{
  "abstract": "We recover a shared constitutive generator from equilibrium locations on weighted graphs. For an even $C^2$ log-coordinate potential with positive curvature, the complete two-site response map determines the generator up to positive scale. A sweep over all positive boundary values at one fixed, possibly unknown, unequal weight ratio gives global identification through a Schröder-Koenigs iteration. We extend this result to a three-vertex chain with two observed free vertices under a sweep condition. For variable-ratio control, we prove finite-target recovery, local Lipschitz stability, and noisy-bisection bounds. Fixed-ratio stability and nonparametric estimation under uncertain controls remain open. In the reciprocal family $J_p$, an exact Gaussian model-selection probability benchmarks synthetic experiments under observation noise and errors in variables. These are identifiability results under controls; no measured data or physical system is analyzed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30146",
  "author_total": 2,
  "authors": [
    {
      "name": "Jonathan Washburn"
    },
    {
      "name": "Megan Simons"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fa8shjf8pdf90.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30146",
  "fulltext_url": null,
  "id": "fa8shjf8pdf90",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30146",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223373920",
  "pdf_url": "https://arxiv.org/pdf/2610.30146",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fa8shjf8pdf90.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.30146",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30146"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Uniqueness and reconstruction of reciprocal constitutive generators from equilibrium response maps",
  "title_text": "Uniqueness and reconstruction of reciprocal constitutive generators from equilibrium response maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fa8shjf8pdf90",
  "venue": "arXiv",
  "versions": []
}