{
  "abstract": "Classical continuous-time non-linear filtering fails in generic non-linear state spaces due to an infinite Lie algebraic derivative explosion ($\\dim(\\mathcal{E}) = \\infty$), leading to filter divergence. To resolve this four-decade crisis, we introduce the SMG-Yau-Yau filter and lossless data assimilation framework built on Statistical Fiber Theory over an Orlicz manifold $\\mathcal{M}$. By equipping $\\mathcal{M}$ with a Riemannian submersion and an Ehresmann connection, the unconstrained Duncan-Mortensen-Zakai score velocity field is orthogonally decomposed into Statistically Verifiable Directions ($\\text{SVD}χ_f$) and Structural Internal Directions ($\\text{SID}_f$). System non-linearities and unclosed Lie commutators are orthogonally quarantined in $\\text{SID}_f$, protecting macroscopic base parameters from spatial derivative pollution while preserving total score variance energy. We unify the asymptotics through a Dual-Axis Collapse Mechanism: proving our model identically recovers classical Yau-Yau dynamics when $\\dim(\\mathcal{E}) < \\infty$, while large-sample limits ($N \\to \\infty$) induce a thermodynamic quench that flattens infinite-dimensional geometry under $\\dim(\\mathcal{E}) = \\infty$. Finally, we formulate the Active Acausal Tension (AAT) functional to monitor accumulated model misspecification online. Exceeding a topological capacity threshold triggers Gauge Symmetry Breaking (GSB), which dynamically expands base coordinates ($d \\to d+1$) to ensure non-asymptotic stability and convergence to the exact state density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28062",
  "author_total": 4,
  "authors": [
    {
      "name": "Bing Cheng"
    },
    {
      "name": "Yi-Shuai Niu"
    },
    {
      "name": "Howell Tong"
    },
    {
      "name": "Shing-Tung Yau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9pb0hhnd3vda.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28062",
  "fulltext_url": null,
  "id": "e9pb0hhnd3vda",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28062",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "1702|Target Tracking and Data Fusion in Sensor Networks"
    ]
  ],
  "openalex": "W7214158208",
  "pdf_url": "https://arxiv.org/pdf/2609.28062",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9pb0hhnd3vda.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:06Z",
      "native_id": "2609.28062",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28062"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "The SMG-Yau-Yau Filter and Lossless Data Assimilation: Resolving Infinite Lie Algebras via Statistical Fiber Theory",
  "title_text": "The SMG-Yau-Yau Filter and Lossless Data Assimilation: Resolving Infinite Lie Algebras via Statistical Fiber Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/e9pb0hhnd3vda",
  "venue": "arXiv",
  "versions": []
}