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

syntaxUniversalsCert

show as:
view Lean formalization →

The declaration assembles a certificate structure asserting that phrase categories and syntactic roles each number exactly five. Linguists modeling universal grammar from Recognition Science would cite it to link syntactic universals to the five-dimensional configuration space. The definition is a direct constructor that supplies the two fields from prior cardinality theorems.

claimLet $C$ be the certificate structure with fields $C.5phrases$ and $C.5roles$. Then $|PhraseCategory| = 5$ and $|SyntacticRole| = 5$.

background

The module derives syntactic universals from configDim equal to 5, which forces the five core phrase structure categories (NP, VP, AP, PP, AdvP) as the 5-dimensional recognition taxonomy of the D=3 lattice. This setting treats syntactic categories as forced by the underlying spatial dimension rather than as arbitrary linguistic primitives.

proof idea

The definition is a direct constructor that supplies the two fields of SyntaxUniversalsCert by referencing the theorems phraseCategoryCount and syntacticRoleCount.

why it matters in Recognition Science

This definition packages the cardinality claims that realize the syntactic universals forced by configDim D=5. It supports the module's goal of deriving Chomsky-style principles from the five-dimensional taxonomy of the D=3 lattice. No downstream uses appear yet, leaving open its integration with broader linguistic derivations in the monolith.

scope and limits

formal statement (Lean)

  35def syntaxUniversalsCert : SyntaxUniversalsCert where
  36  five_phrases := phraseCategoryCount

proof body

Definition body.

  37  five_roles := syntacticRoleCount
  38
  39end IndisputableMonolith.Linguistics.SyntaxUniversalsFromConfigDim

depends on (3)

Lean names referenced from this declaration's body.