Empirical Characterization of an Autonomous Accessibility Flow: A Universal β-Function and Continuous IR Fixed-Point Spectrum from Out-of-Time-Order Correlators

We report the first systematic empirical characterization of an autonomous accessibility flow extracted from out-of-time-ordered correlators (OTOCs) across eleven quantum many-body models spanning four dynamical classes. The effective β-function β_eff(Ω) ≡ dΩ/d(ln N), where Ω_late is the late-time OTOC saturation value, collapses onto the universal logistic form β = −c Ω(1 − Ω) across models (slope = 1.003, χ²/dof = 1.11, p = 0.31), demonstrating that the flow is autonomous—depending only on the current value of Ω and not on the system size N at which it is measured. The scaling exponent c provides a continuous, observable-independent diagnostic of the effective infrared (IR) fixed point, spanning c ∈ [0.17, 4.30] from integrable-adjacent (Luttinger class, c ≈ 1) to maximal scramblers (Schwarzian/JT class, c ≈ 3.9–4.3). A pre-registered prediction—c ∈ [1, 4] for intermediate-range interactions—is confirmed with c = 3.41 ± 0.48 for power-law coupling J(r) = J₀/r. The exponent c is invariant under change of local observable (1.2% variation) and UV symmetry class (4% variation), establishing it as an infrared property insensitive to ultraviolet structure—the standard signature of renormalization group universality. Corrected precision of Schwarzian/JT class description: c is a finite-size scaling exponent distinct from the Schwarzian coupling constant. Use paper3_main_v02.tex.