trureturingGitHub MATHEMATICAL ATLAS

Geometry / CONCEPT

General cost probability transport

General cost probability transport

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH3
DOCUMENT LINKS0
THEOREM

Symmetry of coupling cost

RELATIONSHIP ATLAS

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Direct recorded relationships
Finite Attainment for Extended Linear ProgramsFinite Attainment for ExtendedLinear ProgramsGeneral cost probability transportGeneral cost probabilitytransportFiniteMartingaleCouplingFiniteMartingaleCoupling
Proof dependencyStructural affinityDocument link

Certified topology / UPSTREAM

Prerequisites

Certified topology / DOWNSTREAM

Consequences

RELATED KNOWLEDGE

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Documents & exposition

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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
3
Layer
D5/S3
Domain
Geometry
Node ID
D5/S3/Geometry/ProbabilityTransport/CostCoupling
Repository path
D5/S3/Geometry/ProbabilityTransport/CostCoupling.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.