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April 16, 20260 citationsOpen Access

Holonomic Derivative-Order Geometry: Companion Transport, Projective Packet Closure, and WKB Fingerprints

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MAMohammad Abu-Ghuwaleh

Key Points

  • This work aims to expand the derivative-order program to include holonomic packets and analyze their dynamics.
  • Developed an exact companion transport for holonomic derivative-order packets.
  • Established a projective closure that describes packet closure in projective space.
  • Derived second-order dynamics for packet evolution.
  • Obtained a WKB-type fingerprint encoding the asymptotic behavior of holonomic packets.
  • Introduced new tools for analyzing holonomic derivative-order geometry.
  • Demonstrated systematic connections between holonomic packets and WKB methods.
  • Revealed insights into projective packet dynamics.

Abstract

This preprint extends the derivative-order program beyond constant-coefficient spectral packets to general holonomic packets. It develops an exact companion transport that governs the evolution of holonomic derivative-order packets and a projective closure that shows how packets close in projective space. Second-order packet dynamics are derived and a WKB-type fingerprint is obtained that encodes the asymptotic behavior of holonomic packets. These tools enable a systematic analysis of holonomic derivative-order geometry and reveal new connections with WKB methods and projective packet dynamics.

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Cite This Study

Mohammad Abu-Ghuwaleh (2026) studied this question.

synapsesocial.com/papers/69e07d3c2f7e8953b7cbe376https://doi.org/10.5281/zenodo.19567866
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