geoengineeringCert
plain-language theorem explainer
The declaration constructs a certificate asserting exactly five canonical geoengineering approaches whose safe-deployment band contains the canonical J(φ) point at 0.118. Climate modelers working within the Recognition framework would cite this to confirm the configDim=5 setting matches the J-cost ladder. The definition is a direct record construction that assembles the three required fields from sibling theorems.
Claim. Let GeoengineeringCert be the structure requiring that the set of geoengineering approaches has cardinality 5, that the safe-deployment band is nondegenerate, and that the band contains the point 0.118 corresponding to the J(φ) value. The definition supplies the concrete instance satisfying these three conditions.
background
The module treats geoengineering as five canonical approaches (SAI, MCB, OIF, CDR, CC) whose risk profiles sit on a recognition J-cost ladder. The safe-deployment threshold is the canonical J(φ) band on the perturbation ratio, taken as the open interval (0.11, 0.13). The structure GeoengineeringCert packages three assertions: the set of approaches has exactly five elements, the band lower bound is strictly below the upper bound, and the interval brackets the numerical value 0.118.
proof idea
The definition is a direct record constructor. It assigns the cardinality field to the theorem that computes the number of approaches as 5 by decision, the nondegeneracy field to the theorem that unfolds the band bounds and applies norm_num, and the containment field to the theorem that likewise unfolds the bounds and confirms the numerical bracketing by norm_num.
why it matters
This definition supplies the concrete certificate required by the Recognition Science treatment of climate geoengineering under configDim = 5. It closes the module by exhibiting an instance of the GeoengineeringCert structure whose safe band aligns with the canonical J(φ) interval. No downstream uses are recorded, but it supports any higher-level claim that the five approaches lie within the safe J-cost window.
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