Discussing the article: "Ollivier-Ricci Curvature: Reading the Shape of a Correlation Network, Not Its Level"

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Check out the new article: Ollivier-Ricci Curvature: Reading the Shape of a Correlation Network, Not Its Level.

The article builds an Ollivier–Ricci curvature library in MQL5 for multi‑symbol analysis. A basket becomes a correlation network, and the reading captures network geometry rather than correlation level. It includes an exact optimal transport solver with an internal certificate, a rolling fragility metric with two informative nulls, an indicator that plots the reading against its null band, and a demonstration expert that uses it as a risk gate.

Every correlation dashboard on this site answers the same question: how strongly are these instruments moving together right now? That number is useful, but it is a level, and a level cannot say whether the market still has any internal structure left. A market where metals move with metals, indices with indices, and the yen moves against everything is different from one where all twenty-six instruments collapse onto a single driver. Yet both can report the same average correlation.

Sandhu, Georgiou and Tannenbaum made the case in 2016 that the missing quantity is a geometric one. Build a network whose nodes are the instruments and whose edge lengths come from their correlations, then ask a question from Riemannian geometry: is this network locally curved? On a positively curved edge the endpoints share most of their neighborhoods, so there are many ways round and no connection is load bearing. On a negatively curved edge there is one way across, and cutting it splits the market in two. Curvature is a statement about shape that barely moves with the correlation level, which is the property no correlation average can have.

Author: Hammad Dilber