This paper tests whether the mesoscopic repulsion phenomenon proven for Riemann zeta zeros extends to financial event timing — and finds that it does not. Motivated by the companion paper establishing a rigorous repulsion bound for zeta zeros via the explicit formula, we construct an empirical multi-scale framework to test the repulsion hypothesis on real market data. Using 5,000 consecutive high-frequency trades from the Binance BTCUSDT spot market (REST API: /api/v3/trades, millisecond-precision timestamps), we compare three stochastic models for inter-event gap distributions: (1) Poisson process — exponential gaps, memoryless(2) Repulsion model — Wigner-surmise inspired, f(u) ∝ u² exp(-u²/σ²), zero probability mass near u = 0(3) Hawkes self-exciting process — λ(t) = μ + Σ α·exp(-β(t-tᵢ)) Results (exact MLE log-likelihoods): • Poisson: -251.9999701578 • Repulsion: -1359.3096494762 LRT statistic Λ = 2,214.6, p ≈ 0 • Hawkes: +75.2660286535 ΔAIC = -650.5 vs Poisson Fitted Hawkes parameters: μ = 1.318, α = 4.102, β = 10.0, branching ratio n* = α/β = 0.41 (stationary, 41% endogenous excitation). The repulsion model is catastrophically rejected. At coarse 1-minute candle resolution, gaps are approximately Poisson (KS test D < 0.03). At trade-level resolution, the Hawkes process is strongly preferred, with conditional intensity λ(t) exhibiting sharp cascade spikes (peak λ ≈ 88 events/sec) with ~69 ms exponential decay half-life. These findings establish that mesoscopic repulsion is a genuinely deep property of the Riemann zeta zeros — not a generic feature of complex event sequences. Financial markets are structurally self-exciting, not repulsive: the economic mechanisms that drive sequential trade arrival are the structural opposite of the quantum-mechanical level-avoidance that generates zeta zero repulsion. This work originated as an empirical test during the development of the companion analytic number theory paper (DOI: 10.5281/zenodo.19373941).
Mohhomad Farman (2026) studied this question.