{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-12T06:20:57Z",
    "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": {
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      "engine": "claude",
      "producedAt": "2026-10-06T00:10:00Z",
      "ingestedAt": "2026-10-05T20:54:25+00:00",
      "fields": [
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  "metaModel": {
    "id": "THING-Q7233199",
    "registryId": "vr.tr.positional-game",
    "name": "positional game",
    "version": "0.2.0-wave.2",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.REL"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q7233199/",
  "model": {
    "registry_id": "vr.tr.positional-game",
    "name": "positional game",
    "purpose": "Let an agent explain positional games and their variants and examples, describe the main theoretical results and strategy methods, support analysing specific games, and support learning in combinatorics and game theory.",
    "definition": "A finite two-player game in which players alternately claim previously unclaimed elements of a set, such as cells of a board or edges of a graph, with the winner determined by which player completes a winning configuration or prevents the other from doing so, including tic-tac-toe, Hex and the Shannon switching game, and the Maker-Breaker, Avoider-Enforcer and strong variants studied in combinatorics; positional games are analysed by strategy stealing, pairing strategies and potential methods.",
    "what_it_is_for": "Games of claiming elements to form configurations.",
    "affordances": [
      "explain variants and examples",
      "describe theory and methods",
      "support analysis",
      "support learning"
    ],
    "distinguishing_features": [
      "Claiming moves",
      "Winning sets",
      "Variants by objective",
      "Strategy theorems"
    ],
    "appearance": "Not physical; abstract games on boards or graphs.",
    "visual_identification": [
      "Alternate claiming of elements to complete configurations",
      "Tic-tac-toe, Hex, Maker-Breaker games",
      "Chess is not a positional game in this sense; general combinatorial games are wider"
    ],
    "physical_properties": [],
    "families_and_kinds": [
      "strong positional games such as tic-tac-toe",
      "Maker-Breaker games",
      "Avoider-Enforcer games",
      "games on graphs such as Hex and Shannon switching",
      "biased and random variants"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "finite two-player zero-sum game",
        "why": "category"
      },
      {
        "relation": "is related to",
        "target": "Semi-Open Game",
        "why": "chess openings as another studied game structure"
      },
      {
        "relation": "is related to",
        "target": "binary relation",
        "why": "graphs underlying positional games"
      },
      {
        "relation": "is related to",
        "target": "determinant",
        "why": "algebraic tools in combinatorics"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "Mathematical notation conventions",
      "No regulation of the concept",
      "Competition rules for specific games such as Hex"
    ],
    "failure_modes_and_hazards": [
      "Confusing variants",
      "Misapplying strategy stealing",
      "Overgeneralising results"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Explain positional games such as tic-tac-toe and Maker-Breaker games and their theory.",
        "Compute or describe strategies in a user's own analysis."
      ],
      "must_not": [
        "Claim a game is solved or a strategy winning without proof.",
        "Assist a player during a competitive game where outside help is prohibited.",
        "Misattribute theorems or results to researchers."
      ],
      "requires_human": [
        "Publishing a claimed proof or new result."
      ]
    },
    "ethics": {
      "considerations": [
        "Credit for mathematical results matters to researchers.",
        "Unfair assistance spoils games for honest players."
      ],
      "affected_parties": [
        "Mathematicians",
        "Players"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical concept held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q7233199: positional game",
      "url": "https://www.wikidata.org/wiki/Q7233199",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Positional game",
      "url": "https://en.wikipedia.org/wiki/Positional_game",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "understand",
        "name": "Understand",
        "description": "What positional games are.",
        "rationale": "Mathematics.",
        "layers": [
          {
            "id": "concept",
            "name": "Concept",
            "description": "Concept and variants.",
            "findings": [
              {
                "id": "concept-finding",
                "name": "Concept",
                "description": "Concept.",
                "questions": [
                  {
                    "text": "What is a positional game, and how do strong, Maker-Breaker and Avoider-Enforcer variants differ?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which variant or game is meant?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "examples",
            "name": "Examples",
            "description": "Examples.",
            "findings": [
              {
                "id": "examples-finding",
                "name": "Examples",
                "description": "Examples.",
                "questions": [
                  {
                    "text": "How are tic-tac-toe, Hex and the Shannon switching game positional games, and who wins them?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits a specific game?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Theory and methods.",
        "rationale": "Scholarship.",
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          {
            "id": "theorems",
            "name": "Theorems",
            "description": "Key results.",
            "findings": [
              {
                "id": "theorems-finding",
                "name": "Theorems",
                "description": "Theorems.",
                "questions": [
                  {
                    "text": "What do strategy stealing, the Erdos-Selfridge criterion and pairing strategies establish?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits combinatorial game theory?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "open",
            "name": "Open",
            "description": "Open problems.",
            "findings": [
              {
                "id": "open-finding",
                "name": "Open",
                "description": "Open.",
                "questions": [
                  {
                    "text": "What open problems and recent results exist in positional game theory, with findings attributed?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which findings are current?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "analyse",
        "name": "Analyse",
        "description": "Analysing games.",
        "rationale": "Practice.",
        "layers": [
          {
            "id": "analyse",
            "name": "Analyse",
            "description": "Analysing a game.",
            "findings": [
              {
                "id": "analyse-finding",
                "name": "Analyse",
                "description": "Analysis.",
                "questions": [
                  {
                    "text": "How can the winner or a strategy for this positional game be determined?",
                    "kind": "action"
                  },
                  {
                    "text": "Which entry fits game solving?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "compute",
            "name": "Compute",
            "description": "Computation.",
            "findings": [
              {
                "id": "compute-finding",
                "name": "Compute",
                "description": "Computation.",
                "questions": [
                  {
                    "text": "How are positional games solved computationally, and what is their complexity?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits computational complexity?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "learn",
        "name": "Learn",
        "description": "History and teaching.",
        "rationale": "Education.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did the theory of positional games develop from Hales-Jewett and Erdos-Selfridge onward?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "teach",
            "name": "Teach",
            "description": "Teaching.",
            "findings": [
              {
                "id": "teach-finding",
                "name": "Teach",
                "description": "Teaching.",
                "questions": [
                  {
                    "text": "How can positional games be taught in combinatorics?",
                    "kind": "action"
                  },
                  {
                    "text": "Which misconceptions arise?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should Hex be a separate entry?",
    "How should research literature be linked?",
    "How should game implementations be linked?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}