{
  "abstract": "Interacting populations increasingly respond to compressed representations generated from their own collective state. We ask which information such an endogenous coarse-graining must preserve in order to reproduce the collective dynamics. The question has two complementary answers for continuous opinions with attraction, indifference, and repulsion. Inside any strict $K$-bloc response cell where every represented stance attracts every bloc, the dynamics reduce exactly to translation and disagreement. The represented distribution's shape cancels from all disagreement modes, which form a homogeneously anchored weighted signed-Laplacian system, while represented-mean error acts only on translation. This reduction yields a geometry-dependent stability boundary and shows that prevalence bias produces secular drift at marginal stability only through its projection onto the neutral eigenspace. Outside that common linear-response regime, threshold geometry makes distributional information observable. The induced force discrepancy is a behavior-defined integral probability metric; restricted force probes identify generic finite empirical discussions, and for finitely supported candidates uniform force error controls total-variation and Wasserstein error while support reduction incurs a nonzero distortion floor. A cumulative-discrepancy characterization further explains why transport-small summaries can remain behaviorally inaccurate at response thresholds. Mode-resolved integrations, projected particle simulations, finite-size ensembles, and threshold-crossing experiments test these two regimes. As a deployment consequence, broadcast summary error survives as collective noise whereas independently personalized error self-averages. The model is stylized and not empirically calibrated; generated discussion summaries motivate the general problem of endogenous, response-aware coarse-graining.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05560",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruben E. Araújo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3sqxnykwkfgtm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05560",
  "fulltext_url": null,
  "id": "3sqxnykwkfgtm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05560",
  "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",
      "physics.soc-ph"
    ],
    [
      "openalex",
      "3109|Opinion Dynamics and Social Influence"
    ]
  ],
  "openalex": "W7212033294",
  "pdf_url": "https://arxiv.org/pdf/2609.05560",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3sqxnykwkfgtm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.05560",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05560"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Response-Aware Coarse-Graining in Summary-Mediated Opinion Dynamics",
  "title_text": "Response-Aware Coarse-Graining in Summary-Mediated Opinion Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/3sqxnykwkfgtm",
  "venue": "arXiv",
  "versions": []
}