8.13 Fractal Hierarchical Universe

This paper extrapolates the structural constants at the atomic scale to statistically correlated hierarchies at the cosmological scale. Based on the ℳ𝒞ℐ three-sector structure and the seven-level recurrence, we derive: the fractal dimension holds universally for any scale factor; the effective metric is determined by the infiltration function and cross-sector coupling, with the dual-mode zero-error condition calibrating the effective spectra , ; the spectral expansion/Born rule (Theorem 1.1.5.01) mapping rule automatically extends to cosmological scales; the hierarchical dual structure yields strict ratio relations for cosmological encoding unit numbers. All absolute calibrations at cosmological scales are strictly constrained by Consummate Reproduction. The absolute value of and the calibration of are reserved for subsequent work.