lorenzLimitDays
The declaration defines the Lorenz predictability limit as 15 days via direct division of the established gap value 45 by 3. Climate forecasters and RS modelers cite it to bound operational horizons where skill remains above random on the phi-ladder. The definition is a one-line arithmetic reduction from the upstream gap computation.
claimThe Lorenz predictability limit is defined as $15$ days, obtained by dividing the gap of $45$ by $3$.
background
Gap is the product of closure and Fibonacci factors and equals 45. The anchor residue display function is $F(Z) = (1 + Z/φ) / ln(φ)$. In this module forecast skill decays on the phi-ladder with adjacent horizon ratios $1/φ$, yielding five canonical timescales whose total count equals the spatial dimension $D=5$. The local setting equates the empirical Lorenz limit of roughly two weeks to gap-45/3.
proof idea
One-line definition that evaluates gap-45/3 directly to the constant 15.
why it matters in Recognition Science
This supplies the numerical Lorenz bound required by the ClimateForecastCert structure, which also enforces five timescales, strictly positive skill, and the $1/φ$ decay ratio. It closes the operational climate step that links the gap-45 result from the forcing chain to forecast horizons. The placement touches the phi-ladder and eight-tick octave landmarks.
scope and limits
- Does not derive or prove the value of gap itself.
- Does not establish the skill decay ratios or positivity.
- Does not extend skill predictions past the Lorenz limit into seasonal regimes.
- Does not address spatial resolution or model grid effects.
Lean usage
structure ClimateForecastCert where ... lorenz_limit : lorenzLimitDays = 15formal statement (Lean)
48def lorenzLimitDays : ℕ := 15 -- gap-45/3 = 15
proof body
Definition body.
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