{
  "vercy": "1.0-draft",
  "publication": {
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    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T12:34:42Z",
    "providers": [
      "Claude"
    ],
    "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify",
    "pass": 2,
    "wave": 1,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-05T17:00:00Z",
      "ingestedAt": "2026-10-05T13:29:21+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "revisions": [
      {
        "at": "2026-10-06T22:51:46+00:00",
        "engine": "codex",
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          "definition"
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    "gate": {
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      "version": "1.0",
      "at": "2026-10-07T10:10:31+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
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  },
  "metaModel": {
    "id": "THING-Q43260",
    "registryId": "vr.tr.polynomial",
    "name": "polynomial",
    "version": "0.2.0-wave.1",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q43260/",
  "model": {
    "registry_id": "vr.tr.polynomial",
    "name": "polynomial",
    "purpose": "Let an agent explain polynomials by degree, operations, roots, factorisation and applications, for learners and practitioners.",
    "definition": "A mathematical expression built from variables and coefficients using addition, subtraction, multiplication and non-negative integer powers, such as monomials, binomials and trinomials; the degree of a nonzero polynomial is the greatest total degree of its monomials with nonzero coefficients, where total degree is the sum of the exponents of the variables in a monomial, reducing to the highest exponent in the univariate case, and by the fundamental theorem of algebra a nonconstant univariate polynomial with complex coefficients has as many complex roots as its degree, counted with multiplicity.",
    "what_it_is_for": "Algebra, modelling, approximation and computation.",
    "affordances": [
      "add, multiply and divide polynomials",
      "find roots and factorise",
      "use polynomials for interpolation and approximation",
      "explain key theorems"
    ],
    "distinguishing_features": [
      "Non-negative integer exponents",
      "Has a degree",
      "Roots determined by degree",
      "Closed under addition and multiplication"
    ],
    "appearance": "Not physical; expressions such as 3x^2 + 2x - 5 and their graphs.",
    "visual_identification": [
      "Sums of terms with whole-number powers",
      "Graphs such as parabolas and cubics",
      "Expressions with negative or fractional powers are not polynomials"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "monomials, binomials and trinomials",
      "linear, quadratic and cubic polynomials",
      "multivariate polynomials",
      "orthogonal polynomials",
      "invariant and knot polynomials"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "algebraic expression",
        "why": "category"
      },
      {
        "relation": "has",
        "target": "root",
        "why": "property"
      },
      {
        "relation": "is studied in",
        "target": "algebra",
        "why": "field"
      },
      {
        "relation": "is related to",
        "target": "invariant",
        "why": "related concept"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "No specific regulation"
    ],
    "failure_modes_and_hazards": [
      "Numerical instability with high-degree fitting",
      "Sign and exponent errors"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Manipulate, factor and evaluate polynomials and find their roots.",
        "Explain degree, roots and the fundamental theorem of algebra."
      ],
      "must_not": [
        "Fit high-degree polynomials to data without warning of instability and overfitting.",
        "Report roots without stating the numerical precision used.",
        "Extrapolate a polynomial fit far outside the data as if it were reliable."
      ],
      "requires_human": [
        "Using a polynomial model in engineering or financial decisions that affect people."
      ]
    },
    "ethics": {
      "considerations": [
        "Overfitted models give false confidence in predictions that people rely on."
      ],
      "affected_parties": [
        "Students and learners",
        "People affected by model-based decisions"
      ]
    },
    "owners": {
      "steward": "Nobody owns the concept; it is held in common by mathematics.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q43260: polynomial",
      "url": "https://www.wikidata.org/wiki/Q43260",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Polynomial",
      "url": "https://en.wikipedia.org/wiki/Polynomial",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "basics",
        "name": "Basics",
        "description": "Definitions.",
        "rationale": "Terms and degree.",
        "layers": [
          {
            "id": "identify",
            "name": "Identify",
            "description": "Is it a polynomial.",
            "findings": [
              {
                "id": "identify-finding",
                "name": "Identify",
                "description": "Identification.",
                "questions": [
                  {
                    "text": "Is this expression a polynomial, and what is its degree?",
                    "kind": "boundary"
                  },
                  {
                    "text": "What are its coefficients?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "operations",
            "name": "Operations",
            "description": "Arithmetic.",
            "findings": [
              {
                "id": "operations-finding",
                "name": "Operations",
                "description": "Operations.",
                "questions": [
                  {
                    "text": "What is the result of adding, multiplying or dividing these polynomials?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Is there a remainder?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "roots",
        "name": "Roots",
        "description": "Solving.",
        "rationale": "Roots follow theorems.",
        "layers": [
          {
            "id": "solve",
            "name": "Solve",
            "description": "Finding roots.",
            "findings": [
              {
                "id": "solve-finding",
                "name": "Solve",
                "description": "Finding roots.",
                "questions": [
                  {
                    "text": "What are the roots of this polynomial?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Which method is appropriate, such as the quadratic formula?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "theorems",
            "name": "Theorems",
            "description": "Key results.",
            "findings": [
              {
                "id": "theorems-finding",
                "name": "Theorems",
                "description": "Key theorems.",
                "questions": [
                  {
                    "text": "What do the fundamental theorem of algebra and Abel-Ruffini theorem say?",
                    "kind": "definition"
                  },
                  {
                    "text": "Why is there no general formula beyond degree four?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "applications",
        "name": "Applications",
        "description": "Uses.",
        "rationale": "Polynomials model data.",
        "layers": [
          {
            "id": "fitting",
            "name": "Fitting",
            "description": "Interpolation.",
            "findings": [
              {
                "id": "fitting-finding",
                "name": "Fitting",
                "description": "Interpolation and fitting.",
                "questions": [
                  {
                    "text": "How can a polynomial be fitted to these data points?",
                    "kind": "action"
                  },
                  {
                    "text": "Is there a risk of overfitting?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "computing",
            "name": "Computing",
            "description": "Algorithms.",
            "findings": [
              {
                "id": "computing-finding",
                "name": "Computing",
                "description": "Algorithms.",
                "questions": [
                  {
                    "text": "How are polynomials evaluated efficiently, such as by Horner method?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which libraries help?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "learning",
        "name": "Learning",
        "description": "Teaching.",
        "rationale": "Learners need practice.",
        "layers": [
          {
            "id": "explain",
            "name": "Explain",
            "description": "Explaining.",
            "findings": [
              {
                "id": "explain-finding",
                "name": "Explain",
                "description": "Explanation.",
                "questions": [
                  {
                    "text": "How can factorising be explained step by step?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions are common?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "graphs",
            "name": "Graphs",
            "description": "Graphing.",
            "findings": [
              {
                "id": "graphs-finding",
                "name": "Graphs",
                "description": "Graphs.",
                "questions": [
                  {
                    "text": "How does the degree affect the shape of the graph?",
                    "kind": "definition"
                  },
                  {
                    "text": "Where are the turning points?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should polynomial families be separate entries?",
    "How should computer algebra tools be linked?",
    "How should teaching materials be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}