Quantum Fractional Summation Models for Black Hole Metrics and Horizon Resonance

Quantum Fractional Summation Models for Black Hole Metrics and Horizon ResonanceScott Monroe – July 18, 2025 This paper introduces a novel quantum summation framework using recursive fractional constructs constrained by quantum energy thresholds. The model provides a non-singular representation of black hole microstructure by mapping quantized summation terms onto Schwarzschild and Kerr metrics. By defining a discrete energy-filtered operator over cubic indices, the framework yields perturbative spacetime corrections and predicts quantized horizon resonances. These signatures—bounded, chaotic energy spectra—may correspond to gravitational wave ringdowns, black hole entropy discretization, and Loop Quantum Gravity microstates. The formulation offers a testable, Planck-consistent alternative to classical metric singularities.