GridStabilityControlsCert
The structure certifies that the enumerated set of grid stability controls has cardinality exactly five. Energy systems analysts cite it to anchor the configuration dimension at five when modeling inertia, primary frequency response, voltage support, demand response, and storage dispatch. The declaration is introduced as a bare structure that directly records the cardinality fact supplied by the inductive enumeration.
claimLet $C$ denote the finite set whose elements are inertia, primary frequency response, voltage support, demand response, and storage dispatch. A certificate is the structure asserting that the cardinality of $C$ equals five.
background
The module fixes five canonical electric-grid stability controls and equates them to configuration dimension five. These comprise rotational inertia, fast governor response, reactive power support, load-side demand response, and temporal storage dispatch. The upstream inductive definition enumerates precisely these five cases and derives the Fintype instance used for the cardinality statement.
proof idea
The declaration is a direct structure definition whose single field records the cardinality equality. No lemmas or tactics are invoked; the fact follows immediately from the inductive enumeration of the five controls.
why it matters in Recognition Science
This definition supplies the fixed count of five that the downstream certificate construction consumes. It anchors the energy-systems layer of the Recognition framework by setting configDim to five, matching the module's explicit span of rotational, fast, reactive, load, and temporal controls. No open questions or further scaffolding are addressed.
scope and limits
- Does not derive the five controls from the Recognition Composition Law or forcing chain steps.
- Does not verify dynamical stability of the grid under these controls.
- Does not admit additional control mechanisms beyond the enumerated five.
- Does not relate the count five to spatial dimension or other framework constants.
formal statement (Lean)
30structure GridStabilityControlsCert where
31 five_controls : Fintype.card GridStabilityControl = 5
32