oceanographyCert
plain-language theorem explainer
The oceanographyCert definition assembles a certificate confirming exactly five canonical ocean layers by assigning the decidable cardinality result to the structure field. Researchers modeling thermohaline circulation or surface waves in the Recognition Science framework would reference this to align the ocean decomposition with configDim equal to 5. The construction is a direct one-line wrapper that invokes the oceanLayerCount theorem without additional reasoning steps.
Claim. Let OceanLayer be the finite type of canonical ocean layers. The structure OceanographyCert requires that its cardinality equals 5. The definition oceanographyCert supplies an instance of this structure by setting the five_layers field to the theorem establishing |OceanLayer| = 5.
background
The module states that five canonical ocean layers (surface, thermocline, intermediate, deep, abyssal) equal configDim D = 5. In RS, ocean depth follows the phi-ladder of recognition density, surface wave periods lie in the 5-10 s range approximating 5φ/φ, and thermohaline circulation has 5 canonical gyres matching the same dimension. The upstream oceanLayerCount theorem proves Fintype.card OceanLayer = 5 by decision procedure. OceanographyCert is the structure type whose single field encodes this cardinality equality.
proof idea
The definition is a one-line wrapper that applies the oceanLayerCount theorem to populate the five_layers field of the OceanographyCert structure.
why it matters
This definition supplies the concrete certificate for the five-layer ocean model in RS Earth science applications. It directly implements the claim from the module documentation that five ocean layers equal configDim D = 5, linking to the phi-ladder for recognition density. No downstream uses are recorded, leaving it available for integration into larger geophysical models or wave propagation theorems.
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