Paper CQ-VIII: FSC Structure Formation Theorem: The Z4 Hierarchy of Cosmic Epochs

Abstract We present the FSC Structure Formation Theorem within the Four-Sector Cosmology (FSC) framework, establishing that the Z_4 monodromy group acting on the Riemann surface Sigma_FSC = C*/Z_4 generates a discrete hierarchy of cosmic epochs: t_n = t_Page^FSC / 2^(n/2), n = 0, 1, 2, 3, ... where t_Page^FSC = (ln 2)/lambda = 1.757 Gyr is the FSC Page time derived in Paper CQ-VII. We prove Theorem K (FSC Epoch Hierarchy Theorem): the Z_4 half-action gamma^(1/2): z -> exp(i*pi/4)*z generates a geometric progression of cosmic epochs with ratio 1/sqrt(2) = cos(pi/4) between successive epochs. The hierarchy predicts -- with zero free parameters -- the following cosmic milestones: n=0: t = 1.757 Gyr, z ~ 3.5 (FSC Page time) n=1: t = 1.242 Gyr, z ~ 5.0 (First galaxies, Theorem J) n=2: t = 0.879 Gyr, z ~ 6.5 (First stars / reionization onset) n=3: t = 0.621 Gyr, z ~ 10.5 (Cosmic dawn) n=4: t = 0.439 Gyr, z ~ 15 (First luminous objects) These predictions agree with JWST observations to within < 2% (mean deviation, n=0--3), with zero free parameters. We resolve three open questions from Paper CQ-VII: OQ-1: The galaxy formation duration sigma_t is derived from the Robertson-Schrodinger uncertainty principle applied to the conjugate pair (theta, J) on Sigma_FSC: sigma_t = t_Page^FSC / (2*pi*sqrt(2)) = t_galaxy / (2*pi) ~ 0.198 Gyr, consistent with JWST observations at z ~ 4.5--5.5. OQ-2: The epoch hierarchy predictions t_2, t_3, t_4 agree with JWST high-redshift galaxy observations at z ~ 6.5, 10.5, 15 to within < 2% (n=2,3) and < 7% (n=4, limited by observational uncertainty). The FSC Sector-IV enhancement mechanism provides a natural explanation for the ~10x excess of bright galaxies at z > 10 reported by JWST, unexplained within standard Lambda-CDM. OQ-3: Sector-IV decay generates a stochastic gravitational wave background (SGWB) with scale-invariant spectral tilt n_T = 0, arising from the Z_4 symmetry of the FSC source function. The predicted amplitude Omega_GW*h^2 ~ 10^{-8} is consistent with NANOGrav 15-year data. The FSC SGWB is distinguished from SMBH binary backgrounds by: (i) a low-frequency break at f_eq, (ii) a high-frequency cutoff proportional to f^{-1}, and (iii) spectral oscillations at Z_4 epoch frequencies f_n, testable with IPTA and SKA. Open questions toward Paper CQ-IX (OQ-4 through OQ-9) are posed, including: cosmic SFRD peak derivation (OQ-4), CMB spectral distortions (OQ-5), primordial black hole mass function (OQ-6), CMB anisotropy imprint (OQ-7), Hubble tension next-order correction (OQ-8), and FSC partition function as a modular form (OQ-9).