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| Main Author: | |
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| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2026
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| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.19600331 |
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Table of Contents:
- <p>We introduce Geometric Transfer Entropy (GTE), a measure of directional<br>information flow between time series that preserves the grade structure of the<br>Clifford-algebraic embedding underlying the Geometric Signal Dynamics (GSD)<br>programme. Building on the kinematic embedding and geometric product of Vázquez<br>Broquá (2026a), the spectral bivector identity of Vázquez Broquá (2026b), the joint<br>embedding for cointegration of Vázquez Broquá (2026c), and the antisymmetric<br>entropy HAS of Vázquez Broquá (2026d), we define GTEX→Y (τ ) as the sum of<br>two grade-resolved channels: a scalar channel T(0)X→Y that captures transfer of alignment/level information, and a bivector channel T(2)X→Y that captures transfer of rotational information (velocity, curvature, phase). The net flow ΦXY = GTEX→Y −GTEY →X decomposes analogously into a scalar and a rotational flow, ΦXY = Φ(0) XY + Φ(2) XY . Across seven benchmark systems, GTE recovers the classical Schreiber transfer entropy on level-coupled linear systems, detects velocity-coupled systems four times more strongly than Schreiber TE, and correctly identifies the direction<br>of coupling in stochastic oscillators where classical TE reverses sign. The bivariate signature (Φ(0), Φ<br>(2)) produces a taxonomy of dynamical coupling mechanisms and yields geometric diagnostics of cointegration, common confounding, and pure rotational transfer that classical information flow measures cannot provide.</p>