Quantitative finance
Structured market dynamics for options research, connecting geometric forecasts to portfolio outcomes under costs, risk and causal evaluation.
Quantitative finance
A production-oriented option-surface system with a coherent price representation, analytic sensitivities and reproducible numerical validation.
Machine Learning
JEPAs usually target an isotropic latent cloud; HamJEPA instead predicts between views with a symplectic map on phase space.
Quantitative finance
We fit an arbitrage-carrying forward-discounted call surface directly in price space, enforce static no-arbitrage through sparse linear operators, and use a local fog layer where quotes are inconsistent.
Geometric Analysis
Identity-holonomy minimizing foliations at every rational rotation force zero vertical force; ordinary all-slope foliations do not.
Geometric Analysis
All-slope minimizing foliations coexist with nonzero force. A common preserved volume yields a sharp slope-span criterion for rigidity.
Geometric Analysis
A smooth convex body is totally integrable in its own gauge exactly when it is an origin-centred ellipse. Positive curvature follows from the dynamics.
Machine Learning
Identical current predictions can hide different future updates. Sharp memory requirements reveal the evidence that cumulative learning and attention must preserve.