trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Directed all-minors matrix-tree identity

Signed directed spanning forests compute every ascending complementary minor over an arbitrary commutative ring.

Closed Authored exposition
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES1
PROOF DEPTH0
DOCUMENT LINKS1
THEOREM

The complete signed complementary-minor identity

RELATIONSHIP ATLAS

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Direct recorded relationships
Directed all-minors matrix-tree identityDirected all-minors matrix-treeidentityDirected forest gluing signsDirected forest gluing signs
Proof dependencyStructural affinityDocument link

Certified topology / UPSTREAM

Prerequisites

None recorded in this release.

Certified topology / DOWNSTREAM

Consequences

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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
0
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/Graph/DirectedAllMinorsMatrixTree
Repository path
D5/S3/Combinatorics/Graph/DirectedAllMinorsMatrixTree.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.