Black Hole Interior as a Skyrmion Crystal: Dimensional Reduction, Modified Coupling Constants, and Observable Consequences

We propose a microscopic model for the black hole interior derived from a geometric framework for fundamental constants. The framework encodes the fine structure constant through a mode-counting integral on the three-sphere S³, where the integrand ρ(ω) = 12ω² + 2ω + 1 decomposes into three families tied to distinct spatial dimensionalities: bulk (12ω², requiring 3D), surface (2ω, requiring 2D), and axial (1, requiring 1D). Central hypothesis. At densities above ~2.7 times nuclear saturation density, the inter-baryon spacing drops below the proton Compton wavelength λ_C = h/(m_p c) = 1.32 fm. We hypothesise that this compression restricts the baryon field's effective configuration space, pushing the bulk representation family to inaccessible energies while preserving the surface and axial families. The effective geometric constant reduces from G_π ≈ 137 to G(2D) = π² + π ≈ 13, yielding an effective electromagnetic coupling ~10× stronger at the lattice scale. This is a mode-projection in representation content, not a physical flattening of space. Interior structure. The resulting dense phase is a half-skyrmion honeycomb crystal lattice with calculable properties: lattice spacing ~2.73 fm, torsional phonon spectrum with a robust spectral gap (gap frequency ω₀ = √(12/5)), and a heuristic topological stability indicator S = N/4 that captures why macroscopic black holes are stable against thermal disassembly. Testable predictions. (i) Post-merger gravitational wave echoes with comb-like multi-reflection morphology, testable with targeted template searches in current and next-generation observatories. (ii) A phase transition signature in the neutron star equation of state near 2–3ρ₀. (iii) Frequency-dependent corrections to the EHT black hole shadow profile. Supporting analysis. Appendix A derives the phonon spectrum from the Skyrme dynamical matrix. Appendix B presents a Berger sphere (squashed S³) spectral analysis demonstrating the mode-projection mechanism for scalar harmonics, with an explicit pass/fail proposition for the vector (coexact 1-form) case that determines whether the model predicts a sharp phase transition or a continuous crossover. Epistemic transparency. The paper classifies every claim into six tiers: proven identity, toy-model support, ansatz, scale-fixed hypothesis, non-load-bearing conjecture, and speculative astrophysical mapping. The vector harmonic extension is identified as the make-or-break open calculation. Framework context. The geometric framework independently reproduces three fundamental constants with zero free parameters: α⁻¹ = 137.035999215 (0.8σ from Rb 2020), sin²θ_eff = π/(4π+1) = 0.231572 (0.26σ from PDG 2024), and α_s(M_Z) = 1/(3π−1) = 0.1187 (0.8σ from PDG 2024). These matches motivate the framework but are not proof; the black hole predictions are independently falsifiable. Supplementary material. An accompanying Python script (supplementary_calculations.py) independently verifies every numerical claim in the paper, including integral identities, coupling constant calculations, transition density estimates, phonon spectrum algebra, baryon counting, and Berger sphere eigenvalue analysis with band structure demonstration.