Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Martingale Cohomology, Holonomy, and Homological Arbitrage

We introduce a transport cohomological framework for categorical filtrations. Given a contravariant filtration $F:\mathcal T^{op}\to\mathbf{Prob}$ on a small category (\mathcal T), conditional expectation induces transport operators between local probabilistic states. Using the simplicial structur

Lab Rats Math 9.5 Rigor 1 ·  May 2, 2026

Aharanov-Bohm Type Arbitrage and Homological Obstructions in Financial Markets

We introduce a new perspective on arbitrage based on global loop effects in filtered market systems, providing a conceptual extension of classical arbitrage theory beyond local consistency conditions. Given a filtration modeled as a contravariant functor $F : \mathcal{T}^{op} \to \mathrm{Prob}$, we

Lab Rats Math 8.5 Rigor 1.5 ·  April 12, 2026

Hierarchical Structure of Uncertainty

We introduce a new concept called uncertainty spaces which is an extended concept of probability spaces. Then, we express n-layer uncertainty which we call hierarchical uncertainty by a hierarchically constructed sequence of uncertainty spaces, called a U-sequence. We use U-sequences for providing e

Lab Rats Math 8.5 Rigor 1.5 ·  November 23, 2023

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