riemann_hypothesis_conditional
plain-language theorem explainer
The theorem shows that if a cost-covering package ensures the defect topological floor is covered for every sensor, then the Riemann zeta function has no zeros with real part exceeding 1/2. Number theorists studying conditional proofs of the Riemann hypothesis would cite this result as the final step linking Recognition Science carrier budgets to the critical line. The proof is a one-line term application of the main rh_from_cost_covering theorem to the universal covering hypothesis.
Claim. Let $pkg$ be a cost-covering package. If for every defect sensor the annular topological floor is bounded above by the carrier budget scale, then for any defect sensor with nonzero charge a contradiction follows. Equivalently, every non-trivial zero of the Riemann zeta function satisfies Re$(s)=1/2$.
background
CostCoveringPackage is an explicit structure containing a BudgetedCarrier witness for the realized carrier trace and its annular excess budget. DefectSensor records a potential zero location with integer charge (multiplicity of the zero of zeta) and realPart strictly between 1/2 and 1. DefectTopologicalFloorCovered pkg sensor asserts that for all N the annularTopologicalFloor N (sensor.charge) is at most the carrierBudgetScale of pkg.carrier. The module sets up the RS cost-covering bridge after the budget interface is realized, with the carrier C(s) holomorphic and nonvanishing on Re(s)>1/2 and annular excess O(R^2). Upstream, rh_from_cost_covering supplies the core implication that a covered defect sensor with nonzero charge yields False.
proof idea
The proof is a one-line term wrapper. It takes an arbitrary sensor and the hypothesis that its charge is nonzero, then directly applies rh_from_cost_covering to the supplied package, that sensor, the nonzero-charge fact, and the covering predicate instantiated at the given sensor.
why it matters
This corollary completes the conditional Riemann hypothesis result inside the RS cost-covering architecture. It feeds the statement that all non-trivial zeros lie on Re(s)=1/2 once the covering assumption holds for every sensor. The parent theorem rh_from_cost_covering already excludes zeros with Re(s)>1/2; symmetry via the functional equation then forces the critical line. In the Recognition framework the result closes the number-theoretic bridge that begins with phi-cost bounds and the annular carrier trace, leaving open only whether the cost-covering hypothesis itself holds unconditionally.
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