complexDim
plain-language theorem explainer
Recognition Science defines the complex plane dimension as 2 to equal D-1 at D=3. Researchers certifying links between complex analysis and the RS framework cite this when counting five canonical theorems against configDim D=5. The entry is a direct constant assignment with no computation or lemmas.
Claim. The dimension of the complex plane is defined to be $2$, which equals $D-1$ for $D=3$ spatial dimensions.
background
The module treats complex numbers as recognition phase space (amplitude times phase), with $|ψ|^2 = J(|ψ|/|ψ_0|)$ as the recognition cost of amplitude. Five canonical theorems (Cauchy, residue, Riemann mapping, Liouville, maximum modulus) correspond to configDim D=5, while complex numbers equal ℝ² and thus supply the 2-dimensional count D-1 when D=3. Each |ℂ| corresponds to a face of Q₃.
proof idea
Direct definition that assigns the natural number 2.
why it matters
The definition is referenced inside ComplexAnalysisCert (complex_dim : complexDim = 3-1) and by the theorem complexDim_eq_Dm1. It supplies the concrete value required by the module's statement that complex numbers are ℝ² at D=3, consistent with T8 forcing of three spatial dimensions and the assignment of five theorems to configDim D=5.
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