{
  "schema_version": 1,
  "problem_number": "AMR-021-0016",
  "title": "A Finite Moment-Cone Criterion for Derivative-Root Configurations",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We give a necessary and sufficient finite criterion for prescribed numerical positions of all derivative roots of a real-rooted polynomial-like function. Polynomial-like degree n means that the nth derivative is nowhere zero; the function need not be an ordinary polynomial of degree n. Eliminating integration constants produces m=n(n-1)/2 explicit piecewise polynomial Peano kernels. Realizability is equivalent to zero being interior to their essential-trace convex hull, and to representing an explicit baseline vector by at most m nonnegative trace terms. This gives a finite semialgebraic criterion and a terminating decision procedure for algebraic coordinates. Permitted cross-order coincidences are included. Every feasible array also has an ordinary-polynomial realization of unspecified larger degree.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.CA",
    "math.NA"
  ],
  "keywords": [
    "AMR-021-0016"
  ],
  "manuscript_version_date": "2026-09-30",
  "publication_date": "2026-09-30",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-09-30",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/amr-021-0016/",
  "pdf_url": "https://eulersolve.org/papers/amr-021-0016/paper.pdf?v=09647f7982e9",
  "doi": "10.5281/zenodo.23054600",
  "zenodo_record_url": "https://zenodo.org/records/23054600",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete criterion for source-defined polynomial-like derivative-root positions, not symbolic-order classification or ordinary degree-n root rows. Classical moment and interpolation precedents are credited. Whether this application is already-known remains uncertain; an inaccessible jet-specific1979 source is retained as an overlap risk. No independent human review, formal certificate or absolute priority claim. Self-audited and unrefereed, with AI assistance; no independent human peer review or absolute priority is claimed.",
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      "sha256": "09647f7982e908dc434085e0d7f49ee6cc5a954250bee805d5c8934cbb6587ce"
    },
    "source.zip": {
      "sha256": "45e8f5688f25a97cc4fc2d8d22234b4c5f318ccfbb271e379d96effd37ffe45c"
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    "verification_report.md": {
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  },
  "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."
}