{
  "abstract": "We prove a restricted reconstruction theorem for proper trees: if their weighted skeleton has all vertex weights in one congruence class modulo some integer at least two, at least two uniquely occurring weights, and an independent set of all repeated-weight vertices, equality of the first power-sum derivative of the chromatic symmetric function for proper-tree competitors implies isomorphism.\n\nAn explicit two-edge Gram decoder and acyclic neighborhood reconstruction yield the result. The theorem depends on cited results in Saad A. Awan, arXiv:2609.13464. It does not resolve Stanley’s unrestricted conjecture. Independent human peer review and historical priority are not certified.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Casey Atwell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/amczq8sgfxavz.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23627747",
  "fulltext_url": null,
  "id": "amczq8sgfxavz",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23627747",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23627747/files/01_Stanley_Manuscript_v1.3.1.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/amczq8sgfxavz.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:20:34Z",
      "native_id": "23627747",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23627747"
    }
  ],
  "subjects": [],
  "title": "Congruence-Class Gram Reconstruction for Proper Trees: Multiple Repeated-Weight Classes Without a Common-Divisor Hypothesis",
  "title_text": "Congruence-Class Gram Reconstruction for Proper Trees: Multiple Repeated-Weight Classes Without a Common-Divisor Hypothesis",
  "type": "preprint",
  "updated_at": "2026-11-07T12:20:34Z",
  "url": "https://research.draconitic.com/paper/amczq8sgfxavz",
  "venue": "Zenodo",
  "versions": []
}