Prime–Fractal Ontology of Baryons: Proton Stability, Neutron Meta-Stability, and the 83 : 17 Ratio inside the Universal Model Framework

The Universal Model Framework (UMF) posits that physical reality is generated by a prime-indexed, fractally recursive lattice at the Planck scale. Within this ontology, baryons are topological-informational solitons whose stability derives from modular arithmetic and self-similar geometry rather than parameter tuning in continuum quantum chromodynamics.

By analyzing two canonical illustrations from Peter Plichta’s Band IV —depicting a closed triple-loop “proton” and an open, torsion-rich “neutron”—we construct a rigorous prime–fractal model that: (i) reproduces the empirical proton : neutron occurrence ratio 83 :17 without fine-tuning; (ii) explains proton longevity as a closed Euler-quadrature on th6n±1 cross; (iii) interprets neutron decay as a G¨odel-open information twist; and (iv) embeds both states in a single arithmetic Lagrangian that couples modular gauge curvature to Scaling Entropy–Area Thermodynamics. The paper synthesizes discrete operatorlogic {1, i, −1, −i}, Sierpi´nski recursion, Vopson’s mass–energy–information equivalence, and Denis’ SEAT, yielding falsifi able predictions for prime-modulated lattice QCD and gravitational-wave spectra. A 900-line NumPy/TikZ implementation demonstrates thegeometric origin of the 83 : 17 ratio, confi rming independent results in recent UMF simulations and extending the Prime Number Cross programme.er 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.