current_vectorC_attempt_data
plain-language theorem explainer
The declaration packages three properties of the zero defect for complex ρ: vanishing exactly on the critical line, nonnegativity of the doubled defect, and the explicit recurrence relating doubled defect to the square of the original defect. Researchers examining the Riemann hypothesis via the Recognition Science functional equation and J-symmetry would cite this as the strongest current Vector C data point. The proof is a one-line term that assembles the three upstream lemmas on the defect and its doubled form.
Claim. For any complex number $ρ$, let $D(ρ)$ be the zero defect and $D_2(ρ)$ the doubled zero defect. Then $(D(ρ)=0 ↔ Re(ρ)=1/2) ∧ 0 ≤ D_2(ρ) ∧ D_2(ρ)=2D(ρ)^2 + 4D(ρ)$.
background
The Zero Doubling Law module records the strongest concrete Vector C instantiation obtained from the functional-equation/J-symmetry bridge. The zero defect is the Recognition Science defect of exp(zero deviation of ρ), which is zero precisely when Re(ρ)=1/2. The doubled zero defect is the J-log applied to twice the zero deviation, serving as the virtual next-step observable suggested by FE reflection plus RCL self-composition.
proof idea
The proof is a one-line term-mode wrapper that directly assembles the equivalence from zeroDefect_zero_iff_on_critical_line, the nonnegativity from doubledZeroDefect_nonneg, and the recurrence from doubledZeroDefect_recurrence.
why it matters
This packages the strongest currently instantiated Vector C data from the functional-equation/J-symmetry bridge. It supplies concrete evidence for the doubling recurrence on the defect observable, linking to the Recognition Composition Law and the J-uniqueness step in the forcing chain. No downstream uses are recorded, leaving open whether this advances to the full d'Alembert interface.
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