosmological constant matching) and inherited standard model values. Prior searches in JWST JADES DR3/DR4 and DESI DR1 are documented as null results at current sensitivity. All predictions are pre-registered for forthcoming data from Euclid DR1 (October 2026), Rubin Observatory, NANOGrav, Fermilab Muon g−2, ATLAS CMS, MEG II, and ADMX/CASPEr. Key Predictions (Pre-registered at DOI 10. 5281/zenodo. 19323070) Euclid DR1 (October 2026): Step feature in P (k) at k_τ ≈ 0. 143 h/Mpc; w0 = −1. 000 ± 0. 003Axion: mₐ ≈ 4. 2 × 10−6 eV, g₀⏒⏒ ≈ 1. 3 × 10−12 GeV−1Neutron EDM: dₙ < 10−28 e·cmMuon g−2 Run 6: δa_μ ≈ +1. 8 × 10−13