What question did this study set out to answer?

The research aims to understand how derivative-order ladders can be precisely recovered using polynomial constructs.

April 16, 2026Open Access

All-Orders Asymptotic Fingerprints and Exact Packet Recovery for Derivative-Order Ladders

Key Points

The research aims to understand how derivative-order ladders can be precisely recovered using polynomial constructs.
Developed higher-difference fingerprints for universal application.
Constructed a full Laurent hierarchy encoding all asymptotic expansion orders.
Proved the exact determination of packets using a finite jet.
Established that derivative-order ladders are governed by an exact packet polynomial.
Provided a complete system for all-orders asymptotic fingerprints.
Demonstrated successful exact recovery of packets for derivative-order ladders.

Abstract

This paper establishes that derivative-order ladders are governed by an exact packet polynomial and provides a full Laurent hierarchy that encodes all orders of the asymptotic expansion. It develops universal higher-difference fingerprints and proves that a finite jet determines the packet exactly. These results yield all-orders asymptotic fingerprints and exact packet recovery for derivative-order ladders.

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