{
  "abstract": "Sensory adaptation provides a concrete setting in which low-order system identification can fail qualitatively. We show that one fixed higher-order adaptive system composed entirely of real first-order relaxation modes can be reduced to opposite sides of the second-order pole boundary: low-frequency moment matching gives $ρ_{\\rm moment}=4.50$, whereas finite-window fitting gives $ρ_{\\rm window}=3.31$, and the inferred pole class changes further with sampling protocol. Thus the real-versus-complex classification of a reduced model is not itself reduction invariant. We then use the general two-state spectrum to connect stochastic identifiability to adaptation: for nontrivial coupling and one-state observation, cross diffusion drops out of the scalar spectrum when the hidden state has no self-relaxation. In the adaptive model, this condition is precisely the integral-memory limit that produces exact adaptation, while leaky memory restores spectral sensitivity. For the exact-adaptation model, the Gaussian path-space irreversibility nevertheless depends on the hidden cross-diffusion channel. Hence $\\{H,S_x\\}$ does not determine the irreversibility rate. Independently, for a specified all-even reduced two-state drift with $ρ<4$, the drift-only lower bound is $σ\\ge τ_x^{-1}(4/ρ-1)$. Published \\textit{E.~coli} and \\textit{C.~elegans} responses provide biological examples of these limits. The distinction established here between transfer-function invariants, reduction-dependent properties, and hidden-state quantities provides a concrete framework for evaluating the limitations of low-dimensional models of adaptive biological dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01329",
  "author_total": 1,
  "authors": [
    {
      "name": "Gunn Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3qj3bfz2n68q9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01329",
  "fulltext_url": null,
  "id": "3qj3bfz2n68q9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01329",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "physics.bio-ph"
    ],
    [
      "openalex",
      "2207|Control Systems and Identification"
    ]
  ],
  "openalex": "W7206153942",
  "pdf_url": "https://arxiv.org/pdf/2609.01329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3qj3bfz2n68q9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.01329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01329"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.bio-ph",
      "subfield": "biological-medical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Pole-Zero Geometry, Model Reduction, and Identifiability in Sensory Adaptation",
  "title_text": "Pole-Zero Geometry, Model Reduction, and Identifiability in Sensory Adaptation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/3qj3bfz2n68q9",
  "venue": "arXiv",
  "versions": []
}