GC-60 Modular Model and Affine Dynamics of Multiples Modulo 60
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| Formato: | Recurso digital |
| Lenguaje: | italiano |
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2026
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| _version_ | 1866901182395449344 |
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| author | Govi, Claudio |
| author_facet | Govi, Claudio |
| contents | <p>This work presents the theoretical formalization of the GC-60 modular model, which constitutes the structural foundation of the MicroPrime engine for the construction and marking of multiples within translated numerical windows.</p> <p>The model is based on the decomposition N=60R+10+r</p> <p><br>with rrr belonging to the set of residues coprime with 60. Within this compressed representation, the progression of multiples of an odd integer ppp, coprime with 60, is described as a discrete affine dynamical system in the coordinate space (R,r). The global component evolves linearly in the index R, while the local component follows a cyclic modular dynamics determined exclusively by 2p mod 60.</p> <p>The formalization presented here follows a previously developed conceptual experiment that was empirically verified through C++ implementations. These implementations were designed to demonstrate the structural reliability of a translational marking framework, formulated independently from traditional sieve constructions based on explicit number enumeration, including classical wheel-based reductions modulo 30, 60, or 210.</p> <p>GC-60 is not introduced as a new primality criterion and does not alter the theoretical requirement of considering divisors up to sqrt{N}. The model does not modify the fundamental logic of MicroPrime, but provides a structurally compact representation of multiple progression based on scale separation between global growth and local modular dynamics.</p> <p>The present PDF document is written in Italian and contains the complete mathematical formalization of the model. The associated computational implementations and experimental validation are available in the GitHub repository.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18630244 |
| institution | Zenodo |
| language | ita |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | GC-60 Modular Model and Affine Dynamics of Multiples Modulo 60 Govi, Claudio Numeri primi Setaccio modular arithmetic wheel factorization sieve methods affine dynamics GC-60 model modular compression computational number theory prime number generation Primes <p>This work presents the theoretical formalization of the GC-60 modular model, which constitutes the structural foundation of the MicroPrime engine for the construction and marking of multiples within translated numerical windows.</p> <p>The model is based on the decomposition N=60R+10+r</p> <p><br>with rrr belonging to the set of residues coprime with 60. Within this compressed representation, the progression of multiples of an odd integer ppp, coprime with 60, is described as a discrete affine dynamical system in the coordinate space (R,r). The global component evolves linearly in the index R, while the local component follows a cyclic modular dynamics determined exclusively by 2p mod 60.</p> <p>The formalization presented here follows a previously developed conceptual experiment that was empirically verified through C++ implementations. These implementations were designed to demonstrate the structural reliability of a translational marking framework, formulated independently from traditional sieve constructions based on explicit number enumeration, including classical wheel-based reductions modulo 30, 60, or 210.</p> <p>GC-60 is not introduced as a new primality criterion and does not alter the theoretical requirement of considering divisors up to sqrt{N}. The model does not modify the fundamental logic of MicroPrime, but provides a structurally compact representation of multiple progression based on scale separation between global growth and local modular dynamics.</p> <p>The present PDF document is written in Italian and contains the complete mathematical formalization of the model. The associated computational implementations and experimental validation are available in the GitHub repository.</p> |
| title | GC-60 Modular Model and Affine Dynamics of Multiples Modulo 60 |
| topic | Numeri primi Setaccio modular arithmetic wheel factorization sieve methods affine dynamics GC-60 model modular compression computational number theory prime number generation Primes |
| url | https://doi.org/10.5281/zenodo.18630244 |