Discrete Multi-Modal Structure in Black Hole Mass Distributions Across Scales: LIGO Stellar-Mass Gaps, φ-Harmonic Mass Quantization, and a Bimodality Prediction for JWST Supermassive Black Hole–Galaxy Ratios

Black hole mass distributions at stellar and supermassive scales show discrete multi-modal structure where smooth power laws are predicted. At the stellar scale, LIGO/Virgo/KAGRA observations reveal two peaks at ~10 and ~35 solar masses matching a φ-harmonic sequence with seed mass M₀ = 3.25 M☉ (φ² and φ⁵), and 16 systematic gaps whose scaling ratio of 1.754 equals φ^(7/6) to 0.05% precision. At the supermassive scale, JWST overmassive black hole–galaxy ratios at z > 4 decompose to sixth-harmonic multiples of φ across three orders of magnitude (median residual 1.8%). A specific, falsifiable prediction is presented: the M_BH/M★ distribution at z ≈ 5 should show bimodal clustering when tested with Gaussian mixture models, with modes at ratios ~0.070 and ~0.043 separated by log₁₀(φ) = 0.209 dex. No other current framework makes this prediction. The JWST sample is approaching the 50–100 objects needed for statistical discrimination.