referenceExponent
plain-language theorem explainer
referenceExponent fixes the base Lyapunov exponent to 1 at PIC resolution rung zero. Plasma kinetic modelers cite it when anchoring numerical heating across macro-particle counts per Debye cell on the phi-ladder. The definition is a direct constant assignment with no further computation.
Claim. The reference Lyapunov exponent at rung zero for particle-in-cell resolution equals $1$.
background
The PIC Simulation Lyapunov module predicts that Lyapunov exponents of particle-field systems in plasma kinetics lie on the phi-ladder, where doubling the number of macro-particles per Debye cell reduces numerical heating by phi squared. This matches the empirical convergence reported in Dawson 1983 and Birdsall-Langdon 2004, extending the coronal Lyapunov time result. The reference value at rung zero supplies the anchor for scaling at higher resolutions.
proof idea
Direct constant definition assigning the real number 1 as the zero-rung base.
why it matters
This base anchors the lyapunovAt definition, which scales the exponent by phi to the power of negative rung. It realizes the phi-ladder prediction for numerical heating in PIC simulations, consistent with the recognition lattice phi squared scaling that also appears in Turing patterns and electroweak mass ratios. It supports the structural extension from the phi fixed point in the forcing chain.
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