trureturingGitHub MATHEMATICAL ATLAS

Weil / CONCEPT

Cosine-Modulated Packet

A normalized convolution-square Weil packet has positive transform near zero, and cosine modulation gives uniform prime control and finite-side decay.

Closed Authored exposition
DIRECT PREREQUISITES7
DIRECT CONSEQUENCES2
PROOF DEPTH17
DOCUMENT LINKS1
THEOREM

The seed is normalized at zero

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Fourier: Fourier Laplace EntireFourier: Fourier Laplace EntireWeil: Prime Pole TermsWeil: Prime Pole TermsConvolution-Square PositivityConvolution-Square PositivityFourier-Laplace Closed-Strip DecayFourier-Laplace Closed-StripDecayWeil: Classic Explicit FormulaWeil: Classic Explicit FormulaWeil: Explicit Formula BridgeWeil: Explicit Formula BridgeWeil: Zero SummabilityWeil: Zero SummabilityCosine-Modulated PacketCosine-Modulated PacketExplicit-Formula Obstruction to a Finite Zero CarrierExplicit-Formula Obstruction toa Finite Zero CarrierA Nontrivial Zero in Every Fixed-Width WindowA Nontrivial Zero in EveryFixed-Width Window
Proof dependencyStructural affinityDocument link

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Lean sourceResearch workspace
Status
Closed
Depth
17
Layer
D5/S3
Domain
Weil
Node ID
D5/S3/Weil/ZeroInfinitude/CosinePacket
Repository path
D5/S3/Weil/ZeroInfinitude/CosinePacket.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.