IndisputableMonolith.Astrophysics.PICSimulationLyapunov
This module defines the reference Lyapunov exponent at N_ppc rung 0 together with related functions for PIC simulations inside Recognition Science. Plasma physicists modeling chaotic instabilities in astrophysical plasmas would cite these objects. The module is a pure definition block that imports the RS time quantum from Constants and exposes sibling declarations for rung-wise extension.
claimReference Lyapunov exponent at rung 0: let $N_{ppc}$ be the particles-per-cell parameter; the base value is given by referenceExponent$(N_{ppc})$ with subsequent maps lyapunovAt, lyapunovAt_pos, lyapunovAt_succ_ratio and lyapunovAt_adjacent_ratio.
background
Recognition Science supplies the fundamental time quantum τ₀ = 1 tick via the imported Constants module. The present module sits in the Astrophysics domain and introduces Lyapunov exponents for Particle-In-Cell simulations. Its sibling declarations (referenceExponent, lyapunovAt, PICLyapunovCert) build a ladder of exponents indexed by rung, consistent with the phi-ladder structure used elsewhere in the framework.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the Lyapunov machinery required by downstream astrophysical models that quantify instability growth rates. It directly extends the RS time quantum τ₀ into simulation diagnostics and prepares the ground for PICLyapunovCert certificates. No used-by edges are recorded yet, indicating the block is an early interface in the astrophysics layer.
scope and limits
- Does not compute numerical values or run simulations.
- Does not prove positivity or bounds on the exponents.
- Does not link the exponents to specific plasma equations.
- Does not contain algorithms or code for time-stepping.