{
  "schema_version": 1,
  "problem_number": "AIM-ANALYSIS-0055",
  "title": "Exact Degrees for a Fixed-Double-Pole Rational Hénon Family",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We give an all-parameter degree calculation for the birational maps F(x,y)=(beta/x+gamma/x^2-delta*y,x) over the complex numbers, with gamma*delta nonzero. Outside the nontrivial root-of-unity resonances of -delta^3, the first dynamical degree is 2. At a resonance of order ell, two explicit rational generating functions describe the pure inverse-square and mixed cases, with the usual QRT exception at delta=1. The proof counts all finite zero/pole patterns and the boundary contributions on generic coordinate lines. In the mixed case an analytic product chart justifies repeated cancellations, including linearly growing singularity multiplicities that nevertheless yield the same degree series as constant-multiplicity patterns. Classical degree sequences and delayed-confinement polynomials are explicitly credited. The result concerns this fixed-double-pole family, not the full AIM investigation of quadratic rational Henon maps. This is a self-audited, AI-assisted, unrefereed preprint; no independent review, formal verification or absolute priority is claimed.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.DS",
    "math.AG"
  ],
  "keywords": [
    "rational Henon map",
    "dynamical degree",
    "algebraic entropy",
    "singularity confinement",
    "birational surface map",
    "root-of-unity resonance",
    "degree growth"
  ],
  "manuscript_version_date": "2026-10-11",
  "publication_date": "2026-10-11",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-11",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-analysis-0055/",
  "pdf_url": "https://eulersolve.org/papers/aim-analysis-0055/paper.pdf?v=80f79d06c2ef",
  "doi": "10.5281/zenodo.23289384",
  "zenodo_record_url": "https://zenodo.org/records/23289384",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "The fixed-double-pole all-parameter theorem is proved. The general AIM investigation of arbitrary quadratic rational Henon maps remains partial. Classical sequences and delayed-confinement polynomials are credited, not claimed new. Self-audited and unrefereed; no independent review, formal verification or certified priority.",
  "files": {
    "paper.pdf": {
      "sha256": "80f79d06c2ef2583f7887ce125ce81949da673570f4caa5f9ce2a2bb796e18d8"
    },
    "source.zip": {
      "sha256": "d6775ac97a0a64b46ef8ed317f64059a0ea4b996d0ba305693c2aed0415d77ee"
    },
    "verification_report.md": {
      "sha256": "a5eb8a28339c37e8b8e0f53c5ec06c5c1813c91a873ffbf0302a95725309167d"
    }
  },
  "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."
}