This site documents research on the P System, a framework based on the hypothesis of a grammatical origin of prime numbers. The goal is to explore an alternative computational paradigm, making the theory and implementations accessible for verification and scientific debate.
The research is structured around a rigorous theoretical foundation, validated by computational experiments, and a series of exploratory applications in various domains. The main sections of this laboratory are Theory, the study of Prime Numbers, and practical implementations.
The system identifies prime numbers through grammatical saturation processes, where indivisibility emerges as an intrinsic structural property of the formal language.
Computational operations are implemented as grammatical transformations, offering an alternative paradigm to traditional binary logic.
The framework enables simulation of physical and biological phenomena through the application of grammatical rules to symbolic structures.
The system manifests complex behaviors arising from the interaction of simple grammatical rules, suggesting applications in artificial intelligence.
The grammatical structure allows autonomous generation of new symbolic configurations through iterative transformation processes.
The framework finds application in various scientific fields, from number theory to theoretical physics, from cryptography to computational biology.
The framework's validity has been tested through the Selective Genealogical Algorithm (SGA), a constructive engine that translates theory into computational implementation. The main results demonstrate:
The Rust implementation of the SGA correctly calculated the 37,607,912,018 prime numbers up to 10¹², empirically validating the theoretical model's consistency and efficiency. The SGA is a generative process that does not rely on factorization.
Performance analysis of the Selective Genealogical Algorithm (SGA) and study of the Morphogenetic Signature (φ) as a metric of the structural quality of numbers.
Development of the P-Signature scheme, which uses the Morphogenetic Signature as part of the key generation and encoding process.
Exploratory application of P System grammar to describe particle physics phenomena and dynamic systems as emergent symbolic structures.
Long-term research on AI models based on grammatical coherence and the SyntaxOS project, an experimental operating system based on the non-binary grammar of the P System.