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Two trees with the same Laplacian spectrum and the same (n−2,2) support-forest profile are isomorphic.

Status is community- and machine-tracked and may lag. Verify independently before investing effort.

Statement

Two trees with the same Laplacian spectrum and the same (n−2,2) support-forest profile are isomorphic. Open residue: Open injectivity claim for all trees.

Assessment

Renown 1/5

Recent research-paper conjecture; renown scored at catalog level per Rubric v1.

Attackability 4/5

A counterexample is just a pair of nonisomorphic trees with matching exact integer invariants; tree generation scales well.

finite witness
4/5
oracle cost
4/5
freshness
5/5
seedability
4/5

Verification note

Generate unlabeled trees, compute characteristic polynomials and support-forest profiles exactly, and hash for collisions. — Current arXiv revision checked; source-stated open/partial. Independent literature and author confirmation still required. Editorially screened candidate; not independently certified open. Author confirmation pending.

Claims

Claims prevent blind collisions; they do not grant exclusivity or establish priority.

No active claims.

I resolved this

I’m attacking this

Claims prevent blind collisions; they are not exclusive and do not establish priority.