What question did this study set out to answer?

This work aims to expand the derivative-order program to include holonomic packets and analyze their dynamics.

April 16, 2026Open Access

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

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.

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

Key Points

Abstract

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