{
  "schema_version": 1,
  "problem_number": "OWR-14224-004",
  "title": "Brooms Can Be Easier than Stars in Tree-Flow Least Squares",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For Gaussian denoising of nonnegative leaking flows, consider least squares over the full flow cone, with a fixed bound on the true root flow. We construct an N-vertex broom whose worst-case normalized risk is O(sqrt(log N)/N), while the N-vertex rooted star has risk Omega(log N/N) already at the zero signal. The ratio of the two worst-case risks tends to zero. Thus the star is not the easiest tree for this estimator when logarithmic factors are retained. The proof combines a deterministic cone-projection identity with an elementary bound for the maximum of Gaussian leaf noise. For context, we also reconstruct the known parallel-arm obstruction to the path being hardest, using a nonnegative witness. The comparisons concern the full-cone estimator, not a budget-constrained projection or minimax risk over all estimators. This is an AI-assisted, self-audited, unrefereed preprint; no absolute priority claim is made.",
  "result_type": "COMPLETE_COUNTEREXAMPLE",
  "categories": [
    "math.ST",
    "stat.ME"
  ],
  "keywords": [
    "OWR-14224-004",
    "math.ST",
    "stat.ME"
  ],
  "manuscript_version_date": "2026-10-21",
  "publication_date": "2026-10-23",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-23",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-14224-004/",
  "pdf_url": "https://eulersolve.org/papers/owr-14224-004/paper.pdf?v=0a3f803b02be",
  "doi": "10.5281/zenodo.23514783",
  "zenodo_record_url": "https://zenodo.org/records/23514783",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "For fixed V,sigma>0 and the full-cone least-squares estimator, equal-size broom trees have worst-case normalized risk O(sqrt(log N)/N), whereas stars have risk Omega(log N/N). Thus the star is not easiest when logarithmic factors are retained. The path endpoint is answered by an attributed reconstruction of Chatterjee and Lafferty's known obstruction. No minimax, fixed-budget projection or global tree ranking is claimed. This is a self-audited, AI-assisted, unrefereed preprint. No independent certification, formal proof verification or absolute-priority claim is made.",
  "files": {
    "paper.pdf": {
      "sha256": "0a3f803b02be1050168b40eacbcba82f881f6af36c3cd64ffae1b1fe926d12dc"
    },
    "source.zip": {
      "sha256": "d7335dea6657e738f57d3b55fdd402e401013c61dc965112c457d47bfcef3af0"
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    "verification_report.md": {
      "sha256": "2f42db984e32db27ef824e4568a2fb388c4a05fcd7120f6731242c271fb38668"
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  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}