Work

Observers on N: A Lyapunov–Entropy Taxonomy of Integer Programs

Year: 2025

Type: article

Abstract: We introduce a Lyapunov–entropy framework for classifying accelerated integer programs as minimizers, oscillators, or exploders. The method constructs a state-only functional L(n) that decreases strictly under acceleration. This provides a taxonomy of integer dynamical systems, clarifies the role of cancellation and injection, and situates Collatz as a canonical minimizer. Extensions include blockwise surplus criteria, explicit examples, and an operator embedding into prime-based Hilbert spaces.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.17081153

Author: Schepis, Sebastian

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7080419607

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