{
  "abstract": "Rumor models of the Daley--Kendall and Maki--Thompson family anchor the statistical mechanics of social contagion, yet the stifler composition a rumor leaves behind has resisted closed-form analysis. Inspired by the asymmetric two-step pairing (A2SP) process of step-growth polymerization, we import its common-factor cancellation into a minimal two-stage MT variant in which re-contacted spreaders are re-activated into a senior class at rate $αk_1$ rather than stifled, and obtain exact terminal-state theorems. (i) Saturation: the rumor exhausts the ignorant pool for every stifling-to-recruitment ratio $μ>0$, with a three-way tail classification and a logarithmically critical line at $μ=1$. (ii) Final size: the terminal stifler pool splits as $(x_1,x_2)=(μ/(α+μ),α/(α+μ))$, independent of seed size; the fingerprint inverts linearly ($α=μx_2/x_1$) and matches Gillespie simulations within $0.95\\%$. (iii) Pooled versus history-resolved: pooled statistics are exactly $α$-free on any static graph; only the history-resolved composition carries $α$. Restoring the classic teller-retires channel breaks the exact closure beyond quantified gates (contact rates of $1$--$3\\%$ of $k_1$ for spreader channels at $μ\\leq1.5$, up to $32\\%$ at $μ=2$), and on configuration-model networks the composition bias decays as $\\langle k\\rangle^{-0.71}$. An exploratory inversion of 354,930 Higgs--Twitter retweet episodes, screened by an identity check and four negative controls, yields $\\hatα=2.21\\%$ (joint cluster-bootstrap CI $[1.6\\%,3.0\\%]$; $\\approx3.7\\%$ after calibration at the matched threshold). Terminal compositions identify this effective re-activation rate, an upper bound on contact-coupled re-activation; the mechanism itself requires timing information beyond the terminal state.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41206",
  "author_total": 1,
  "authors": [
    {
      "name": "Qingquan Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4nx1gwwkyck9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41206",
  "fulltext_url": null,
  "id": "b4nx1gwwkyck9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41206",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.soc-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41206",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4nx1gwwkyck9.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.41206",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41206"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Terminal-state theorems for a two-stage Maki--Thompson rumor model: final size, stifler composition, and non-identifiability from pooled statistics",
  "title_text": "Terminal-state theorems for a two-stage Maki--Thompson rumor model: final size, stifler composition, and non-identifiability from pooled statistics",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/b4nx1gwwkyck9",
  "venue": "arXiv",
  "versions": []
}