Most market indicators are statistics of size: how far did prices move, how wide is the spread, how big is the variance. Topological methods ask a stranger question — what shape are the dynamics making? Take a sliding window of daily returns across several markets: each day is a point, the window is a cloud. Persistent homology (the core tool of topological data analysis) measures the cloud's robust geometric structure — loops, clusters, voids — in a way that's invariant to the distortions that fool linear statistics.
The landmark result is Gidea & Katz (2018): a norm built on this machinery rose months before the 2000 and 2008 crashes, before volatility itself moved. Alongside it sits an older, more institutional cousin — Mantegna's (1999) minimum spanning tree, the correlation network's skeleton, which famously contracts toward a star when diversification dies. Central-bank financial-stability research has used it for two decades.
Both are impressive. Both are also exactly the kind of thing a quant site adds because it sounds sophisticated. So before shipping either, we ran the test that matters: do they know anything our existing gauges — Turbulence and the Absorption Ratio — don't?
The TDA gauge earned a place. Its overlap with turbulence is low (rank correlation 0.24) — it is genuinely measuring something different. It rose to the 90th percentile before the 2015–16 global drawdown and climbed from the 40s to the 90s into the 2021–22 top, both while turbulence read calm. And on the decisive test: on days when turbulence saw nothing, a hot TDA reading preceded roughly 55% worse average 60-day drawdowns than a calm one. That is incremental information, from geometry alone.
It also failed twice — silent before the 2018 Q4 slide and the February 2025 break. We publish that on the tool's own page, because a fragility gauge you trust blindly is worse than none.
The market tree survived as a picture, not a signal. Its tightness does contract in every stress episode — but once turbulence is controlled for, the statistical signal essentially dissolves. Mantegna's tree is on the page because seeing which markets carry the connections, and watching the network collapse toward a hub in real time, is structural information a percentile can't convey. The caveat is printed next to it, not buried.
The audit code, parameters and the episodes where the new gauge failed are all described on the live page. Five episodes is a small sample; we'll re-run the study as the record grows, and the page will say whatever the data says.
The obvious extension is a market-specific version — rebuild each market's own dynamics via time-delay embedding and ask whether that geometry warns before that market's drawdowns. We ran the same audit on the S&P 500, Nifty 50, Euro Stoxx 50 and Nikkei 225, against each market's own realized volatility.
It failed on every count that matters. Correlation with the market's own volatility ran 0.45–0.64 — mostly re-measuring vol with extra mathematics. The event studies were inconsistent (Nifty's gauge read the 0th percentile before the 2015 slide). And the incremental test flipped sign across markets: hot readings preceded worse drawdowns in the S&P, milder ones in the Nifty and Nikkei. A signal whose sign depends on which market you ask is noise in a topology costume.
The failure is informative: strip the "cross" out of cross-market geometry and the information disappears. The joint gauge's edge lives in how markets move relative to each other — which is exactly what a single series cannot see.
So the per-market table doesn't ship, the system-level gauge stands, and this note will keep saying whatever the data says.
When the board expanded to twenty markets (July 2026), the study was re-run — first on the full 18-market panel, then, after a calendar data-quality fix, per asset class. Two findings survived everything: the TDA gauge works for equities and the cross-asset panel (hot readings while turbulence was calm preceded a >5% drawdown within 60 days ~44–48% of the time, versus ~17–20% from quiet readings, with forward volatility ~30% higher), and hub concentration works only inside commodities (a commodity tree collapsing onto one hub preceded >10% drawdowns 44% of the time vs 15%).
One retraction, disclosed in full: an interim version of this study reported cross-asset hub concentration at ~2× worse drawdowns. That result was an artifact — mixed Sun–Thu/Mon–Fri trading calendars had been silently deleting days from the panel, and after the fix the effect vanished. Commodity TDA also carries no drawdown information despite producing impressive-looking percentiles. The Market Geometry page now shows each asset class one verdict, from the one signal that passed that class's audit, with the historical odds printed next to it — and lists the failures underneath. A conservative block bootstrap puts the surviving spreads at p≈0.10–0.16: odds-shifters from ~a dozen episodes, not certainties, and the page says that too.
See the live Market Geometry page →