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RPR Closure Period Theorem in a Base-12 Cyclic Framework: Exact Recurrence Lengths from Divisor Structure in Z12

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Autor principal:	Lesperance, Joel Michael
Formato:	Recurso digital
Publicado:	Zenodo 2026
Materias:	Relative Phase Recursion, RPR operator, Z12 cyclic group, modular arithmetic, closure theorem, minimal recurrence period, gcd structure, divisor completeness, orbit classification, cyclic symmetry, discrete phase evolution, finite group theory, modular indexing, recurrence length, cyclic subcycles, group generators, modular closure, phase recurrence theorem, algebraic symmetry structure, base-12 framework
Acceso en línea:	Acceder al recurso
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_version_	1866902020290510848
author	Lesperance, Joel Michael
author_facet	Lesperance, Joel Michael
contents	<p><span>ABSTRACT<br>This paper formalizes the closure properties of the Relative Phase Recursion (RPR) operator in the cyclic group Z12. The RPR update rule R(n) = (n + Δ) mod 12 generates discrete phase evolution governed entirely by modular arithmetic. We prove that the minimal recurrence length of the system is k = 12 / gcd(12, Δ). This result classifies all possible orbit lengths in Z12 and demonstrates that recurrence structure is determined by the divisor structure of 12. The theorem provides exact predictions for phase-cycle stability in any C12-indexed system and establishes a precise algebraic foundation for modular phase closure.</span></p>
format	Recurso digital
id	zenodo_https___doi_org_10_5281_zenodo_18748269
institution	Zenodo
language
publishDate	2026
publisher	Zenodo
record_format	zenodo
spellingShingle	RPR Closure Period Theorem in a Base-12 Cyclic Framework: Exact Recurrence Lengths from Divisor Structure in Z12 Lesperance, Joel Michael Relative Phase Recursion, RPR operator, Z12 cyclic group, modular arithmetic, closure theorem, minimal recurrence period, gcd structure, divisor completeness, orbit classification, cyclic symmetry, discrete phase evolution, finite group theory, modular indexing, recurrence length, cyclic subcycles, group generators, modular closure, phase recurrence theorem, algebraic symmetry structure, base-12 framework <p><span>ABSTRACT<br>This paper formalizes the closure properties of the Relative Phase Recursion (RPR) operator in the cyclic group Z12. The RPR update rule R(n) = (n + Δ) mod 12 generates discrete phase evolution governed entirely by modular arithmetic. We prove that the minimal recurrence length of the system is k = 12 / gcd(12, Δ). This result classifies all possible orbit lengths in Z12 and demonstrates that recurrence structure is determined by the divisor structure of 12. The theorem provides exact predictions for phase-cycle stability in any C12-indexed system and establishes a precise algebraic foundation for modular phase closure.</span></p>
title	RPR Closure Period Theorem in a Base-12 Cyclic Framework: Exact Recurrence Lengths from Divisor Structure in Z12
topic	Relative Phase Recursion, RPR operator, Z12 cyclic group, modular arithmetic, closure theorem, minimal recurrence period, gcd structure, divisor completeness, orbit classification, cyclic symmetry, discrete phase evolution, finite group theory, modular indexing, recurrence length, cyclic subcycles, group generators, modular closure, phase recurrence theorem, algebraic symmetry structure, base-12 framework
url	https://doi.org/10.5281/zenodo.18748269