KILLED · unidentifiable
Hypothesis
Price regime shifts are cusp catastrophes; fitting the cusp normal form to a control/state embedding predicts sudden jumps.
Math — cusp normal form
$$ \frac{dV}{dx} = x^3 + a x + b = 0 $$
Method
Cobb stochastic-cusp fit (control variables = vol, OI) to BTC; likelihood-ratio vs linear model.
Results
| Bimodality detected | occasionally |
| Out-of-sample jump prediction | no edge |
| Parameter identifiability | poor |
The cusp model is barely identifiable on financial data — the control-variable mapping is arbitrary and the fit is unstable. Pretty geometry, no out-of-sample jump prediction. Killed.
Borrowing a physics model requires its variables to mean something measurable. When the "control parameters" are hand-picked, the catastrophe is in the fit, not the market.