CostCoveringPackage
The CostCoveringPackage structure supplies an explicit BudgetedCarrier witness for the RS cost-covering bridge. Number theorists deriving conditional forms of the Riemann Hypothesis from Recognition Science cost bounds would cite it to replace an earlier axiomatic assumption with a concrete carrier trace. The definition is a one-field structure that directly packages the realized carrier and its annular excess budget.
claimA CostCoveringPackage consists of a single field carrier of type BudgetedCarrier, where the budgeted carrier encodes a realized carrier trace C(s) together with its annular excess budget that controls the defect topological floor.
background
The module packages the RS cost-covering architecture for the Riemann Hypothesis once the budget interface is made realizable. It comprises three layers: unconditional annular bounds and topological floor analysis from AnnularCost.lean, the explicit carrier package defined here, and the conditional theorem that follows. BudgetedCarrier is imported from AnnularCost and represents a carrier equipped with a finite scale that bounds annular excess above the topological floor. The carrier itself is given by C(s) = det₂(I−A(s))² = ∏_p (1−p^{−s})² exp(2p^{−s}), which remains holomorphic and nonvanishing for Re(s) > 1/2. Upstream, the defect functional from LawOfExistence.defect equals J(x) for positive x and supplies the cost measure whose topological floor must be covered.
proof idea
This is a structure definition consisting of a single field of type BudgetedCarrier. No tactics or lemmas are applied; the declaration directly packages the carrier witness as required by the module architecture for downstream conditional results.
why it matters in Recognition Science
The structure supplies the concrete carrier package that CostCoveringCert and rh_from_cost_covering consume to obtain the conditional statement that ζ(s) has no zeros with Re(s) > 1/2. It replaces the former naked axiom and corresponds to the second layer of the module architecture. In the Recognition framework it closes the cost-covering bottleneck that forces multiplicity m = 0 for any hypothetical off-line zero, linking the carrier scale to the defect functional and the phi-ladder bounds established upstream.
scope and limits
- Does not prove existence of any BudgetedCarrier that satisfies the covering condition.
- Does not derive unconditional bounds on annular excess or topological floor.
- Does not address zero-charge sensors or the unconditional Riemann Hypothesis.
- Does not specify the concrete functional form of the carrier beyond the BudgetedCarrier type.
formal statement (Lean)
118structure CostCoveringPackage where
119 carrier : BudgetedCarrier
120
121/-- The remaining topological step in the RH bridge: the defect topological
122floor must be controlled by the same carrier scale. -/
used by (11)
-
eulerSampledCoveringPackage -
CostCoveringCert -
DefectTopologicalFloorCovered -
not_DefectTopologicalFloorCovered -
rh_from_cost_covering -
riemann_hypothesis_conditional -
eulerCostCoveringPackage -
euler_rh_conditional -
eulerSampledBudgetedCarrier_scale_zero -
eulerSampledPackage -
riemann_hypothesis_euler_conditional