IndisputableMonolith.Meteorology.WeatherPredictabilityFromJCost
This module applies the six-clause J-cost template to meteorology, defining PredictionRange and WeatherPredictabilityCert to bound forecast ratios via non-negative J-cost with zero at unity. Atmospheric scientists and Recognition Science researchers cite it when deriving predictability limits from the forcing chain. The module structure is purely definitional, instantiating the imported CanonicalJBand template on weather data ratios without new lemmas.
claimLet $J(x) = (x + x^{-1})/2 - 1$. The module defines PredictionRange as the admissible interval of forecast ratios and WeatherPredictabilityCert as the proposition that $J(1) = 0$ and $J(r) > 0$ for $r > 0$ in meteorological contexts.
background
The module sits in the meteorology domain of Recognition Science, where quantities are expressed on ratio scales governed by the J-cost function satisfying the Recognition Composition Law. It imports CanonicalJBand, whose doc-comment states: 'The six-clause J-cost-on-ratio template is used across the master cert chain (B-tier whole-science openings, the Plan v7 forty-something domain certs). Each domain cert proves: 1. matched-zero: J(1) = 0 2. nonneg: J(x) ≥ 0 for x > 0'. Sibling definitions introduce PredictionRange for forecast horizons, predictionRangeCount for discrete steps, and WeatherPredictabilityCert for the domain certification.
proof idea
This is a definition module, no proofs. It imports the CanonicalJBand template and declares the four sibling objects to instantiate the matched-zero and nonnegativity clauses for weather predictability ratios.
why it matters in Recognition Science
The module supplies the meteorology entry in the master cert chain, extending the J-band to atmospheric predictability and supporting T5 J-uniqueness and T7 eight-tick octave applications. It serves as a terminal domain module with no downstream uses listed.
scope and limits
- Does not derive numerical forecast horizons from data.
- Does not incorporate chaotic attractor analysis.
- Does not address multi-scale turbulence beyond J-cost bounds.
- Does not prove equivalence to standard meteorological models.