{
  "schema_version": 1,
  "problem_number": "OWR-14298803-004",
  "title": "Uniformly Accurate EDMD Generators Can Give Unbounded Auxiliary Optima",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We construct noiseless data for which extended dynamic mode decomposition (EDMD) converges uniformly to the true generator on a fixed polynomial auxiliary space, while the associated unregularized auxiliary optimum is minus infinity instead of 1. For dx/dt = -x^5 on [-1,1], we use quadratic auxiliaries and a degree-six dictionary. The regression has full column rank. The theorem holds for every N >= 9 Chebyshev-node design and, almost surely, for all sufficiently large iid datasets from the full-support arcsine measure. A uniform negative-derivative certificate holds for every 0 < tau <= 2^(-26), while the operator error is bounded by 156 tau in the stated coefficient norm. Adding the valid constraint U >= 0 makes the approximate value finite but still incorrect. The qualitative strict-feasibility obstruction is known from Bramburger and Fantuzzi; this note gives an actual exact-flow realization and elementary regularization bounds. It does not close the general optimal-value error-estimation problem or contradict prior convergence theorems. This is an unrefereed, AI-assisted preprint without an absolute priority claim.",
  "result_type": "COMPLETE_COUNTEREXAMPLE",
  "categories": [
    "math.DS",
    "math.OC",
    "math.NA"
  ],
  "keywords": [
    "OWR-14298803-004",
    "EDMD",
    "auxiliary functions",
    "ergodic optimization",
    "strict feasibility"
  ],
  "manuscript_version_date": "2026-10-25",
  "publication_date": "2026-10-25",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-25",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-14298803-004/",
  "pdf_url": "https://eulersolve.org/papers/owr-14298803-004/paper.pdf?v=3e3e76a1e497",
  "doi": "10.5281/zenodo.23627738",
  "zenodo_record_url": "https://zenodo.org/records/23627738",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "For the exact flow of dx/dt=-x^5 on [-1,1], quadratic auxiliaries and a degree-six least-squares dictionary, population arcsine EDMD, every N>=9 Chebyshev-node design, and almost surely all sufficiently large iid arcsine designs have uniform generator error at most 156*tau in the quotient coefficient norm but auxiliary optimum minus infinity rather than 1, for every 0<tau<=2^-26. A valid U>=0 constraint gives approximate value 0. The original quantitative N,m,tau research program remains open. This is a complete fixed-dictionary exact-flow counterexample; the qualitative instability warning is prior work, credited to Bramburger and Fantuzzi. This preprint is AI-assisted, self-audited and unrefereed; no independent or formal verification or certified novelty or absolute-priority claim is made.",
  "files": {
    "paper.pdf": {
      "sha256": "3e3e76a1e49792e083b621f3227f889d3b13a5120255f3ef1376154e3c56d6e1"
    },
    "source.zip": {
      "sha256": "0f45a614818c3eb04ffb1a5a653e22e6af29268341a3e7f6e125207b2403f0a7"
    },
    "verification_report.md": {
      "sha256": "6537608be376af156c163bd917d49b5552d33801c5d3dda611aaf742ce80f014"
    }
  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}