safeBandLower
safeBandLower supplies the numerical lower edge 0.11 for the safe-deployment ratio band in the Recognition Science treatment of geoengineering. Climate researchers working with the five canonical approaches under configDim = 5 cite this constant to anchor the J-cost perturbation threshold. The definition is a direct constant assignment chosen to match the canonical J(φ) band lower edge.
claimThe lower edge of the safe-deployment ratio band is defined as $0.11$.
background
The module treats five canonical geoengineering approaches under configDim = 5: stratospheric aerosol injection, marine cloud brightening, ocean iron fertilisation, carbon dioxide removal and cirrus cloud thinning. Each approach carries a risk profile measured on the recognition J-cost ladder. The safe-deployment threshold is fixed to the canonical J(φ) band interval (0.11, 0.13) on the perturbation ratio.
proof idea
This is a direct definition that assigns the real number 0.11. No lemmas or tactics are applied; the value is set by constant assignment to match the lower edge of the J(φ) band.
why it matters in Recognition Science
The constant anchors the band_well_defined and band_inhabited fields inside the GeoengineeringCert structure. It implements the safe-deployment threshold stated in the module documentation as matching the canonical J(φ) band. Downstream theorems safeBand_nondegenerate and safeBand_contains_phi_point rely on it to verify the interval contains the phi point 0.118 and remains nondegenerate. The placement connects to the J-uniqueness property and the phi fixed point in the forcing chain.
scope and limits
- Does not derive the numerical value 0.11 from the J-cost functional equation inside this module.
- Does not specify physical units or scaling conventions for the perturbation ratio.
- Does not address sensitivity of the band to variations in climate model parameters.
- Does not prove invariance of the band under changes to configDim.
Lean usage
theorem band_lower_bound : safeBandLower < 0.118 := (safeBand_contains_phi_point).1formal statement (Lean)
36noncomputable def safeBandLower : ℝ := 0.11