{
  "abstract": "Exploiting the equality restrictions that nested Markov models encode requires their tangent-space geometry. For strictly positive finite-state models on arbitrary acyclic directed mixed graphs (ADMGs), we differentiate the recursive-head chart and prove that the range of its score map is the full tangent space. Intrinsic-set coordinate blocks form an algebraic direct sum, blocks of distinct districts are orthogonal, and the resulting Gram projection needs neither mb-shieldedness nor a district order. Exact counterexamples show that observational centering and kernel normalization alone do not certify tangency. For the node, complete-source edge, and compatible path-specific intervention targets considered here, boundary substitution yields a normalized configured active law and an order-free canonical-gradient formula, extended to finite mixtures by independent source redraws. A coherent one-step estimator with an exact remainder identity and a model-valid chart-flow targeted maximum likelihood estimator are efficient under stated local conditions. On a narrower source-isolated fixed-node subclass, a sequential estimator has an exact transition-factorized drift and up to $2^m$ nuisance-correctness regimes over $m$ active-district transitions; its all-correct influence function projects onto the canonical gradient, and an exact rational law exhibits a strict variance gap. These results separate order-free efficiency on arbitrary finite-state ADMGs from multiple robustness of a narrower construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17939",
  "author_total": 1,
  "authors": [
    {
      "name": "Haoyu Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ktcbgk1vmhqb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17939",
  "fulltext_url": null,
  "id": "6ktcbgk1vmhqb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17939",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "econ.EM"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.17939",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ktcbgk1vmhqb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17939",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17939"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Recursive-Head Geometry and Order-Free Efficient Inference in Finite-State Nested Markov Models",
  "title_text": "Recursive-Head Geometry and Order-Free Efficient Inference in Finite-State Nested Markov Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/6ktcbgk1vmhqb",
  "venue": "arXiv",
  "versions": []
}