pith. sign in
module module high

IndisputableMonolith.NumberTheory.DefectSampledTrace

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DefectSampledTrace supplies the sampled annular mesh construction for defect phase families. It converts each family into an AnnularMesh by evaluating at the canonical 8n equispaced angles per ring. Researchers closing the cost-covering bridge for the Riemann hypothesis cite this to obtain explicit defect data for budget comparisons. The module consists entirely of definitions.

claimThe module defines the annular mesh obtained from a defect phase family by sampling each ring at the $8n$ equispaced angles $ heta_k = 2 rac{ heta}{n} k$ for $k=0, o,8n-1$.

background

AnnularCost supplies the $\phi$-weighted cost $ ext{phiCost } u := ext{cosh}(( ext{log }\phi) ext{·}u)-1 = J( ext{phi}^u)$. CostCoveringBridge organizes the three-layer architecture that makes the RS cost-covering realizable after the budget interface. MeromorphicCircleOrder supplies the local factorization $f(z)=(z- ho)^n g(z)$ for a meromorphic function of order $n$ at $ ho$.

The module lies in the NumberTheory domain and realizes the defect side of annular sampling by turning abstract phase families into concrete meshes at the eight-tick octave angles.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The construction supplies the defect sampled trace data required by ArgumentPrincipleProved to eliminate the argument_principle_sampling axiom. It also supports CarrierBudgetComparison by providing the defect topological floor on the same circles used for carrier bounds, and feeds EulerInstantiation together with HonestPhaseBudgetBridge for phase-family realizations. It fills the concrete sampling step inside the RS cost-covering bridge.

scope and limits

used by (4)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (3)

Lean names referenced from this declaration's body.

declarations in this module (25)