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inductive definition def or abbrev high

GWSourceClass

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GWSourceClass enumerates the five canonical gravitational wave source types fixed by configuration dimension five. Researchers simulating LIGO-Virgo or LISA data would reference this partition to assign distinct frequency bands and waveform templates to each population. The declaration is an inductive type whose five constructors automatically inherit decidable equality and finite cardinality via the derived instances.

claimLet $S$ be the set of gravitational wave source classes. Then $S$ consists of the five elements compact binary inspiral-merger-ringdown, core-collapse supernova, continuous emission from rotating neutron stars, stochastic background, and memory effect, equipped with decidable equality and finite cardinality.

background

The module fixes configuration dimension at five to produce exactly five gravitational wave source classes. These are compact binary inspiral-merger-ringdown, core-collapse supernova, continuous emission from rotating neutron stars, stochastic background, and memory effect. Each class is stated to occupy a distinct frequency interval ranging from millihertz scales accessible to LISA down to kilohertz scales observed by LIGO. The definition requires no imported lemmas and carries zero axioms or sorry markers.

proof idea

The declaration is a direct inductive definition that introduces five constructors. The Fintype, DecidableEq, Repr, and BEq instances are obtained automatically by the Lean compiler with no explicit proof body or tactic steps.

why it matters in Recognition Science

This enumeration supplies the finite set whose cardinality is certified as five by the downstream theorem gwSourceClass_count. It directly implements the module claim that gravitational wave sources are partitioned into five classes when configDim equals five. The structure is used by GWSourcesCert to record the cardinality fact as a certificate. Within the Recognition Science framework it anchors the mapping from abstract configuration dimension to concrete astrophysical source populations.

scope and limits

formal statement (Lean)

  18inductive GWSourceClass where
  19  | compactBinary
  20  | coreCollapse
  21  | continuous
  22  | stochasticBackground
  23  | memory
  24  deriving DecidableEq, Repr, BEq, Fintype
  25

used by (2)

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