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| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.20141963 |
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Table of Contents:
- <div class="markdown markdown-main-panel stronger enable-updated-hr-color"> <p>The James Webb Space Telescope has revealed ordered, rotationally supported disk galaxies at redshifts <span class="math-inline">$z \sim 6\text{--}8$</span>, well before the <span class="math-inline">$\gtrsim 1 \text{ Gyr}$</span> of dynamical evolution typically required for disk settling in <span class="math-inline">$\Lambda\text{CDM}$</span>. We derive a parameter-free disk formation timescale <span class="math-inline">$\tau_{\text{align}} = 2 t_{\text{dyn}}$</span> from the temporal geometry of the twelve-dimensional Riemannian framework <span class="math-inline">$\mathcal{M}_{12} = (S^1_{\text{Sol}} \times S^3) \times K_8$</span>, in which the temporal sector <span class="math-inline">$S^1_{\text{Sol}}$</span> is a Sol 3-manifold with hyperbolic <span class="math-inline">$\text{SL}(2, \mathbb{Z})$</span> monodromy. The monodromy eigenvalues <span class="math-inline">$\phi = (1 + \sqrt{5})/2$</span> and <span class="math-inline">$\phi^{-1}$</span> generate an Anosov flow on the internal <span class="math-inline">$K_8$</span> 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 <span class="math-inline">$(0,0)$</span> component of the twelve-dimensional Einstein equation, evaluated in the FLRW background, then fixes the proportionality constant: <span class="math-inline">$T_{\text{Sol}} = 2 \ln \phi \times t_{\text{dyn}}$</span>, whence <span class="math-inline">$\tau_{\text{align}} = T_{\text{Sol}} / \ln \phi = 2 t_{\text{dyn}}$</span>. The factor of 2 is not chosen; it is exact, a consequence of the golden ratio identity <span class="math-inline">$\phi^2 = 1 + \phi$</span>. At <span class="math-inline">$z = 8$</span> this enables ordered disk settling in protocluster environments (<span class="math-inline">$\delta \sim 10\text{--}50$</span>, <span class="math-inline">$\tau_{\text{align}} \approx 66\text{--}150 \text{ Myr}$</span>) and forbids it in voids (<span class="math-inline">$\tau_{\text{align}} \gtrsim 340 \text{ Myr}$</span>). Three falsifiable predictions are stated. The cosmological corollaries (<span class="math-inline">$S^3$</span> halo suppression, BAO sound horizon, CMB low-multipole suppression) are addressed in the companion long-form Paper X.</p> </div>