ComplexTheoremRS
plain-language theorem explainer
Recognition Science maps five canonical theorems of complex analysis to configuration dimension D=5. A researcher deriving complex analysis from the recognition functional equation would cite the enumeration when linking those theorems to the two-dimensional complex plane at spatial dimension D=3. The declaration is a direct inductive construction that introduces the five cases and derives the standard type-class instances.
Claim. Let $T$ be the finite type whose elements are the five canonical theorems of complex analysis: Cauchy's integral theorem, the residue theorem, the Riemann mapping theorem, Liouville's theorem, and the maximum modulus principle.
background
Complex numbers are treated as recognition phase space (amplitude times phase), with squared modulus equal to the J-cost of the amplitude ratio. The module states that these five theorems correspond to configDim D=5 while the complex plane itself is two-dimensional, hence equal to D-1 when spatial dimension D=3. The upstream liouville definition supplies the arithmetic function λ(n)=(-1)^Ω(n), though the enumeration here simply names the corresponding complex-analysis theorem.
proof idea
Direct inductive definition with five constructors; no lemmas or tactics are applied.
why it matters
The definition supplies the finite type whose cardinality is asserted equal to five inside the downstream ComplexAnalysisCert structure, which also records complex dimension equal to D-1. It fills the complex-analysis slot in the RS derivation at the point where D=3 forces the complex plane to be two-dimensional. The module doc-comment records zero sorry and zero axiom for this component.
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