{
  "abstract": "Continuing \\cite{NWX} and Part I \\cite{AOSI}, we further investigate symmetry for spacetime observability of wave equations. Building on asymptotic observable symmetry (AOS) introduced in \\cite{AOSI}, we study symmetry under glancing propagation and caustics. We prove that, on every smooth bounded domain in $\\R^2$ and for every positive observation time, there is a fixed measurable set satisfying the essential spacetime measurable geometric control condition. However, the observability inequality fails on this set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35610",
  "author_total": 2,
  "authors": [
    {
      "name": "Jingrui Niu"
    },
    {
      "name": "Shengquan Xiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/arv9b3f0qrg8e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35610",
  "fulltext_url": null,
  "id": "arv9b3f0qrg8e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35610",
  "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.AP"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7223892734",
  "pdf_url": "https://arxiv.org/pdf/2610.35610",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/arv9b3f0qrg8e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35610",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35610"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains",
  "title_text": "Asymptotic observable symmetry for spacetime observability of waves II: Smooth bounded domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/arv9b3f0qrg8e",
  "venue": "arXiv",
  "versions": []
}