Particle Physics Predictions and Experimental Tests of the Fractal-Spectral Framework

A theoretical framework is only as good as its experimental tests. This paper consolidates all particle physics predictions of the fractal-spectral framework into a single document and designs five concrete experimental protocols with specified signals, systematics, null hypotheses, and falsification criteria. The predictions span four domains. For neutrinos, the framework suggests a mass hierarchy mᵢ ∝ (√2) ^nᵢ and log-periodic corrections to oscillation probabilities at the ~7% level (current bound), testable to ~1% by DUNE and T2HK. For precision spectroscopy, atomic transition frequencies should deviate from QED predictions by log-periodic corrections with period ln√2 — currently constrained to |a₁| < 6 × 10⁻¹⁵, indicating that fractal corrections to individual atomic levels in flat spacetime are negligibly small (consistent with the framework's prediction that √2 effects emerge from collective temporal gradient dynamics, not isolated atoms). For high-energy astrophysics, (√2) ⁿ-spaced spectral features in gamma-ray bursts and temporal modulations in nova light curves are predicted. For gravitational physics, precision clock comparisons should show fractal corrections to the standard redshift with coupling ξ < 10⁻³ (current), improvable to 10⁻⁵ by AION/MAGIS. The five experimental protocols are: (1) differential optical clock comparisons (⁸⁷Sr or ¹⁷¹Yb) at varying gravitational heights, searching for log-periodic deviations from Δf/f = gΔh/c²; (2) spectroscopic QED residual analysis across microwave-to-UV transitions, searching for log-periodic structure with period ln√2; (3) neutrino oscillation analysis at DUNE for fractal corrections to P (ν_μ → νₑ) ; (4) GRB spectral stacking analysis for √2-periodic features in Band function residuals; (5) atom interferometry phase shift measurements for fractal coupling signatures. A summary table provides current bounds and future sensitivity for each test. The hierarchy of constraints is stated honestly: QED spectroscopy gives the tightest bound (10⁻¹⁵), confirming that fractal effects on isolated atoms are tiny. The most promising detection channel is the CMB log-periodic signature (predicted amplitude ~10⁻³–10⁻⁴, near current sensitivity). The glueball mass ratio M₁/M₀ = √2 remains the cleanest parameter-free test in the strong sector.