{
  "schemaVersion": "1.0",
  "slug": "when-polynomials-cannot-hide",
  "title": "When polynomials cannot hide the difference",
  "url": "https://evidencepress.org/articles/when-polynomials-cannot-hide/",
  "standfirst": "A short argument from complex dynamics offers a general answer to Furter's rigidity problem—and changes which calculations are worth doing next.",
  "summary": "A popular explanation of the candidate polynomial-composition rigidity proof, its critical-value argument, and what it does and does not settle for seven Evidence Press releases.",
  "datePublished": "2026-09-12",
  "dateModified": "2026-09-12",
  "articleClass": "commentary",
  "status": "published",
  "byline": "Evidence Press",
  "bylineType": "organization",
  "banner": {
    "src": "/assets/articles/rigidity-curves.svg",
    "alt": "An ivory identity line and a gold polynomial curve meet near the centre, then separate against a dark teal grid.",
    "caption": "The identity and z − 2z³ + z⁴ on a real slice near zero. Their matching low-order terms conceal a cubic difference. This illustration is not a picture of complex attracting basins."
  },
  "audio": {
    "src": "/assets/audio/when-polynomials-cannot-hide.mp3",
    "transcript": "/assets/audio/when-polynomials-cannot-hide.txt",
    "provenance": "/assets/audio/when-polynomials-cannot-hide.provenance.json",
    "durationSeconds": 506.28,
    "voiceLabel": "OpenAI API synthetic voice (fable)"
  },
  "topics": [
    "polynomials",
    "complex dynamics",
    "Furter rigidity",
    "polydegree conjecture",
    "mathematical explanation"
  ],
  "readingMinutes": 6,
  "wordCount": 1253,
  "newResearchClaims": false,
  "claimBoundary": "AI-assisted explanation of liqsweep's external unrefereed candidate at source commit b17b6b9. Internal mathematical source review found no load-bearing gap in the central argument; formal verification, unaffiliated specialist review and priority have not been established. Consequences depend on that argument and the cited prior theorems. This article is not a new Evidence Press research result or an independent verification.",
  "sources": [
    {
      "citation": "liqsweep, Polynomial composition rigidity via critical values, reviewed source b17b6b9 (September 2026)",
      "url": "https://github.com/blueberryvertigo/polynomial-composition-rigidity/blob/b17b6b9f7440b12fd85df2c2db9c98209ecc174d/proof.pdf"
    },
    {
      "citation": "Jean-Philippe Furter, Polynomial composition rigidity and plane polynomial automorphisms, Journal of the London Mathematical Society 91(1), 180–202 (2015), Theorem B",
      "url": "https://www.math.u-bordeaux.fr/~jpfurter/polynomialCompositionRigidityAndPlanePolynomialAutomorphisms.pdf"
    },
    {
      "citation": "Eric Edo and Arno van den Essen, The strong factorial conjecture, Theorem 2.25(5)",
      "url": "https://arxiv.org/html/1304.3956v2"
    },
    {
      "citation": "Drew Lewis, Kaitlyn Perry and Armin Straub, An algorithmic approach to the Polydegree Conjecture for plane polynomial automorphisms",
      "url": "https://arminstraub.com/downloads/pub/polydegree-conjecture.pdf"
    },
    {
      "citation": "Evidence Press, External composition-rigidity development: mathematical and scope audit (12 September 2026)",
      "url": "https://github.com/ipitchford/evidence-press-site/blob/5a7bf52d200b28916bf776d8dc59cd95d4892a6c/docs/RIGIDITY_EXTERNAL_REVIEW_2026-09-12.md"
    }
  ],
  "relatedReleases": [
    {
      "slug": "furter-r3-through-299",
      "relation": "Finite rigidity certificates and the universal target"
    },
    {
      "slug": "full-e3-column-polydegree-conjecture",
      "relation": "Containment conclusion covered by the general argument"
    },
    {
      "slug": "full-e4-polydegree-column",
      "relation": "A second column covered by the general argument"
    },
    {
      "slug": "irreducible-pushforwards-quartic-transitions",
      "relation": "Earlier structural route to quartic rigidity"
    },
    {
      "slug": "smooth-point-certificates-polydegree-containments",
      "relation": "Stronger geometric obligations remain separate"
    },
    {
      "slug": "lps-structural-reductions",
      "relation": "Determinant and certificate obligations are not implied"
    },
    {
      "slug": "o01d0-polar-fibre-structural-reductions",
      "relation": "Polar-ideal obligations are not implied"
    }
  ],
  "relatedArticles": [],
  "corrections": [],
  "license": "CC0-1.0",
  "markdownUrl": "https://evidencepress.org/articles/when-polynomials-cannot-hide/index.md",
  "sourceUrl": "https://github.com/ipitchford/evidence-press-site/blob/main/articles/when-polynomials-cannot-hide/body.md",
  "editUrl": "https://github.com/ipitchford/evidence-press-site/edit/main/articles/when-polynomials-cannot-hide/body.md",
  "metadataEditUrl": "https://github.com/ipitchford/evidence-press-site/edit/main/articles/when-polynomials-cannot-hide/meta.json"
}