What question did this study set out to answer?

The central aim is to introduce a new AGOSS calculus for organizing derivative structures and prove its effectiveness in recovery processes.

April 16, 2026Open Access

Derivative-Order AGOSS: Canonical Shell Hierarchies, Exact Packet Peeling, and Atomic Jordan Decomposition

Key Points

The central aim is to introduce a new AGOSS calculus for organizing derivative structures and prove its effectiveness in recovery processes.
Introduced derivative-order AGOSS calculus with modular shells.
Defined shell and packet projectors.
Constructed anchored Jordan atoms.
Developed and proved methods for exact packet peeling.
Established laws for finite-window recovery.
Proved that finite-window information recovers canonical shells, packets, and atoms exactly.
Demonstrated a comprehensive framework for derivative-order hierarchies.
Established atomic Jordan decomposition within the AGOSS hierarchy.

Abstract

This preprint introduces a derivative-order AGOSS calculus that organizes the derivative spectrum into canonical modulus shells and defines shell projectors and packet projectors. It constructs anchored Jordan atoms and develops exact packet peeling methods, proving that finite-window information recovers shells, packets and atoms exactly. The work provides a comprehensive framework for derivative-order ladders and establishes atomic Jordan decomposition and finite-window recovery laws for the AGOSS hierarchy.

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Cite This Study

Mohammad Abu-Ghuwaleh (Tue,) studied this question.

synapsesocial.com/papers/69e07e582f7e8953b7cbf5b1 https://doi.org/https://doi.org/10.5281/zenodo.19565660

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