Five candidates that measure the shape of the price trajectory across multiple bars, distinct from the scalar-moment features in the original 64-list. None existed in the original FRAMEWORK.md family taxonomy โ TDA is the first net-new family surfaced during the broader 56-candidate research extension after PR #493.
Imagine you took the last 100 BTC price moves and plotted them as a path through 3D space. Most of the time that path is either smoothly trending or aimlessly noisy โ both produce simple shapes. But when the market is between regimes โ buyers and sellers fighting, no winner emerging โ the path makes loops as price revisits the same regions repeatedly. TDA lets us count those loops, weighted by how persistent they are, with one number per bar. Scalar features (volume, OFI, kyle_lambda, etc.) can't see the loops โ they only measure within-bar moments. That's why TDA is genuinely orthogonal to everything we ship today.
Bubenik 2015's functional summary of the persistence diagram, distilled to one scalar per 100-bar window. The single empirical spike of this family โ used as the pilot application of FRAMEWORK.md before Terry's accuracy review.
Shannon entropy of the normalized birth-death lifespans of the persistence diagram. Empirically robust on Indian stock markets (Sornapudi 2024).
Curves Bk(ฮต) counting alive k-dim topological features as filtration radius grows. Integral encodes curvature of the bar-correlation network.
Topological change-point per bar transition. Distinct from sliced-Wasserstein (parallel-session-claimed); full-W is open territory.
Concatenated Betti curves over rolling windows; extract CROCKER-variance and contour-length scalars. Captures chronotopological evolution.