The Matsuura Structural Hierarchy: A Unified Depth Framework for Odd Integers and Collatz-Type Dynamics
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2025
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| _version_ | 1866901821488889856 |
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| author | Matsuura, Yoshihito |
| author_facet | Matsuura, Yoshihito |
| contents | <p>We introduce the Matsuura Structural Hierarchy (MSHD), a canonical depth structure on the odd integers generated by the inverse dynamics of the Collatz map. Each odd integer h admits a uniquely defined mother ancestor, and iterating the mother map produces a finite depth chain terminating at 1. This hierarchy provides a structural classification independent of probabilistic heuristics and supports applications to prime layering, density transfer, and additive decomposition problems such as Goldbach-type constructions. The framework is purely structural and dynamical, requiring no analytic number theory or heuristic randomness assumptions.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17488167 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Matsuura Structural Hierarchy: A Unified Depth Framework for Odd Integers and Collatz-Type Dynamics Matsuura, Yoshihito Collatz Conjecture Inverse Dynamics Matsuura Structural Hierarchy (MSHD) Depth Function Mother Map Structural Number Theory Prime Layering Additive Number Theory Goldbach-Type Problems Discrete Dynamical Systems <p>We introduce the Matsuura Structural Hierarchy (MSHD), a canonical depth structure on the odd integers generated by the inverse dynamics of the Collatz map. Each odd integer h admits a uniquely defined mother ancestor, and iterating the mother map produces a finite depth chain terminating at 1. This hierarchy provides a structural classification independent of probabilistic heuristics and supports applications to prime layering, density transfer, and additive decomposition problems such as Goldbach-type constructions. The framework is purely structural and dynamical, requiring no analytic number theory or heuristic randomness assumptions.</p> |
| title | The Matsuura Structural Hierarchy: A Unified Depth Framework for Odd Integers and Collatz-Type Dynamics |
| topic | Collatz Conjecture Inverse Dynamics Matsuura Structural Hierarchy (MSHD) Depth Function Mother Map Structural Number Theory Prime Layering Additive Number Theory Goldbach-Type Problems Discrete Dynamical Systems |
| url | https://doi.org/10.5281/zenodo.17488167 |