PLANNED · research
Hypothesis
Persistence diagrams of a sliding point-cloud of returns capture topological "holes" whose birth/death (persistence landscapes) precede crashes (Gidea–Katz).
Math — persistence of homology classes
Track features across filtration scale $\epsilon$; persistence is death minus birth:
$$ \text{pers}(f) = \epsilon_{\text{death}}(f) - \epsilon_{\text{birth}}(f) $$
$L^p$ norm of the persistence landscape as a crash early-warning.
Method
Plan: sliding-window point clouds of (multi-asset) returns, Vietoris–Rips filtration, monitor landscape norm. Not yet built.
Gidea–Katz reported rising persistence-landscape norms before 2000 and 2008 crashes. Queued as a multi-asset crash early-warning gate — the open question is the same as always: lead time net of false alarms.
Topology gives a coordinate-free view of structure. Whether that view leads price by enough to de-risk on is the only thing that matters — and is untested for us.