The F-Theory Origin of the Holographic Corq Sector: Flux Stabilization and the 55 TeV Scale from First Principles

We elevate the phenomenological Holographic Corq Model to a UV-complete construction within F-Theory. We demonstrate that the requisite bulk symmetry group, SO(6) × U(1)A, is not an ad‑hoc choice but arises inevitably from a Kodaira type I4 singularity along the GUT divisor, stabilized by a Mordell–Weil rank‑1 group. Furthermore, we solve the moduli‑stabilization problem using GKP fluxes, deriving the precise 55.3 TeV confinement scale—essential for the Hierarchy Problem and Baryon Asymmetry—from first principles. We identify a discrete “Golden Solution” with minimal flux integers (K = 3, M = 1) that naturally generates the required hierarchy without fine‑tuning. This geometric configuration fixes the walking‑dynamics parameter at ε ≈ 0.032, leading to a precise post‑diction of the scalar spectral index ns ≈ 0.968, placing the model within the 1σ region of Planck 2018 data. The analysis confirms that the Standard Model’s flavor structure and the cosmological initial conditions are dictated by the rigid topology of the compactification manifold.