trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Actual Path Families Retain the Same Cycle Inventory

An actual path family covering each vertex once earns the full support and retained-edge inventories of the same Hamilton cycle.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH1
DOCUMENT LINKS0
THEOREM

Vertex Ownership Eliminates Repeated Edges

RELATIONSHIP ATLAS

Every connection, in context.

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Direct recorded relationships
Cutting Actual Graph Walks into PathsCutting Actual Graph Walks intoPathsActual Path Families Retain the Same Cycle InventoryActual Path Families Retain theSame Cycle InventoryActual Native Half PartitionsActual Native Half PartitionsSame-Cycle Native Joint ComponentsSame-Cycle Native JointComponents
Proof dependencyStructural affinityDocument link

RELATED KNOWLEDGE

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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
Combinatorics
Node ID
D5/S3/Combinatorics/Graph/Walks/ActualPathFamilyInventory
Repository path
D5/S3/Combinatorics/Graph/Walks/ActualPathFamilyInventory.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.