trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Even looped paths allow the non-symmetric Strong Spectral Property

Exact-support witnesses for every positive even double path and every nonempty loop set.

Closed Authored exposition
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH9
DOCUMENT LINKS0
THEOREM

The complete all-orders and all-loop-sets event

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Even double paths with a nonempty loop setEven double paths with anonempty loop setA simple-spectrum Gibbs-stochastic matrix for every positive vectorA simple-spectrum Gibbs-stochastic matrix for everypositive vectorEven looped paths allow the non-symmetric Strong Spectral PropertyEven looped paths allow thenon-symmetric Strong SpectralProperty
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Certified topology / DOWNSTREAM

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None recorded in this release.

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Lean sourceResearch workspace
Status
Closed
Depth
9
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/SpectralGraph/KoljancicOblakEvenPathNSSP
Repository path
D5/S3/Combinatorics/SpectralGraph/KoljancicOblakEvenPathNSSP.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.