Numerical Implementation of Plichta's Prime Number Cross within the Universal Model Framework
Year: 2025
Type: article
Abstract: Peter Plichta’s Prime Number Cross (PNC) arranges primes on the four rays 6n ± 1 and maps them, via Euler’s discrete quarter-turn eiπ/2 , onto a unit-disc “cross” {±1, ±i}. In the Universal Model Framework (UMF) the PNC is embedded in a Planck-scale Sierpi´nski lattice that serves as spacetime’s arithmetic substrate. Here we supply the first vectorised NumPy/SciPy implementation of (i) Euler-cross quadrature loops, (ii) prime-to-complex mapping, (iii) path-length comparison between the discrete square Ldisc and the continuous half-circle Lcont = πr, and (iv) closure tests on Sierpi´nski-masked lattices. For shells r ≤ 150 we find Ldisc = 4√ 2 r with systematic relative error ε = (4√ 2 − π)/π ≈ 0.800%. The loop remains closed after 97.6% of random Sierpi´nski masks, confirming robustness of prime-fractal geodesy. These findings strengthen the UMF claim that spacetime geodesics are prime-modulated and provide an open-source Python toolkit for further exploration. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.
Author: Gericke, Marco
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6911860327
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