Explain the Lean theorem `pureVectorCDoublingData_not_enough_for_critical_line` in module `IndisputableMonolith.NumberTheory.VectorCSymmetryOnlyNoGo`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

(1) In plain English, pureVectorCDoublingData_not_enough_for_critical_line asserts that symmetry data alone does not force every zero onto the critical line: it is false that for all completed-ξ surfaces Ξ and all ρ, if PureVectorCDoublingData Ξ ρ holds then OnCriticalLine ρ holds.

(2) In Recognition Science this is a Vector C stage gate. It shows that functional-equation reflection, conjugation symmetry, and the current FE/RCL doubling recurrence are insufficient to derive the critical-line property; extra analytic input (e.g., Euler/Hadamard side) is required.

(3) The formal statement is the negation ¬(∀ (Ξ : CompletedXiSurface) (ρ : ℂ), PureVectorCDoublingData Ξ ρ → OnCriticalLine ρ). The proof assumes the universal claim, instantiates it on the offline toy example, and obtains a contradiction with the known off-critical zero.

(4) Visible dependencies in the supplied source are pureVectorCDoublingData_offline_example, toyCompletedXiSurface_has_off_critical_zero, pureVectorCDoublingData_of_zero, and the structure PureVectorCDoublingData; the module also defines toyXi and toyCompletedXiSurface.

(5) The declaration does not prove that the critical line holds for actual zeta zeros, does not supply the missing analytic input, and does not address the full Riemann Hypothesis.