IndisputableMonolith.Climate.PredictabilityFromJCost
This module defines forecast J-cost on uncertainty growth ratios to support climate predictability analysis within Recognition Science. Climate modelers and predictability theorists cite it when bounding forecast horizons via J-cost thresholds. The module consists of definitions establishing basic algebraic properties of the cost function and horizon predicates.
claimThe module defines forecastCost$(r) = J(r)$ for uncertainty growth ratio $r$, together with PredictabilityThreshold, IsPastHorizon, IsWithinHorizon, and ClimatePredictabilityCert.
background
The Constants module supplies the RS-native time quantum τ₀ = 1 tick. The Cost module provides the J-cost function J(x) = (x + x⁻¹)/2 - 1 that quantifies deviation from self-similarity. This climate module applies those primitives to uncertainty growth ratios that govern forecast horizons.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the definitions that feed ClimatePredictabilityCert and the horizon-state lemmas, placing J-cost at the center of climate predictability certification. It extends the T5 J-uniqueness step of the forcing chain to forecast applications.
scope and limits
- Does not perform numerical climate simulations.
- Does not derive specific atmospheric models.
- Does not address units outside RS-native scaling.
- Does not prove long-term climate stability.
depends on (2)
declarations in this module (12)
-
def
forecastCost -
theorem
forecastCost_zero_at_unit -
theorem
forecastCost_reciprocal_symm -
theorem
forecastCost_nonneg -
theorem
forecastCost_pos_off_unit -
def
PredictabilityThreshold -
def
IsPastHorizon -
def
IsWithinHorizon -
theorem
horizon_states_exclusive -
theorem
predictability_threshold_band -
structure
ClimatePredictabilityCert -
def
climatePredictabilityCert