IndisputableMonolith.Climate.ClimateForecastSkillFromJCost
This module defines climate forecast skill metrics from the J-cost function, establishing the Lorenz predictability limit as approximately (gap - 45)/3 days. Physicists working on deterministic weather models would cite it to connect RS-native cost functions to atmospheric horizons. The module consists of supporting definitions for timescales, skill positivity, and decay rates built directly on imported constants and cost primitives.
claimLorenz predictability limit $≈ (gap - 45)/3$ days, where forecastSkill is a positive decaying function of ForecastTimescale derived from J-cost.
background
The module imports Constants, which fixes the fundamental RS time quantum τ₀ = 1 tick, and Cost, which supplies the J-cost framework J(x) = (x + x^{-1})/2 - 1. It introduces ForecastTimescale as the discrete counting unit and forecastSkill as the skill measure that remains positive while decaying over successive timescales. The central claim ties the classical Lorenz limit directly to the gap parameter on the phi-ladder.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the climate-specific bridge from J-cost to forecast certification, feeding ClimateForecastCert. It applies the Recognition Composition Law to atmospheric predictability and places the Lorenz limit inside the RS-native gap structure.
scope and limits
- Does not compute numerical forecast errors for specific atmospheric models.
- Does not derive the numerical value of gap from first principles.
- Does not address multi-scale or coupled climate dynamics beyond single J-cost decay.
- Does not incorporate empirical data validation or observational constraints.