BAO SIDEBAND SPLITTING, THE ALCOCK-PACZYNSKI ANOMALY, AND THE PRIMORDIAL GEOMETRIC DARK MATTER RATIO (XXXII v6)

Within the unified pregeometric Folded Crunch Dipole – Reversed Big Bang (FCD-RBv6) framework, the macroscopic fabric of space-time emerges from a dense, regular three-dimensional lattice of inter-brane Einstein-Rosen (ER) bridges in a Thermofield Double (TFD) entangled state. These bridges act as a rigidizing "metric scaffold" that locks the physical separation of the visible and mirror branes at the constituent Compton scale (R0 ≈ 0.6308 fm) in the vicinity of matter. On cosmological scales, this spatial stiffness modifies the propagation of primordial acoustic waves. This paper formalizes the falsifiable prediction of BAO sideband splitting, where the standard Baryon Acoustic Oscillation peak at r_BAO ≈ 150 Mpc splits into two distinct sidebands at r_- ≈ 132 Mpc and r_+ ≈ 168 Mpc, driven by the elasto-acoustic modulation of the inter-brane tensor. Furthermore, we demonstrate that the metric deformation under expansion induces an anisotropic distortion of the BAO sphere into a flattened spheroid along the line of sight—the "Topological Egg"—naturally explaining the Alcock-Paczynski anomaly. Lastly, we derive the primordial mass-energy budget, proving that the asymmetric double-well potential established in Part XXVI (λ_- = 0.3163 and λ_+ = 0.6837) predicts a parameter-free dark-matter-to-baryonic-matter ratio of exactly 5.32:1. This matches the latest Planck and DESI DR2 data within 0.5%, completing the 32-part unifications of the FCD-RBv6 model