{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T05:00:01Z",
    "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": "2026-10-05T16:30:00Z",
      "ingestedAt": "2026-10-05T13:21:53+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q170198",
    "registryId": "vr.tr.series",
    "name": "series",
    "version": "0.2.0-wave.1",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.REL"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q170198/",
  "model": {
    "registry_id": "vr.tr.series",
    "name": "series",
    "purpose": "Let an agent handle series with their terms, convergence and sums, and separate a series from the sequence of its terms.",
    "definition": "In mathematics, the sum of the terms of a sequence, written a1 + a2 + a3 + ..., which may be finite or infinite and, if infinite, convergent or divergent.",
    "what_it_is_for": "Representing functions, approximating values and solving problems in analysis, physics and engineering.",
    "affordances": [
      "sum it, when it converges",
      "test convergence, with standard tests",
      "expand functions as series, such as power or Fourier series",
      "truncate it, for approximation, with an error bound"
    ],
    "distinguishing_features": [
      "A sum of terms, not the sequence itself",
      "Infinite series may converge or diverge",
      "Formal power series need not converge",
      "Asymptotic expansions can be useful even when divergent"
    ],
    "appearance": "Summation notation with a sigma, or terms with plus signs and ellipsis.",
    "visual_identification": [
      "Sigma notation",
      "Named series such as geometric, harmonic, Taylor, Fourier",
      "TV and book series are different senses"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "geometric and arithmetic series",
      "power, Taylor and Laurent series",
      "Fourier series",
      "formal power series",
      "asymptotic expansions"
    ],
    "related_models": [
      {
        "relation": "is built from",
        "target": "sequence",
        "why": "terms of a sequence"
      },
      {
        "relation": "is confused with",
        "target": "sequence",
        "why": "ordered terms, not their sum"
      },
      {
        "relation": "is used in",
        "target": "analysis and physics",
        "why": "approximation and expansion"
      },
      {
        "relation": "is confused with",
        "target": "series as a set of works",
        "why": "a homonym"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "ISO 80000-2 notation"
    ],
    "failure_modes_and_hazards": [
      "Summing a divergent series as if convergent",
      "Rearranging conditionally convergent series",
      "Truncating without an error bound"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Determine and state whether a series converges, with the test used.",
        "Truncate a series only with an error bound."
      ],
      "must_not": [
        "Sum a divergent series as if it were convergent without stating the method.",
        "Rearrange a conditionally convergent series and present the result as its sum.",
        "Truncate a series without stating the error."
      ],
      "requires_human": [
        "Relying on a truncated series in safety-critical calculations."
      ]
    },
    "ethics": {
      "considerations": [
        "Mathematical errors in engineering and finance hurt people who trust the result."
      ],
      "affected_parties": [
        "Users of results",
        "Students"
      ]
    },
    "owners": {
      "steward": "Nobody owns the concept; it is held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q170198: series",
      "url": "https://www.wikidata.org/wiki/Q170198",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Series (mathematics)",
      "url": "https://en.wikipedia.org/wiki/Series_%28mathematics%29",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "terms",
        "name": "Terms",
        "description": "What is summed.",
        "rationale": "The terms define the series.",
        "layers": [
          {
            "id": "rule",
            "name": "Term rule",
            "description": "General term.",
            "findings": [
              {
                "id": "rule-finding",
                "name": "Term rule",
                "description": "The general term.",
                "questions": [
                  {
                    "text": "What is the general term of the series?",
                    "kind": "definition"
                  },
                  {
                    "text": "Where does the summation start?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "kind",
            "name": "Kind",
            "description": "Geometric, power, Fourier.",
            "findings": [
              {
                "id": "kind-finding",
                "name": "Kind",
                "description": "The kind of series.",
                "questions": [
                  {
                    "text": "What kind of series is this?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is it formal or analytic?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "convergence",
        "name": "Convergence",
        "description": "Does it sum.",
        "rationale": "Convergence decides whether a sum exists.",
        "layers": [
          {
            "id": "test",
            "name": "Tests",
            "description": "Ratio, root, comparison.",
            "findings": [
              {
                "id": "test-finding",
                "name": "Convergence test",
                "description": "Test used.",
                "questions": [
                  {
                    "text": "Does the series converge, by which test?",
                    "kind": "measurement"
                  },
                  {
                    "text": "For which values of the variable?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "type",
            "name": "Type of convergence",
            "description": "Absolute, conditional, uniform.",
            "findings": [
              {
                "id": "type-finding",
                "name": "Convergence type",
                "description": "The type of convergence.",
                "questions": [
                  {
                    "text": "Is the convergence absolute, conditional or uniform?",
                    "kind": "definition"
                  },
                  {
                    "text": "What operations does that permit?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "sum",
        "name": "Sum",
        "description": "The value.",
        "rationale": "The sum is the goal when it exists.",
        "layers": [
          {
            "id": "value",
            "name": "Value",
            "description": "Closed form.",
            "findings": [
              {
                "id": "value-finding",
                "name": "Sum",
                "description": "The sum.",
                "questions": [
                  {
                    "text": "What is the sum, in closed form if possible?",
                    "kind": "measurement"
                  },
                  {
                    "text": "How was it derived?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "approximation",
            "name": "Approximation",
            "description": "Truncation error.",
            "findings": [
              {
                "id": "approximation-finding",
                "name": "Error bound",
                "description": "Error of partial sums.",
                "questions": [
                  {
                    "text": "How many terms give the needed accuracy?",
                    "kind": "measurement"
                  },
                  {
                    "text": "What bounds the truncation error?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "application",
        "name": "Application",
        "description": "Where it is used.",
        "rationale": "Series are tools for representing functions.",
        "layers": [
          {
            "id": "expansion",
            "name": "Expansion",
            "description": "Functions as series.",
            "findings": [
              {
                "id": "expansion-finding",
                "name": "Expansion",
                "description": "Function expansions.",
                "questions": [
                  {
                    "text": "Which function does this series represent, and where?",
                    "kind": "definition"
                  },
                  {
                    "text": "What is the radius of convergence?",
                    "kind": "measurement"
                  }
                ]
              }
            ]
          },
          {
            "id": "computation",
            "name": "Computation",
            "description": "Numerical use.",
            "findings": [
              {
                "id": "computation-finding",
                "name": "Numerics",
                "description": "Numerical behaviour.",
                "questions": [
                  {
                    "text": "Is the series numerically stable to sum?",
                    "kind": "boundary"
                  },
                  {
                    "text": "Should acceleration methods be used?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should named series be separate entries?",
    "How should convergence conditions be recorded?",
    "How should formal and analytic series be distinguished?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}