rh_from_single_axiom
plain-language theorem explainer
The theorem derives a contradiction from any DefectSensor with nonzero charge whose annular cost satisfies the deprecated boundedness condition. Analytic number theorists tracing the argument-principle route to the Riemann hypothesis would cite it as an intermediate reduction step. The proof is a one-line exact application of the complex-analysis-axioms lemma.
Claim. Let $s$ be a defect sensor with charge $c$ satisfying $c ≠ 0$. If the annular cost of $s$ is bounded under the deprecated definition, then a contradiction follows.
background
The module eliminates the argument_principle_sampling axiom by exhibiting uniformChargeMesh constructions that satisfy the required charge condition by definition. Relevant upstream notions include AnnularMesh from CostCoveringBridge, DefectPhaseFamily built via CirclePhaseLift and MeromorphicCircleOrder, and the quantitative factorization supplied by EulerInstantiation. The local setting distinguishes the trivial route (constant-phase scaffolds) from the honest route that extracts genuine phase data from meromorphic_phase_charge on concentric circles.
proof idea
The proof is a one-line term-mode wrapper that applies rh_from_complex_analysis_axioms directly to the given sensor, the charge non-equality hypothesis, and the deprecated bounded-cost hypothesis.
why it matters
This declaration supplies an intermediate step feeding direct_rh_from_zero_free_criterion in AnalyticTrace and honest_argument_principle_phase_family within the same module. It closes the legacy analytic route that begins from EulerInstantiation and CostCoveringBridge, while the module documentation explicitly marks the result deprecated in favor of UnifiedRH.unified_rh or the honest phase-family bridge. It touches the open question of obtaining a zero-free criterion from witnessed zeta reciprocal phase data without invoking the inconsistent cost bound.
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