module module moderate

`IndisputableMonolith.Climate.PredictabilityFromJCost`

This module defines forecast J-cost on the uncertainty growth ratio together with horizon predicates and a predictability certificate for climate applications in Recognition Science. Researchers applying RS to climate modeling would cite the forecastCost construction and its elementary properties. The module imports Cost and Constants then supplies direct definitions plus basic lemmas on non-negativity and symmetry.

claimLet $r$ be the uncertainty growth ratio. Define forecastCost$(r) := J(r)$ where $J$ is the J-cost. Introduce predicates IsPastHorizon, IsWithinHorizon, PredictabilityThreshold and the certificate ClimatePredictabilityCert.

background

Recognition Science obtains all physics from a single functional equation whose cost function J satisfies the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). The imported Constants module fixes the RS-native time quantum τ₀ = 1 tick. The imported Cost module supplies the J-cost primitive used here to forecast uncertainty growth in the climate domain.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the core objects ClimatePredictabilityCert and forecastCost that certify predictability within horizons using J-cost forecasts. It extends the general Cost framework into the climate domain and prepares the ground for downstream applications of the eight-tick octave and phi-ladder mass formulas.

scope and limits

Does not compute numerical climate forecasts.
Does not incorporate external observational data.
Does not address specific variables such as temperature.
Does not extend the J-cost formalism beyond uncertainty ratios.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (12)

def forecastCost L38
theorem forecastCost_zero_at_unit L40
theorem forecastCost_reciprocal_symm L42
theorem forecastCost_nonneg L45
theorem forecastCost_pos_off_unit L48
def PredictabilityThreshold L52
def IsPastHorizon L55
def IsWithinHorizon L58
theorem horizon_states_exclusive L60
theorem predictability_threshold_band L65
structure ClimatePredictabilityCert L81
def climatePredictabilityCert L92