IndisputableMonolith.NumberTheory.CostCoveringBridge
The CostCoveringBridge module supplies uniform charged ring samples in which every increment carries an identical phase step, forcing the total winding to equal exactly m. Researchers closing the Riemann Hypothesis via the Recognition Science analytic trace cite it when comparing annular carrier costs to diverging defect topological floors. The module organizes this through a set of sampling definitions and direct cost equalities that link phi-weighted J-cost to topological covering.
claimA uniform charged ring sample is a discretization of the circle in which each arc increment advances the phase by a fixed step, so that the net winding number is precisely the integer $m$.
background
This module sits in the NumberTheory domain and imports the RS time quantum from Constants, the general cost framework from Cost, and the annular machinery from AnnularCost. AnnularCost defines the core object phiCost u := cosh((log φ)·u) − 1 = J(φ^u), the φ-weighted cost function used for ring sampling. These pieces establish the cost-covering bridge that connects carrier budgets to defect topological floors in the analysis of functions such as zeta.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the parent results in AnalyticTrace, ArgumentPrincipleProved, CarrierBudgetComparison, ContourWinding, DefectSampledTrace, EulerInstantiation, MeromorphicCircleOrder, and SampledTrace. It supplies the uniform sampling layer required for the carrier-defect budget comparison in Phase 4a of the RH closure plan, enabling witnessed contradictions for nonzero charge and the removal of earlier axioms in the analytic trace infrastructure.
scope and limits
- Does not prove the Riemann Hypothesis itself.
- Does not compute explicit numerical values for any zeta zeros.
- Does not treat non-uniform charge distributions on the ring.
- Does not address the continuous limit of the discrete samples.
- Does not connect directly to the forcing chain steps T5-T8 or spatial dimension D=3.
used by (8)
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IndisputableMonolith.NumberTheory.AnalyticTrace -
IndisputableMonolith.NumberTheory.ArgumentPrincipleProved -
IndisputableMonolith.NumberTheory.CarrierBudgetComparison -
IndisputableMonolith.NumberTheory.ContourWinding -
IndisputableMonolith.NumberTheory.DefectSampledTrace -
IndisputableMonolith.NumberTheory.EulerInstantiation -
IndisputableMonolith.NumberTheory.MeromorphicCircleOrder -
IndisputableMonolith.NumberTheory.SampledTrace
depends on (3)
declarations in this module (15)
-
def
uniformRingSample -
def
uniformChargeMesh -
structure
EulerCarrier -
def
zetaCarrier -
structure
DefectSensor -
structure
CostCoveringPackage -
def
DefectTopologicalFloorCovered -
theorem
uniformRingSample_cost_eq_topologicalFloor -
theorem
uniformChargeMesh_excess_zero -
theorem
defect_cost_unbounded -
theorem
defect_topological_floor_unbounded -
theorem
not_DefectTopologicalFloorCovered -
theorem
rh_from_cost_covering -
theorem
riemann_hypothesis_conditional -
structure
CostCoveringCert