Black Holes in the Fractal-Spectral Framework: Temporal Concentrators, Singularity Resolution, and Primordial SMBH Seeding

In the fractal-temporal framework, black holes are regions where the collective vibrational frequency of matter approaches zero, producing extreme temporal gradients — the horizon is the surface where local time stops. This paper develops the full consequences. At the individual level, the Schwarzschild radius r_s = 2GM/c² is recovered exactly, with (√2)⁻ⁿ fractal corrections parametrized by the internal vibrational structure of the collapsed matter. The framework proposes a natural singularity resolution: quantum vibrational modes impose a minimum frequency at the Planck scale (f_min = f_P/√2), preventing the temporal gradient from diverging and replacing the classical singularity with a finite-density core at r_min = √2 ℓ_P. The mechanism is distinct from loop quantum gravity (discrete area spectra), string theory (fuzzballs), and noncommutative geometry (minimum length). Hawking radiation acquires fractal corrections: the temperature is modulated by (√2)⁻ⁿ oscillatory terms that are log-periodic in time with period ln√2, encoding the progenitor's vibrational structure. The radiation is not perfectly thermal — it carries subtle modulations that in principle contain information about the collapsed matter. The Page time is predicted at ~15% of the evaporation time (rather than the standard ~50%), distinguishing fractal encoding from random scrambling. Gravitational wave signatures include fractal corrections to quasi-normal mode frequencies during ringdown: ω_nᶠʳᵃᶜᵗᵃˡ = ω₀GR[1 + δ_n/(√2)^n], potentially detectable through stacking of ~100 merger events at current LIGO/Virgo sensitivity. The photon ring structure acquires (√2)⁻ⁿ sub-ring modulations. The most distinctive and testable prediction is cosmological: the (√2)^n scale hierarchy produces a discrete fragmentation spectrum for primordial black holes with seed masses M_n = M₀/(√2)³ⁿ, providing a mechanism for rapid supermassive black hole formation that addresses the JWST high-redshift timing problem. This predicts a log-periodic modulation of the SMBH mass function with spacing Δlog₁₀M ≈ 0.45, testable with current survey data and independent of the strong-field details. Open problems are stated explicitly: strong-field derivation (the framework is validated only in weak field), rigorous information preservation proof, fragmentation dynamics simulation, and consistency with existing primordial black hole constraints.