{
  "abstract": "The Sombor index SO(𝐺) = ∑𝑢𝑣∈𝐸 √𝑑2𝑢 + 𝑑2𝑣is a distinguished member of the family of edge-additive degree-based topological indices. We study what happens to SO when an edge is deleted. Summed over all edges, the deletions obey the exact identity ∑𝑒 SO(𝐺 − 𝑒) = (𝑚 − 1) SO(𝐺) − 𝐶(𝐺) with a single correction term — an edge-additive index with an irrational kernel, which we call the Sombor deletion correction term 𝐶 . The paper develops the theory of 𝐶 along three axes. Structure (Sections 2–3): 𝐶 is a linear functional of the edge-type counts, with sharp two-sided bounds against Zagreb-type polynomials and a star-maximisation theorem with full equality characterisation, closed forms for regular graphs and products, and non-expressibility certificates against (𝑛,𝑚,𝑀1,𝑀2, 𝐹 , SO), the degree sequence, and small spectra. Exact algebra of the drops (Section 4): the per-edge drops Δ𝑒 = SO(𝐺) − SO(𝐺 − 𝑒) lie in a fixed multiquadratic field, a normal-form procedure decides their equalities exactly, and an exhaustive computation classifies all coincidences up to degree bound 8 — cross-type coincidences form exactly two families (based on √ 20 and √ 52), within-type coincidences are governed by a diagonal-union theorem and telescoping identities, and the all-degree classification is conjectural. Deck information (Sections 5–7): over all 288,266 graphs on 𝑛 ≤ 9 vertices and all 89,402 chemical graphs on ten vertices, the Sombor deck and the edge-type deck induce the same partition (53,984 classes); 𝐶 is injective modulo matching components on both ranges, but fails in general: an explicit collision with value 20 √ 2 − 4 √ 5 is constructed. On the 18 octane isomers 𝐶 separates 16 structures and raises a boiling-point regression from 𝑅2 = 0.559 (SO alone) to 0.814 (with 𝐶), an exploratory signal. All claims are proved, exhaustively verified, or machine-checked in Lean 4 (Section 8).",
  "abstract_shown": true,
  "affiliations": [
    "Faculty of Chemistry",
    "Shenzhen MSU-BIT University"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Junyi Gong",
      "orcid": "0000-0001-7592-7132"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/awgwng53t4d49.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15009571/v1",
  "fulltext_url": null,
  "id": "awgwng53t4d49",
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  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009571/v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7214655617",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15009571/v1",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/awgwng53t4d49.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "10.26434/chemrxiv.15009571",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009571/v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Graph theory and applications",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Sombor deletion correction term: extremal structure, exact coincidence classification, and the information content of edge decks, with applications to chemistry",
  "title_text": "The Sombor deletion correction term: extremal structure, exact coincidence classification, and the information content of edge decks, with applications to chemistry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:21Z",
  "url": "https://research.draconitic.com/paper/awgwng53t4d49",
  "venue": "ChemRxiv",
  "versions": []
}