This preprint develops a minimal geometric extension of general relativity in whichthe temporal coordinate carries closed S³ topology, derived from four classicalidentities: the unit-vector relation Ti² + Ci² = 1 (Einstein's energy-momentumrelation normalised by E²), the dimensionless ratio σSB / G₀ = 3 from the Stefan (1879) and Cavendish (1798) measurements, Noether's theorem applied to the closedtemporal coordinate, and the H₄ Coxeter / tetranacci structure of S³ at D = 4. The framework introduces no new fields, no new symmetries, and no fitted parameters. The single geometric coupling α = √3/2 is fixed by the SO (4) /SO (3) coset weight;the single present-epoch value Ti, 0 = Φ₄ − 1 = 0. 92756… is fixed algebraically bythe tetranacci recursion (Φ₄ the unique real root > 1 of x⁴ = x³ + x² + x + 1). Five cosmological observables — σSB / G₀, the Hubble-tension ratio H₀ₗocal /H₀CMB, the dark-energy density Ω_Λ, the primordial spectral index nₛ, and theage of the universe t₀ — follow at ≤ 0. 55σ each, with joint Stouffer-Z significancep ≲ 10⁻⁴. Four further parameter-free predictions across five orders of magnitudein scale (GPS clock rate, MOND acceleration aMOND, the Bullet Cluster collisionlessfraction, and w₀) are consistent with data at sub-σ precision. The BAO sound horizon is inherited from ΛCDM at bitwise precision in the canonicalConfiguration α embedding (verified in hiclass v3. 0) ; the framework thereforeinherits, rather than resolves, the ΛCDM–DESI tension. The decisive future test isthe ELT/ANDES redshift-drift programme, which is projected to resolve the predictedattractor crossing δż/ż = Ti, 0² − 1 = −0. 140 at z ≈ 0. 07 within a multi-decadecampaign. A full Brans–Dicke / Horndeski embedding (cuscuton kinetic structure, cₛ² = 0, γPPN = βPPN = 1 exact) is provided in Appendix A. Tier-1 algebraic identitiesare verified to 50-digit precision; the hiclass v3. 0 patch files are documentedin Appendix C.
Miroslav Yosifov (Sat,) studied this question.