{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-11T19:59:16Z",
    "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": 2,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-05T19:00:00Z",
      "ingestedAt": "2026-10-05T20:48:41+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:51:55+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q177239",
    "registryId": "vr.tr.limit",
    "name": "limit",
    "version": "0.2.0-wave.2",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q177239/",
  "model": {
    "registry_id": "vr.tr.limit",
    "name": "limit",
    "purpose": "Let an agent explain and compute mathematical limits, explain their rigorous definition and role, and separate the everyday and regulatory senses of limit.",
    "definition": "In mathematics, the value that a function or sequence approaches as the input or index approaches some value or infinity, defined rigorously by epsilon-delta and related definitions and underpinning continuity, derivatives, integrals and series, with extensions such as set-theoretic limits and summation methods; outside mathematics the word denotes a boundary or maximum, as in speed limits, liability limits and residue limits.",
    "what_it_is_for": "Foundations of calculus and analysis.",
    "affordances": [
      "compute limits of functions and sequences",
      "explain the rigorous definition",
      "explain the role of limits in calculus",
      "separate regulatory and everyday senses"
    ],
    "distinguishing_features": [
      "Value approached",
      "Rigorous definition",
      "Foundation of calculus",
      "Homonym with bounds and rules"
    ],
    "appearance": "Not physical; notation and definitions.",
    "visual_identification": [
      "lim notation",
      "Approach to a value",
      "A bound is not necessarily a limit"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "limits of sequences",
      "limits of functions",
      "one-sided and infinite limits",
      "set-theoretic limits and summation methods",
      "limits in the sense of bounds and rules (separate sense)"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "mathematical concept",
        "why": "category"
      },
      {
        "relation": "is a kind of",
        "target": "upper and lower bounds",
        "why": "category"
      },
      {
        "relation": "is studied in",
        "target": "mathematical analysis",
        "why": "field"
      },
      {
        "relation": "underlies",
        "target": "integral",
        "why": "definition"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "ISO 80000-2 notation",
      "Regulatory limits are governed by domain-specific rules"
    ],
    "failure_modes_and_hazards": [
      "Treating limits as values reached",
      "Ignoring one-sided differences",
      "Confusing senses"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Compute and explain limits, including the epsilon-delta definition.",
        "Say when a limit does not exist or depends on direction."
      ],
      "must_not": [
        "Report a limit that does not exist as having a value.",
        "Use infinite or limiting arguments carelessly in results others rely on.",
        "Present intuitive explanations as rigorous proof."
      ],
      "requires_human": [
        "Using limit-based approximations in a calculation that is signed off for safety."
      ]
    },
    "ethics": {
      "considerations": [
        "Precise reasoning about limits prevents errors in science and engineering.",
        "Clear teaching helps learners who find the concept difficult."
      ],
      "affected_parties": [
        "Students",
        "Engineers and scientists"
      ]
    },
    "owners": {
      "steward": "Nobody owns the concept; it is held in common by mathematics.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q177239: limit",
      "url": "https://www.wikidata.org/wiki/Q177239",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Limit (mathematics)",
      "url": "https://en.wikipedia.org/wiki/Limit_%28mathematics%29",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "compute",
        "name": "Compute",
        "description": "Finding limits.",
        "rationale": "Techniques.",
        "layers": [
          {
            "id": "evaluate",
            "name": "Evaluate",
            "description": "Evaluating a limit.",
            "findings": [
              {
                "id": "evaluate-finding",
                "name": "Evaluate",
                "description": "Evaluation.",
                "questions": [
                  {
                    "text": "What is the limit of this function or sequence, and which technique shows it?",
                    "kind": "measurement"
                  },
                  {
                    "text": "Does the limit exist, and are one-sided limits equal?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "indeterminate",
            "name": "Indeterminate",
            "description": "Indeterminate forms.",
            "findings": [
              {
                "id": "indeterminate-finding",
                "name": "Indeterminate",
                "description": "Indeterminate forms.",
                "questions": [
                  {
                    "text": "How are indeterminate forms resolved, for example by algebra or the rule of l Hopital?",
                    "kind": "action"
                  },
                  {
                    "text": "When does the rule apply?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "define",
        "name": "Define",
        "description": "Rigorous definition.",
        "rationale": "Epsilon and delta.",
        "layers": [
          {
            "id": "epsilon",
            "name": "Epsilon",
            "description": "Formal definition.",
            "findings": [
              {
                "id": "epsilon-finding",
                "name": "Epsilon",
                "description": "Formal definition.",
                "questions": [
                  {
                    "text": "What is the epsilon-delta definition of this limit, and how is it used in a proof?",
                    "kind": "definition"
                  },
                  {
                    "text": "How does the sequence definition differ?",
                    "kind": "definition"
                  }
                ]
              }
            ]
          },
          {
            "id": "role",
            "name": "Role",
            "description": "Role in calculus.",
            "findings": [
              {
                "id": "role-finding",
                "name": "Role",
                "description": "Role.",
                "questions": [
                  {
                    "text": "How do limits define continuity, derivatives, integrals and series?",
                    "kind": "definition"
                  },
                  {
                    "text": "Why were limits introduced historically?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "advanced",
        "name": "Advanced",
        "description": "Generalisations.",
        "rationale": "Beyond the basics.",
        "layers": [
          {
            "id": "sets",
            "name": "Sets",
            "description": "Set-theoretic limits.",
            "findings": [
              {
                "id": "sets-finding",
                "name": "Sets",
                "description": "Set limits.",
                "questions": [
                  {
                    "text": "What are the limit superior and inferior of a sequence of sets or numbers?",
                    "kind": "definition"
                  },
                  {
                    "text": "Where are they used?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "summation",
            "name": "Summation",
            "description": "Summation methods.",
            "findings": [
              {
                "id": "summation-finding",
                "name": "Summation",
                "description": "Summation methods.",
                "questions": [
                  {
                    "text": "What does Cesaro summation assign to a divergent series, and how does it relate to limits?",
                    "kind": "definition"
                  },
                  {
                    "text": "When are such methods legitimate?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "senses",
        "name": "Senses",
        "description": "Other senses.",
        "rationale": "Bounds and rules.",
        "layers": [
          {
            "id": "regulatory",
            "name": "Regulatory",
            "description": "Limits as rules.",
            "findings": [
              {
                "id": "regulatory-finding",
                "name": "Regulatory",
                "description": "Regulatory limits.",
                "questions": [
                  {
                    "text": "Is a regulatory or contractual limit meant, such as a speed, liability or residue limit?",
                    "kind": "boundary"
                  },
                  {
                    "text": "Which entry or authority applies?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "teach",
            "name": "Teach",
            "description": "Teaching limits.",
            "findings": [
              {
                "id": "teach-finding",
                "name": "Teach",
                "description": "Teaching.",
                "questions": [
                  {
                    "text": "How can limits be taught intuitively before formalising?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should sequence and function limits be separate entries?",
    "How should teaching resources be linked?",
    "How should regulatory senses be split?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}