IndisputableMonolith.Astrophysics.PICSimulationLyapunov
The module defines reference Lyapunov exponents and related functions for PIC simulations in Recognition Science. Astrophysicists modeling plasma instabilities cite it for RS-native chaos measures tied to the time quantum. It consists entirely of definitions extending the imported Constants module.
claimReference Lyapunov exponent $\lambda_{\rm ref}$ at $N_{\rm ppc}$ rung 0, with position-dependent $\lambda(N)$ via lyapunovAt, adjacent ratios, and the certificate predicate PICLyapunovCert.
background
The module imports IndisputableMonolith.Constants, whose doc-comment states the fundamental RS time quantum $\tau_0 = 1$ tick. It introduces referenceExponent as the base value at rung 0 and builds lyapunovAt, lyapunovAt_pos, lyapunovAt_succ_ratio, and lyapunovAt_adjacent_ratio on top. The local setting is the astrophysics domain, where these supply RS-consistent measures for particle-in-cell dynamics.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the Lyapunov machinery for astrophysics applications in Recognition Science. It prepares certification predicates such as PICLyapunovCert for downstream simulation work, connecting directly to the RS time quantum from Constants.
scope and limits
- Does not perform numerical integration or simulation runs.
- Does not prove positivity or bounds on the exponents.
- Does not link exponents to specific physical instabilities.
- Does not import or depend on any simulation libraries beyond Mathlib and Constants.