pith. machine review for the scientific record. sign in
inductive definition def or abbrev high

GridStabilityControl

show as:
view Lean formalization →

Recognition Science encodes grid stability controls as an inductive type with five constructors corresponding to inertia, primary frequency response, voltage support, demand response, and storage dispatch. Energy systems modelers cite this enumeration to fix configDim at five. The inductive declaration automatically provides decidable equality and finite type structure for subsequent cardinality proofs.

claimLet $C$ be the inductive type of grid stability controls generated by the constructors inertia, primary frequency response, voltage support, demand response, and storage dispatch.

background

The module on Grid Stability Controls from configDim posits that electric grid stability is achieved through exactly five canonical controls when the configuration dimension equals five. These controls correspond to rotational buffering via inertia, fast governor response via primary frequency response, reactive power management via voltage support, load-side control via demand response, and temporal energy shifting via storage dispatch. This enumeration supports the Recognition Science derivation of physical systems from the forcing chain and phi-ladder structures.

proof idea

The declaration is a direct inductive definition that lists the five constructors and derives DecidableEq, Repr, BEq, and Fintype.

why it matters in Recognition Science

The type feeds the cardinality theorem gridStabilityControl_count establishing five controls and the certification structure GridStabilityControlsCert. It realizes the energy depth of the framework by specifying the control space dimension as five, consistent with the configDim parameter in the model. The declaration closes the enumeration without open scaffolding.

scope and limits

formal statement (Lean)

  19inductive GridStabilityControl where
  20  | inertia
  21  | primaryFrequencyResponse
  22  | voltageSupport
  23  | demandResponse
  24  | storageDispatch
  25  deriving DecidableEq, Repr, BEq, Fintype
  26

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.