{
  "abstract": "We study how a higher-rank classical collective order parameter can select one dominant projective eigenline and, in a $p=2$ realization, support a dynamically autonomous low-energy director sector. In a fully connected projective-rotor model, the collective second moment is a positive semidefinite tensor $T$ of fixed trace. Conventional projective ordering drives its effective rank toward one, selecting a single dominant eigenline. Rank polarization alone, however, does not determine dynamical autonomy: extrinsic-curvature criteria depend on the chosen state-space metric, and the equilibrium tensor does not determine the transverse free-energy Hessian. A two-harmonic model makes this logical independence explicit by producing families with identical $T$ and $r_{\\rm eff}$ but different transverse quadratic forms. We then construct rotationally invariant locking interactions that leave a prescribed ordered tensor exactly fixed while increasing every non-Goldstone restoring coefficient as $Θ(λ)$ within a globally controlled stable regime. For a phenomenological inertial realization with a finite positive kinetic matrix, the lowest transverse normal-mode frequency grows as $Θ(λ^{1/2})$; more generally, the low-frequency transverse susceptibility is suppressed as $O(λ^{-1})$, including in overdamped dynamics. The construction therefore proves that spectral selection and infrared transverse suppression are independent data. For $p>2$ the selected eigenline has a $(p-1)$-dimensional director manifold; the one-dimensional Goldstone sector used in the dynamical construction is specific to $p=2$. Promoting the selected internal eigenline to a physical clock requires additional soldering and integrability structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15361",
  "author_total": 2,
  "authors": [
    {
      "name": "Shannon Wang"
    },
    {
      "name": "David Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6jhrbcd7gnetz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15361",
  "fulltext_url": null,
  "id": "6jhrbcd7gnetz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15361",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7221807388",
  "pdf_url": "https://arxiv.org/pdf/2610.15361",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6jhrbcd7gnetz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.15361",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15361"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Rank polarization and dynamical autonomy in a projective rotor model",
  "title_text": "Rank polarization and dynamical autonomy in a projective rotor model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/6jhrbcd7gnetz",
  "venue": "arXiv",
  "versions": []
}