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Certificates / CONCEPT

Exact Rational Linear Objective Certificates

Exact rational primal and dual witnesses certify finite linear objective bounds and endpoint optimality.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES5
PROOF DEPTH1
DOCUMENT LINKS0
THEOREM

A rational upper dual certificate proves a universal bound

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Direct recorded relationships
Exact Rational Farkas CertificatesExact Rational FarkasCertificatesExact Rational Linear Objective CertificatesExact Rational Linear ObjectiveCertificatesRational support elimination certificatesRational support eliminationcertificatesRationalSTCutCertificateRationalSTCutCertificateFinite Linear Causal IdentificationFinite Linear CausalIdentificationCanonical Causal Response SignaturesCanonical Causal ResponseSignaturesMarkovian Response-Law FactorizationMarkovian Response-LawFactorization
Proof dependencyStructural affinityDocument link

RELATED KNOWLEDGE

Structural connections

Documents & exposition

None recorded in this release.

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None recorded in this release.

LIBRARY / RELEASE VERSIONS

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Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
1
Layer
D5/S0
Domain
Certificates
Node ID
D5/S0/Certificates/LinearObjectiveDual
Repository path
D5/S0/Certificates/LinearObjectiveDual.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

Authority boundary

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.