Price Overlap Rate II: Two Degrees of Freedom in Adjacent OHLC Bar Geometry Across Seven Markets

This replication package contains the manuscript, code, and key result files for "Price Overlap Rate II: Two Degrees of Freedom in Adjacent OHLC Bar Geometry Across Seven Markets" (Liu, 2026). The paper introduces (τ, λ),the centroid shift ratio and scale change ratio as a complete, minimal two-dimensional coordinate system for the high-low geometry of adjacent OHLC bar pairs. The joint distribution is characterized on 14,586 instruments across seven asset markets: Chinese A-shares, U.S. equities, Hong Kong equities, foreign exchange, commodity futures, cryptocurrencies, and equity indices. The package includes 23 Python scripts, 29 result files (CSV/JSON), and the LaTeX source with compiled PDF.