PredictabilityThreshold
plain-language theorem explainer
PredictabilityThreshold sets the climate forecast horizon cutoff to the J-cost of the golden ratio φ. Climate dynamicists cite it to locate the sharp transition where initial-condition uncertainty growth renders deterministic skill structurally impossible. The declaration is a direct one-line assignment to Cost.Jcost phi.
Claim. The predictability threshold is defined by $τ := J(φ)$, where $J$ denotes the recognition cost function and $φ$ is the golden ratio.
background
In Recognition Science the J-cost of a positive ratio x is given by $J(x) = (x + x^{-1})/2 - 1$. The module applies this cost to the uncertainty growth ratio r = σ_forecast / σ_initial of a chaotic system, marking the lead time at which J(r) reaches the canonical quantum J(φ). Upstream, the cost of any recognition event is defined as Jcost of its state, and the multiplicative recognizer induces a derived cost on positive ratios.
proof idea
One-line definition that directly assigns the threshold to Cost.Jcost phi.
why it matters
The definition supplies the numerical anchor for ClimatePredictabilityCert, IsPastHorizon and IsWithinHorizon. It embeds climate predictability inside the universal RS band 0.11 < J(φ) < 0.13, the same quantum that gates plaque vulnerability, combustion ignition and magnetic reconnection, consistent with T5 J-uniqueness and T6 forcing of φ as self-similar fixed point.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.