Editing Openai/693eaf5a-1494-8007-b1e3-00abefb11523 (section)

===== 1. Geometric indicators - tetra_vol: the volume of the 3D tetrahedron formed by O, A=(day,0), B=(0,price) and apex D=(day, price, h) where h = (perpendicular distance from O to hypotenuse)/2. - h: half the orthogonal distance from O to the triangle’s hypotenuse (as you specified). - hyp_len: the 2D hypotenuse length between A and B. - tri_area: area of the triangle O-A-B. - vol10: rolling volatility (baseline non-geometric comparator). =====
# Predictive evaluation - For each indicator, the script fits a single-feature logistic regression that predicts up_next (1 if next day price is higher). - It reports correlation with the up_next binary, AUC (how well the indicator ranks the days by future up probability), and quartile-based Bayesian posterior probabilities (P(up_next | indicator quartile)). - The table printed at the top ranks indicators by AUC. Indicators with higher AUC and positive correlation are better single-feature predictors of next-day increases.
# Bayesian / posterior lift - The posterior_by_quartile plots show empirical posterior probabilities for each quartile of the indicator value; compare these to the prior probability (overall fraction of days that go up). A strong indicator will show monotonic posteriors and some quartiles with significantly higher posterior than the prior.
# Visual outputs - price_series.png: the price series itself. - example_tetrahedron.png: 3D view of one constructed tetrahedron (final day). - tetra_vol_time.png and h_time.png: indicator time series. - posterior_by_quartile_*.png: posterior vs quartile for top indicators. - roc_curves.png: ROC for each indicator.