FWA-CODE v1: Simulation of Field Dimensionality Phase Transition and Cubic Nonlinear Potential

Abstract

FWA-CODE v1: Simulation of Field Dimensionality Phase Transition and Cubic Nonlinear PotentialAuthors: Igor Kolesnikov (Mark)Framework: Fractal Wave Algebra (FWA) — DOI: [вставь DOI v5 с First Law + Zero Principle]Abstract:This code provides the first numerical implementation of the First Law and Zero Principle of Fractal Wave Algebra (FWA).The simulation demonstrates two core processes:Dimensionality Phase Transition: Implementation of the generative symmetry $\Delta(t0) \equivG \Delta(t)$ with preserved field identity $Id(t0)=Id(t)$ and changing dimensionality $D(t0) \neq D(t)$. The state parameter $w(D) = D/3 - 1$ is computed for the transition $D: 3.515 \rightarrow 1.5$, yielding $w: +0.1717 \rightarrow -0.5$.Cubic Nonlinear Potential $V(\Delta)$: $V(\Delta) = (\lambda/4)\Delta^4 - (\mu^2/2)\Delta^2 - \varepsilon\Delta$. The symmetric baseline ( $\varepsilon=0$) is compared with the FWA potential with chiral asymmetry ( $\varepsilon=0.15$), showing the emergence of a stable resonance $\Delta_{min}$. This illustrates the mechanism of dynamic cloning without singularities.Theoretical Basis:Zero Principle: $Id=0 \Rightarrow \Delta(t)=0 \quad \forall t, \forall D$. No generating field, no manifestations.First Law (Generative Symmetry): $\Delta(t0) \equivG \Delta(t)$, where $\equivG$ denotes that subsequent states are generative clones of the originating field. Valid for $Id \neq 0$: $Id(t0)=Id(t), D(t_0)\neq D(t)$.Triad: Wave self-similarity (principle), Dynamic cloning (mechanism: $\Delta(t{n+1})=C[\Delta(tn)]$), Wave fractality (result).Code:Python / NumPy / Matplotlib. Contains:function for FWA state parameter.Potential $V(\Delta)$ calculation with parameters $\lambda=0.5, \mu=1.0, \varepsilon=0.15$.Visualization of $D(t)$ vs $w(t)$ and $V(\Delta)$ with stable resonance marker.Result:The framework eliminates the need for hypothetical entities such as singularities where classical mathematics breaks down. All structures are derived from a single wave field via changing dimensionality. This code provides a base algorithm for AI simulations scaling from electron to galaxy using a unified scaling law.Keywords: Fractal Wave Algebra, FWA, First Law, Zero Principle, Generative Symmetry, Dynamic Cloning, Dimensionality Transition, Nonlinear Potential, Dark Energy, w-parameterLicense: CC BY 4.0Reference Code File: