safeBand_nondegenerate
plain-language theorem explainer
The theorem establishes that the lower bound of the safe-deployment ratio band is strictly less than its upper bound. Climate researchers applying Recognition Science to geoengineering risk profiles would cite this to confirm the J(φ) band forms a proper interval. The proof is a one-line wrapper that unfolds the two constant definitions and reduces the numerical comparison.
Claim. The safe-deployment ratio band satisfies $0.11 < 0.13$.
background
The module treats five canonical geoengineering approaches (SAI, MCB, OIF, CDR, CC) as instances of configDim = 5. Each approach is assigned a risk profile on the J-cost ladder, and safe deployment requires the perturbation ratio to lie inside the canonical J(φ) band. The module sets this band explicitly to the numerical interval (0.11, 0.13). Upstream definitions supply the concrete constants 0.11 for the lower endpoint and 0.13 for the upper endpoint.
proof idea
The proof is a one-line wrapper. It unfolds the definitions of the lower and upper bounds, then applies norm_num to discharge the resulting numerical inequality.
why it matters
The result supplies the band_well_defined field inside geoengineeringCert, which certifies the five approaches under the safe band. It closes the non-degeneracy requirement for the J(φ) band in the climate module, ensuring the safe-deployment threshold is a proper interval. The construction aligns with the Recognition Science forcing chain in which J-uniqueness and the phi fixed point fix the numerical band.
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