A Parameter-Free Disk Formation Timescale from S¹ₒ₎₋ Temporal Geometry, ApJL Letter, Preprint

The James Webb Space Telescope has revealed ordered, rotationally supported disk galaxies at redshifts z 6--8, well before the 1 Gyr of dynamical evolution typically required for disk settling in. We derive a parameter-free disk formation timescale ₀₋₈₆₍ = 2 t₃ₘ₍ from the temporal geometry of the twelve-dimensional Riemannian framework M₁₂ = (S¹ₒ₎₋ S³) K₈, in which the temporal sector S¹ₒ₎₋ is a Sol 3-manifold with hyperbolic SL (2, Z) monodromy. The monodromy eigenvalues = (1 + 5) /2 and ^-1 generate an Anosov flow on the internal K₈ shape modulus; integration over the internal space yields a rank-2 anisotropic correction to the four-dimensional shear tensor that couples to protogalactic angular momentum through standard tidal torque theory. The (0, 0) component of the twelve-dimensional Einstein equation, evaluated in the FLRW background, then fixes the proportionality constant: Tₒ₎₋ = 2 t₃ₘ₍, whence ₀₋₈₆₍ = Tₒ₎₋ / = 2 t₃ₘ₍. The factor of 2 is not chosen; it is exact, a consequence of the golden ratio identity ² = 1 +. At z = 8 this enables ordered disk settling in protocluster environments (10--50, ₀₋₈₆₍ 66--150 Myr) and forbids it in voids (₀₋₈₆₍ 340 Myr). Three falsifiable predictions are stated. The cosmological corollaries (S³ halo suppression, BAO sound horizon, CMB low-multipole suppression) are addressed in the companion long-form Paper X.