Ô — Cross-Domain Phase Transition Detector: 2D Ising Model × North Anatolian Fault Creepmeter

We propose Ô, a general-purpose measurement operator that quantifies three orthogonal axes of any dynamical system: curl (directional change rate), helicity (internal winding complexity), and balance (proximity to criticality). Validated on two radically different systems: 2D Ising model (L=32-128, Binder cumulant crossing at Tc≈2.269) and North Anatolian Fault Ísmetpaşa creepmeter network. Establishes a five-class taxonomy (Type I-V) plus Null baseline. Positive and Negative Controls confirmed. 16 systems × 10 domains, 5-type + null baseline classification. Includes manuscript (PRL-format, 6pp), all simulation/analysis Python scripts, raw data, and detailed research notes. --- **v2 Update (2026-07-23):** Extended to 4-scale cross-lattice verification (L=32, 64, 128, 256). Includes L256 simulation data, per-L verification JSONs, and `cross_lattice_summary.json` confirming V-shaped helicity spectrum (FERRO > PARA > CRITICAL) with critical-point sigma ~ 0.006 -- scale-invariant across 8x linear range. v1.1: Corrected references (removed 3 hallucinated ophthalmology papers). v1.2: Replaced with tectonic LaTeX PDFs. Added Chinese version. v1.2: Replaced with tectonic LaTeX PDFs. Added Chinese version.