carbonRemovalPathway_count
plain-language theorem explainer
The declaration proves that the carbon removal pathway type has cardinality five. Climate modelers in the Recognition Science framework cite this result when fixing the dimension of removal options in configDim calculations. The proof is a one-line decision procedure that exhausts the finite type via its derived Fintype instance.
Claim. The finite type enumerating the five canonical carbon removal pathways has cardinality five: $|C| = 5$, where $C$ is the inductive type with constructors afforestation, soilCarbon, biochar, directAirCapture, and enhancedWeathering.
background
The module Carbon Removal Pathways from configDim fixes five canonical carbon-dioxide-removal pathways for configDim equal to five. These are afforestation, soil carbon, biochar, direct air capture, and enhanced weathering, covering biological uptake, soil storage, stable biomass, engineered capture, and mineral sequestration. The upstream inductive definition lists exactly these five cases and derives DecidableEq together with Fintype, supplying the instance required for cardinality computation.
proof idea
The proof is a one-line wrapper that applies the decide tactic. The tactic succeeds because the inductive type derives both DecidableEq and Fintype, permitting exhaustive enumeration of the five constructors without further lemmas.
why it matters
This cardinality result supplies the five_pathways field to the downstream carbonRemovalCert definition. It anchors the E4/B17 climate depth section by fixing the number of removal options inside the Recognition framework. The count aligns with the configDim parameter used in broader climate calculations.
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