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