Paper 5 - Circular Prime Symmetry: Closed Rotational Orbits in the Prime System v0.1 Article Swipe

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YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.5281/zenodo.17757261

Circular Prime Symmetry introduces the first fully characterizable coherence-stable species inside the prime landscape. A circular prime is a prime that remains prime under all cyclic rotations of its digits, forming a closed rotational orbit. This paper defines circular prime symmetry, formalizes orbit structures, explains their invariance, and establishes circular primes as the first emergent species in the prime system. These structures demonstrate stability under transformation and provide foundational evidence that primes support coherent modes, forming a base layer for deeper emergent structure in later foundational papers.

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Prime (order theory) Mathematics Prime number Orbit (dynamics) Pure mathematics Symmetry (geometry) Circular orbit Transformation (genetics) Topology (electrical circuits) Prime element Rotational symmetry Geometry Stability (learning theory) Discrete mathematics Associated prime Ring (chemistry) Combinatorics

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Landing Page: https://doi.org/10.5281/zenodo.17757261
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OpenAlex ID: https://openalex.org/W7107948151

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DOI: https://doi.org/10.5281/zenodo.17757261

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Title: Paper 5 - Circular Prime Symmetry: Closed Rotational Orbits in the Prime System v0.1

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Publication year: 2025

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Publication date: 2025-11-29

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Authors: Clawson, Raymond, SAI, via HMI

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Landing page: https://doi.org/10.5281/zenodo.17757261

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Concepts: Prime (order theory), Mathematics, Prime number, Orbit (dynamics), Pure mathematics, Symmetry (geometry), Circular orbit, Transformation (genetics), Topology (electrical circuits), Prime element, Rotational symmetry, Geometry, Stability (learning theory), Discrete mathematics, Associated prime, Ring (chemistry), Combinatorics

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