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April 16, 20260 citationsOpen Access

Integrable-Hierarchy Derivative-Order Geometry: Multitime Tau Ladders, KP/Toda Hirota Closures, and Finite Plücker Recovery

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MAMohammad Abu-Ghuwaleh

Key Points

  • The aim is to enhance derivative-order geometry by connecting it with integrable hierarchies through multitime tau ladders.
  • Introduced multitime tau ladders to track derivative orders along multiple times.
  • Established a universal cube law for the representation of hierarchies.
  • Derived explicit KP/Toda closures using Hirota's approaches.
  • Formulated a finite Plücker recovery theorem to demonstrate jet recovery of the derivative-order spectrum.
  • Successfully linked derivative-order geometry to integrable hierarchies through the proposed methods.
  • Showed that Hirota bilinear transmutation can generate the full hierarchy of derivatives.
  • Demonstrated that a finite jet is sufficient to recover the entire derivative-order spectrum.

Abstract

This paper lifts derivative-order geometry to integrable hierarchies by introducing multitime tau ladders that track derivative orders along multiple times. It establishes a universal cube law and shows that Hirota bilinear transmutation generates the full hierarchy. Explicit KP/Toda closures are derived, and a finite Plücker recovery theorem proves that a finite jet suffices to recover the derivative-order spectrum.

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Cite This Study

Mohammad Abu-Ghuwaleh (2026) studied this question.

synapsesocial.com/papers/69e07de52f7e8953b7cbedfbhttps://doi.org/10.5281/zenodo.19567965
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