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May 27, 2026Open Access

Geometric Origin of Exact Mean-Field Reductions: Möbius Symmetry and the Lorentzian Ansatz

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Authors

HBHugues BerryLTLeonardo Trujillo

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Overview

Randomized trial investigates geometric foundations of mean-field reductions in coupled oscillators, highlighting implications for dynamics.

Key Points

  • This work aims to uncover the geometric principles underlying mean-field reductions in systems of coupled oscillators and spiking neurons.
  • Reformulated dynamics on the circle using Riccati dynamics.
  • Explored the uniqueness of rotation-invariant probability measures.
  • Analyzed the emergence of the Cauchy-Lorentz family through stereographic projection.
  • Established that the Cauchy-Lorentz family is invariant under projective transport.
  • Demonstrated the Lorentzian family arises from the full projective action.
  • Clarified why Gaussian closures fail and identified conditions for exact two-parameter reductions.

Cite This Study

Berry et al. (2026) studied this question.

synapsesocial.com/papers/6a168a090c924ddd1bd58ae2https://doi.org/10.48550/arxiv.2605.23669
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