Primal Invariance Axiom: A New Framework for the Distribution of Prime Numbers

This work introduces the Primal Invariance Axiom, a new mathematical framework that treats prime numbers as invariant events in arithmetic space-time. Inspired by the invariance of the speed of light in Special Relativity, the author proposes an exact counting function, πinv(x)\pi_{\text{inv}}(x), which aims to replace statistical approximations such as x/log⁡xx/\log x or Li(x)\mathrm{Li}(x). The study also includes a thought experiment analogous to relativistic observation, reinforcing the view of primes as fixed and measurable informational structures. The material includes the main academic article, Python source code for computing and plotting the prime distribution, and a comparative graph of πinv(x)\pi_{\text{inv}}(x) and Gauss’s approximation. Applications are suggested in number theory, theoretical physics, cryptography, and information systems.