trureturingGitHub MATHEMATICAL ATLAS

Analytic / CONCEPT

The Sharp Threshold for Positive Prime Evidence

Prime-indexed positive evidence is summable exactly above exponent one.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES8
PROOF DEPTH1
DOCUMENT LINKS1
THEOREM

Every prime contributes positive evidence

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Direct recorded relationships
The Zeta Distribution as an Integer Gibbs MeasureThe Zeta Distribution as anInteger Gibbs MeasureThe Sharp Threshold for Positive Prime EvidenceThe Sharp Threshold forPositive Prime EvidencePrime Precision Marginal GainPrime Precision Marginal GainLocal Evidence Order Determines the Critical ExponentLocal Evidence Order Determinesthe Critical ExponentPrime Density Does Not Determine Evidence SummabilityPrime Density Does NotDetermine Evidence SummabilityEvidence Budget Is a Sum, Not a Coordinate CountEvidence Budget Is a Sum, Not aCoordinate CountGlobal Code Length AdditivityGlobal Code Length AdditivityMultiplicative Complexity as a Random Activation PatternMultiplicative Complexity as aRandom Activation PatternMoments of the Distinct Prime-Factor CountMoments of the Distinct Prime-Factor CountPrime-Time Gramian Energy IdentityPrime-Time Gramian EnergyIdentity
Proof dependencyStructural affinityDocument link

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LIBRARY / RELEASE VERSIONS

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Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
1
Layer
D5/S3
Domain
Analytic
Node ID
D5/S3/Analytic/ZetaEntropyPlane/PrimeEvidenceSharpThreshold
Repository path
D5/S3/Analytic/ZetaEntropyPlane/PrimeEvidenceSharpThreshold.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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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.