{
  "abstract": "We study what noisy data can justify before a manifold and its intrinsic dimension are assumed. For repeated observations with independent isotropic Gaussian errors of unknown variance, we compose a support confidence event with a sound geometric verifier to certify a nearby smooth witness of arbitrary compact latent support. Whole-support inference requires an external lower mass condition; independent validation instead certifies proximity of probability mass. Separate all-scale hypotheses yield true-support structure and dimension recovery: a credited Reifenberg--Dini criterion and positive continuous density give local $C^1$ structure and consistent dimension estimation, while two-sided Ahlfors regularity and positive reach give quantitative covariance separation under the stated sampling and observation-transfer conditions. An exact-arithmetic implementation verifies restricted witness families. A further matrix check certifies linear coordinates on a geometrically verified affine span containing the witness and propagates approximation and decoding errors. This restricted construction neither implements the general minimal-dimension Whitney theorem nor infers exact manifold support from finite approximation. Executed torus and Julia-set experiments test the observation-to-witness-to-coordinate route, including singular-support controls. Dynamical systems and chaos are the primary application context; state-identification and finite-horizon prediction results are conditional on observation embeddings and transition validation. Takens reconstruction is an optional scalar-delay application requiring additional smoothness, dynamics and observable conditions. Image comparisons are auxiliary reconstruction diagnostics. The finite-data verifier establishes neither those dynamical conditions nor the all-scale geometric premises for true-dimension recovery.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21311",
  "author_total": 1,
  "authors": [
    {
      "name": "U Jin Choi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4md37gqz1vb46.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21311",
  "fulltext_url": null,
  "id": "4md37gqz1vb46",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21311",
  "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.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7213877782",
  "pdf_url": "https://arxiv.org/pdf/2609.21311",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4md37gqz1vb46.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2609.21311",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21311"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Manifold Hypothesis: Conditional Certificates and Consistent Intrinsic Dimension Estimation",
  "title_text": "Manifold Hypothesis: Conditional Certificates and Consistent Intrinsic Dimension Estimation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/4md37gqz1vb46",
  "venue": "arXiv",
  "versions": []
}