{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "https://github.com/tamnd/math2/blob/main/schema/node.v1.json",
  "title": "math2 node, schema v1",
  "description": "The front matter of a node file in nodes/. Spec 04.5 gives the form. Each kind has its own fields. The x-m2-sections keyword gives the body sections of each kind, in order. The x-m2-edges keyword lists the 25 edge types: the 23 of spec 05.2 and the two of corpus K8.9. The x-m2-order keyword gives the order of the top-level keys in the canonical form. Nested keys use the order of their properties in this file.",
  "type": "object",
  "required": [
    "tag",
    "kind",
    "name"
  ],
  "properties": {
    "tag": {
      "$ref": "#/$defs/ref"
    },
    "kind": {
      "enum": [
        "concept",
        "definition",
        "statement",
        "conjecture",
        "problem",
        "example",
        "counterexample",
        "object",
        "proof",
        "computation",
        "topic"
      ]
    },
    "name": {
      "type": "string",
      "minLength": 1,
      "maxLength": 200
    },
    "aliases": {
      "type": "array",
      "items": {
        "$ref": "#/$defs/slug"
      },
      "uniqueItems": true
    },
    "msc": {
      "type": "array",
      "items": {
        "$ref": "#/$defs/msc"
      },
      "uniqueItems": true
    },
    "topics": {
      "description": "The topics that this node is part of. This is the part_of edge.",
      "type": "array",
      "items": {
        "$ref": "#/$defs/ref"
      },
      "uniqueItems": true
    },
    "audience": {
      "description": "The lowest curriculum level at which the node is taught (corpus K8.3). The packer and the explanation levels use it.",
      "enum": [
        "school",
        "ug1",
        "ug2",
        "ug3",
        "ug4",
        "grad",
        "research"
      ]
    },
    "uses": {
      "description": "The nodes that this node depends on. This is the uses edge.",
      "type": "array",
      "items": {
        "$ref": "#/$defs/ref"
      },
      "uniqueItems": true
    },
    "analogous_to": {
      "type": "array",
      "items": {
        "$ref": "#/$defs/analogous_to"
      }
    },
    "sources": {
      "type": "array",
      "items": {
        "$ref": "#/$defs/source"
      }
    },
    "same_as": {
      "$ref": "#/$defs/same_as"
    },
    "close_to": {
      "type": "array",
      "items": {
        "$ref": "#/$defs/close_to"
      }
    },
    "aligned": {
      "type": "array",
      "items": {
        "$ref": "#/$defs/aligned"
      }
    },
    "history": {
      "$ref": "#/$defs/history"
    },
    "retired": {
      "$ref": "#/$defs/retired"
    },
    "resolved_by": {
      "description": "The statements that settle this conjecture or problem. This is the resolved_by edge.",
      "type": "array",
      "items": {
        "$ref": "#/$defs/ref"
      },
      "uniqueItems": true
    },
    "inventory": {
      "description": "The ids of the inventory rows that this node accounts for (corpus K8.3 and K04).",
      "type": "array",
      "items": {
        "$ref": "#/$defs/row"
      },
      "uniqueItems": true,
      "minItems": 1
    },
    "conventions": {
      "description": "The conventions that change the meaning of this node, each with the option that the node uses (corpus K10.5). The register of conventions is notation/conventions.yaml.",
      "type": "array",
      "items": {
        "$ref": "#/$defs/convention"
      },
      "minItems": 1
    }
  },
  "x-m2-order": [
    "tag",
    "kind",
    "role",
    "name",
    "aliases",
    "msc",
    "topics",
    "audience",
    "about",
    "defines",
    "proves",
    "instance_of",
    "not_instance_of",
    "illustrates",
    "specializes",
    "conventions",
    "notation",
    "claim",
    "engine",
    "output",
    "certificate",
    "uses",
    "methods",
    "proofs",
    "formal",
    "implies",
    "equivalent",
    "refutes",
    "resolves",
    "resolved_by",
    "generalizes",
    "bounds",
    "analogous_to",
    "sources",
    "same_as",
    "close_to",
    "aligned",
    "inventory",
    "history",
    "retired"
  ],
  "propertyNames": {
    "not": {
      "enum": [
        "status",
        "verified",
        "proved",
        "evidence",
        "fidelity",
        "level",
        "checked"
      ]
    },
    "description": "Rule S03: status is computed. A node file never states it."
  },
  "allOf": [
    {
      "if": {
        "properties": {
          "kind": {
            "const": "concept"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "specializes": {
            "description": "Every instance of this concept is an instance of the target. This is the specializes edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/ref"
            },
            "uniqueItems": true
          },
          "notation": {
            "description": "The symbols that this node introduces (corpus K8.3). Rule N07 checks that the notation register has each one.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/symbol"
            },
            "minItems": 1
          }
        },
        "x-m2-sections": {
          "required": [
            "Summary"
          ],
          "allowed": [
            "Summary",
            "Motivation",
            "Notation",
            "Remarks",
            "Explanations"
          ]
        }
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "definition"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "defines": {
            "$ref": "#/$defs/ref",
            "description": "The concept that this definition defines. This is the defines edge."
          },
          "formal": {
            "type": "array",
            "items": {
              "$ref": "#/$defs/formal"
            }
          },
          "equivalent": {
            "description": "Definitions that are equivalent to this one. This is the equivalent edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/via_edge"
            }
          },
          "notation": {
            "description": "The symbols that this node introduces (corpus K8.3). Rule N07 checks that the notation register has each one.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/symbol"
            },
            "minItems": 1
          }
        },
        "x-m2-sections": {
          "required": [
            "Definition"
          ],
          "allowed": [
            "Definition",
            "Notation",
            "Remarks",
            "Explanations"
          ]
        },
        "required": [
          "defines"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "statement"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "about": {
            "description": "The main subjects of this node. This is the about edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/ref"
            },
            "uniqueItems": true
          },
          "role": {
            "enum": [
              "theorem",
              "lemma",
              "proposition",
              "corollary",
              "fact",
              "axiom"
            ]
          },
          "proofs": {
            "description": "The proof nodes, in the order that readers see them.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/ref"
            },
            "uniqueItems": true
          },
          "formal": {
            "type": "array",
            "items": {
              "$ref": "#/$defs/formal"
            }
          },
          "implies": {
            "description": "This is the implies edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/via_edge"
            }
          },
          "equivalent": {
            "description": "This is the equivalent edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/via_edge"
            }
          },
          "refutes": {
            "description": "This is the refutes edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/via_edge"
            }
          },
          "resolves": {
            "type": "array",
            "items": {
              "type": "object",
              "required": [
                "target",
                "outcome"
              ],
              "additionalProperties": false,
              "properties": {
                "target": {
                  "$ref": "#/$defs/ref"
                },
                "outcome": {
                  "enum": [
                    "proved",
                    "disproved",
                    "settled"
                  ]
                },
                "note": {
                  "type": "string"
                }
              }
            }
          },
          "generalizes": {
            "type": "array",
            "items": {
              "type": "object",
              "required": [
                "target",
                "map"
              ],
              "additionalProperties": false,
              "properties": {
                "target": {
                  "$ref": "#/$defs/ref"
                },
                "map": {
                  "type": "string",
                  "minLength": 1
                }
              }
            }
          },
          "bounds": {
            "type": "array",
            "items": {
              "type": "object",
              "required": [
                "target",
                "side",
                "value",
                "via"
              ],
              "additionalProperties": false,
              "properties": {
                "target": {
                  "$ref": "#/$defs/ref"
                },
                "side": {
                  "enum": [
                    "lower",
                    "upper"
                  ]
                },
                "value": {
                  "type": "string",
                  "minLength": 1
                },
                "via": {
                  "$ref": "#/$defs/ref"
                }
              }
            }
          }
        },
        "x-m2-sections": {
          "required": [
            "Statement"
          ],
          "allowed": [
            "Statement",
            "Remarks",
            "History",
            "Explanations"
          ]
        },
        "required": [
          "role"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "conjecture"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "about": {
            "description": "The main subjects of this node. This is the about edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/ref"
            },
            "uniqueItems": true
          },
          "formal": {
            "type": "array",
            "items": {
              "$ref": "#/$defs/formal"
            }
          }
        },
        "x-m2-sections": {
          "required": [
            "Statement"
          ],
          "allowed": [
            "Statement",
            "Remarks",
            "History",
            "Explanations"
          ]
        }
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "problem"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "about": {
            "description": "The main subjects of this node. This is the about edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/ref"
            },
            "uniqueItems": true
          },
          "formal": {
            "type": "array",
            "items": {
              "$ref": "#/$defs/formal"
            }
          }
        },
        "x-m2-sections": {
          "required": [
            "Problem"
          ],
          "allowed": [
            "Problem",
            "Remarks",
            "History",
            "Explanations"
          ]
        }
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "example"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "instance_of": {
            "description": "This is the instance_of edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/ref"
            },
            "uniqueItems": true
          },
          "formal": {
            "type": "array",
            "items": {
              "$ref": "#/$defs/formal"
            }
          },
          "not_instance_of": {
            "description": "The concepts and definitions that this example is not an instance of. This is the not_instance_of edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/not_instance_edge"
            }
          },
          "illustrates": {
            "description": "The statements that this example shows at work. This is the illustrates edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/ref"
            },
            "uniqueItems": true
          }
        },
        "x-m2-sections": {
          "required": [
            "Example"
          ],
          "allowed": [
            "Example",
            "Remarks",
            "Explanations"
          ]
        }
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "counterexample"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "refutes": {
            "description": "This is the refutes edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/via_edge"
            }
          },
          "formal": {
            "type": "array",
            "items": {
              "$ref": "#/$defs/formal"
            }
          }
        },
        "x-m2-sections": {
          "required": [
            "Counterexample"
          ],
          "allowed": [
            "Counterexample",
            "Remarks",
            "Explanations"
          ]
        }
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "object"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "instance_of": {
            "description": "This is the instance_of edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/ref"
            },
            "uniqueItems": true
          }
        },
        "x-m2-sections": {
          "required": [
            "Description"
          ],
          "allowed": [
            "Description",
            "Remarks",
            "Explanations"
          ]
        }
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "proof"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "proves": {
            "$ref": "#/$defs/ref",
            "description": "The one statement that this proof proves. This is the proves edge."
          },
          "formal": {
            "type": "array",
            "items": {
              "$ref": "#/$defs/formal"
            }
          },
          "methods": {
            "description": "The methods that the proof uses. This is the method edge.",
            "type": "array",
            "items": {
              "$ref": "#/$defs/ref"
            },
            "uniqueItems": true
          }
        },
        "x-m2-sections": {
          "required": [],
          "allowed": [
            "Proof",
            "Idea",
            "Variants"
          ]
        },
        "required": [
          "proves"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "computation"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {
          "claim": {
            "type": "string",
            "minLength": 1
          },
          "engine": {
            "type": "object",
            "required": [
              "image",
              "entry"
            ],
            "additionalProperties": false,
            "properties": {
              "image": {
                "type": "string",
                "pattern": "^[a-z0-9][a-z0-9._-]*@sha256:[0-9a-f]{64}$"
              },
              "entry": {
                "type": "string",
                "minLength": 1
              },
              "inputs": {
                "type": "object"
              },
              "seed": {
                "type": [
                  "integer",
                  "null"
                ]
              },
              "resources": {
                "type": "object",
                "additionalProperties": false,
                "properties": {
                  "cpu": {
                    "type": "integer",
                    "minimum": 1
                  },
                  "mem": {
                    "type": "string"
                  },
                  "wall": {
                    "type": "string"
                  }
                }
              }
            }
          },
          "output": {
            "type": "object",
            "required": [
              "hash"
            ],
            "additionalProperties": false,
            "properties": {
              "hash": {
                "type": "string",
                "pattern": "^blake3:[0-9a-f]{64}$"
              },
              "summary": {
                "type": "string"
              }
            }
          },
          "certificate": {
            "type": "object",
            "required": [
              "kind",
              "artefact",
              "checker"
            ],
            "additionalProperties": false,
            "properties": {
              "kind": {
                "type": "string",
                "minLength": 1
              },
              "artefact": {
                "type": "string",
                "pattern": "^blake3:[0-9a-f]{64}$"
              },
              "checker": {
                "type": "string",
                "pattern": "^[a-z0-9][a-z0-9._-]*@sha256:[0-9a-f]{64}$"
              },
              "checker_entry": {
                "type": "string"
              }
            }
          }
        },
        "x-m2-sections": {
          "required": [
            "Description"
          ],
          "allowed": [
            "Description",
            "Remarks"
          ]
        },
        "required": [
          "claim",
          "engine"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "kind": {
            "const": "topic"
          }
        },
        "required": [
          "kind"
        ]
      },
      "then": {
        "properties": {},
        "x-m2-sections": {
          "required": [],
          "allowed": [
            "Summary",
            "Remarks"
          ]
        }
      }
    }
  ],
  "unevaluatedProperties": false,
  "x-m2-edges": [
    {
      "name": "proves",
      "group": "logical",
      "from": "proof",
      "to": "statement",
      "field": "proves"
    },
    {
      "name": "uses",
      "group": "logical",
      "from": "statement, proof, definition",
      "to": "any",
      "field": "uses"
    },
    {
      "name": "implies",
      "group": "logical",
      "from": "statement",
      "to": "statement",
      "field": "implies"
    },
    {
      "name": "equivalent",
      "group": "logical",
      "from": "statement or definition",
      "to": "the same kind",
      "field": "equivalent"
    },
    {
      "name": "refutes",
      "group": "logical",
      "from": "counterexample or statement",
      "to": "statement or conjecture",
      "field": "refutes"
    },
    {
      "name": "resolves",
      "group": "logical",
      "from": "statement",
      "to": "conjecture or problem",
      "field": "resolves"
    },
    {
      "name": "generalizes",
      "group": "logical",
      "from": "statement",
      "to": "statement",
      "field": "generalizes"
    },
    {
      "name": "bounds",
      "group": "logical",
      "from": "statement",
      "to": "problem",
      "field": "bounds"
    },
    {
      "name": "defines",
      "group": "conceptual",
      "from": "definition",
      "to": "concept",
      "field": "defines"
    },
    {
      "name": "instance_of",
      "group": "conceptual",
      "from": "example or object",
      "to": "concept",
      "field": "instance_of"
    },
    {
      "name": "not_instance_of",
      "group": "conceptual",
      "from": "example",
      "to": "concept or definition",
      "field": "not_instance_of"
    },
    {
      "name": "illustrates",
      "group": "conceptual",
      "from": "example",
      "to": "statement",
      "field": "illustrates"
    },
    {
      "name": "about",
      "group": "conceptual",
      "from": "statement, conjecture or problem",
      "to": "concept",
      "field": "about"
    },
    {
      "name": "specializes",
      "group": "conceptual",
      "from": "concept",
      "to": "concept",
      "field": "specializes"
    },
    {
      "name": "method",
      "group": "conceptual",
      "from": "proof",
      "to": "concept in the methods topic",
      "field": "methods"
    },
    {
      "name": "analogous_to",
      "group": "conceptual",
      "from": "any",
      "to": "any",
      "field": "analogous_to"
    },
    {
      "name": "part_of",
      "group": "conceptual",
      "from": "any",
      "to": "topic",
      "field": "topics"
    },
    {
      "name": "formalizes",
      "group": "record",
      "from": "formal declaration",
      "to": "node",
      "field": "formal"
    },
    {
      "name": "source",
      "group": "record",
      "from": "node",
      "to": "record",
      "field": "sources"
    },
    {
      "name": "aligned",
      "group": "record",
      "from": "paper result",
      "to": "node",
      "field": "aligned"
    },
    {
      "name": "same_as",
      "group": "record",
      "from": "node",
      "to": "external id",
      "field": "same_as"
    },
    {
      "name": "close_to",
      "group": "record",
      "from": "node",
      "to": "external id",
      "field": "close_to"
    },
    {
      "name": "cites",
      "group": "record",
      "from": "record",
      "to": "record",
      "field": null
    },
    {
      "name": "resolved_by",
      "group": "record",
      "from": "conjecture or problem",
      "to": "statement",
      "field": "resolved_by"
    },
    {
      "name": "successor",
      "group": "record",
      "from": "retired node",
      "to": "node",
      "field": "retired.successor"
    }
  ],
  "$defs": {
    "tag": {
      "description": "A permanent tag: 10 characters of Crockford base32, without I, L, O and U, of which the last is a check character, or a legacy tag of 6 characters. Rule T09 checks the check character.",
      "type": "string",
      "pattern": "^([0-9A-HJKMNP-TV-Z]{6}|[0-9A-HJKMNP-TV-Z]{10})$"
    },
    "provisional": {
      "description": "A provisional id: ~ and 8 lowercase hex characters. It is valid only before merge.",
      "type": "string",
      "pattern": "^~[0-9a-f]{8}$"
    },
    "ref": {
      "description": "A reference to a node: a tag, or a provisional id inside its own pull request.",
      "anyOf": [
        {
          "$ref": "#/$defs/tag"
        },
        {
          "$ref": "#/$defs/provisional"
        }
      ]
    },
    "msc": {
      "description": "An MSC2020 code, for example 20D60, 20Dxx, 20-XX or 20-01. Quote codes that contain E, such as \"20E05\".",
      "type": "string",
      "pattern": "^[0-9]{2}(-XX|-[0-9]{2}|[A-Z]xx|[A-Z][0-9]{2})$"
    },
    "slug": {
      "type": "string",
      "pattern": "^[a-z0-9]+(-[a-z0-9]+)*$"
    },
    "via_edge": {
      "description": "An edge that a proof or a computation supports. Rule G10 needs via.",
      "type": "object",
      "required": [
        "target",
        "via"
      ],
      "additionalProperties": false,
      "properties": {
        "target": {
          "$ref": "#/$defs/ref"
        },
        "via": {
          "$ref": "#/$defs/ref"
        },
        "note": {
          "type": "string"
        }
      }
    },
    "source": {
      "description": "Where the node is stated or proved. Give exactly one identifier and a locator.",
      "type": "object",
      "additionalProperties": false,
      "properties": {
        "zbmath": {
          "description": "zbMATH Open document id",
          "type": "string",
          "minLength": 1
        },
        "arxiv": {
          "description": "arXiv id with version",
          "type": "string",
          "minLength": 1
        },
        "doi": {
          "description": "DOI",
          "type": "string",
          "minLength": 1
        },
        "book": {
          "description": "book identifier, for example isbn:9780471433347",
          "type": "string",
          "minLength": 1
        },
        "mr": {
          "description": "MathSciNet MR number",
          "type": "string",
          "minLength": 1
        },
        "stacks": {
          "description": "Stacks Project tag",
          "type": "string",
          "minLength": 1
        },
        "kerodon": {
          "description": "Kerodon tag",
          "type": "string",
          "minLength": 1
        },
        "mathoverflow": {
          "description": "MathOverflow question id",
          "type": "string",
          "minLength": 1
        },
        "mathse": {
          "description": "Math Stack Exchange question id",
          "type": "string",
          "minLength": 1
        },
        "erdos": {
          "description": "Erdős problem number",
          "type": "string",
          "minLength": 1
        },
        "formal_conjectures": {
          "description": "formal-conjectures file and declaration",
          "type": "string",
          "minLength": 1
        },
        "palomar": {
          "description": "Palomar registry entry id",
          "type": "string",
          "minLength": 1
        },
        "hexagon": {
          "description": "Hexagon id and version",
          "type": "string",
          "minLength": 1
        },
        "url": {
          "description": "URL, only when no identifier exists",
          "type": "string",
          "minLength": 1
        },
        "locator": {
          "type": "string",
          "minLength": 1
        },
        "note": {
          "type": "string"
        }
      },
      "oneOf": [
        {
          "required": [
            "zbmath"
          ]
        },
        {
          "required": [
            "arxiv"
          ]
        },
        {
          "required": [
            "doi"
          ]
        },
        {
          "required": [
            "book"
          ]
        },
        {
          "required": [
            "mr"
          ]
        },
        {
          "required": [
            "stacks"
          ]
        },
        {
          "required": [
            "kerodon"
          ]
        },
        {
          "required": [
            "mathoverflow"
          ]
        },
        {
          "required": [
            "mathse"
          ]
        },
        {
          "required": [
            "erdos"
          ]
        },
        {
          "required": [
            "formal_conjectures"
          ]
        },
        {
          "required": [
            "palomar"
          ]
        },
        {
          "required": [
            "hexagon"
          ]
        },
        {
          "required": [
            "url"
          ]
        }
      ]
    },
    "formal": {
      "description": "A binding to a declaration in a formal library. This is the formalizes edge.",
      "type": "object",
      "required": [
        "system",
        "decl",
        "match"
      ],
      "additionalProperties": false,
      "properties": {
        "system": {
          "enum": [
            "lean4",
            "isabelle",
            "rocq",
            "metamath",
            "hol-light"
          ]
        },
        "library": {
          "type": "string"
        },
        "decl": {
          "type": "string",
          "minLength": 1
        },
        "match": {
          "enum": [
            "exact",
            "stronger",
            "weaker",
            "variant",
            "partial"
          ]
        },
        "adapter": {
          "type": "string",
          "description": "The adapter in Math2/Meta/Match.lean for a match that is not exact."
        },
        "fidelity_reviews": {
          "type": "array",
          "items": {
            "type": "string",
            "pattern": "^r-([0-9A-HJKMNP-TV-Z]{6}|[0-9A-HJKMNP-TV-Z]{10}|~[0-9a-f]{8})-[0-9]{2}$"
          },
          "uniqueItems": true
        }
      }
    },
    "same_as": {
      "description": "The same thing in another system. A null value means that somebody checked and no entry exists.",
      "type": "object",
      "additionalProperties": false,
      "properties": {
        "wikidata": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1,
              "pattern": "^Q[1-9][0-9]*$"
            },
            {
              "type": "null"
            }
          ]
        },
        "mardi": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1,
              "pattern": "^Q[1-9][0-9]*$"
            },
            {
              "type": "null"
            }
          ]
        },
        "oeis": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1,
              "pattern": "^A[0-9]{6}$"
            },
            {
              "type": "null"
            }
          ]
        },
        "stacks": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1,
              "pattern": "^[0-9A-Z]{4}$"
            },
            {
              "type": "null"
            }
          ]
        },
        "kerodon": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1,
              "pattern": "^[0-9A-Z]{4}$"
            },
            {
              "type": "null"
            }
          ]
        },
        "nlab": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "wikipedia": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "proofwiki": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "lmfdb": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "zbmath": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "mr": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "arxiv": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "erdos": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "formal_conjectures": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "palomar": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "mathoverflow": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "mathse": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "theoremsearch": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "hexagon": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "pibase": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "dart": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "findstat": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "house_of_graphs": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "gap": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        },
        "atlas": {
          "anyOf": [
            {
              "type": "string",
              "minLength": 1
            },
            {
              "type": "null"
            }
          ]
        }
      }
    },
    "close_to": {
      "type": "object",
      "required": [
        "system",
        "id",
        "note"
      ],
      "additionalProperties": false,
      "properties": {
        "system": {
          "enum": [
            "wikidata",
            "mardi",
            "oeis",
            "stacks",
            "kerodon",
            "nlab",
            "wikipedia",
            "proofwiki",
            "lmfdb",
            "zbmath",
            "mr",
            "arxiv",
            "erdos",
            "formal_conjectures",
            "palomar",
            "mathoverflow",
            "mathse",
            "theoremsearch",
            "hexagon",
            "pibase",
            "dart",
            "findstat",
            "house_of_graphs",
            "gap",
            "atlas"
          ]
        },
        "id": {
          "type": "string",
          "minLength": 1
        },
        "note": {
          "type": "string",
          "minLength": 1
        }
      }
    },
    "aligned": {
      "type": "object",
      "required": [
        "record",
        "match"
      ],
      "additionalProperties": false,
      "properties": {
        "record": {
          "type": "string",
          "pattern": "^[a-z][a-z0-9+.-]*://"
        },
        "match": {
          "enum": [
            "exact",
            "stronger",
            "weaker",
            "variant",
            "partial"
          ]
        }
      }
    },
    "analogous_to": {
      "type": "object",
      "required": [
        "target",
        "source"
      ],
      "additionalProperties": false,
      "properties": {
        "target": {
          "$ref": "#/$defs/ref"
        },
        "source": {
          "$ref": "#/$defs/source"
        },
        "note": {
          "type": "string"
        }
      }
    },
    "history": {
      "type": "object",
      "additionalProperties": false,
      "properties": {
        "first_stated": {
          "type": "string"
        },
        "posed_by": {
          "type": "string"
        },
        "notes": {
          "type": "string"
        }
      }
    },
    "retired": {
      "type": "object",
      "required": [
        "date",
        "reason"
      ],
      "additionalProperties": false,
      "properties": {
        "date": {
          "type": "string",
          "pattern": "^[0-9]{4}-[0-9]{2}-[0-9]{2}$"
        },
        "reason": {
          "enum": [
            "duplicate",
            "false",
            "out-of-scope",
            "split",
            "merged"
          ]
        },
        "successor": {
          "description": "The nodes that replace this node. This is the successor edge.",
          "type": "array",
          "items": {
            "$ref": "#/$defs/ref"
          },
          "uniqueItems": true
        },
        "note": {
          "type": "string"
        }
      }
    },
    "row": {
      "description": "The id of an inventory row: 9 characters of Crockford base32 and a check character. Rule T09 checks the check character.",
      "type": "string",
      "pattern": "^[0-9A-HJKMNP-TV-Z]{10}$"
    },
    "convention": {
      "description": "A convention and the option of it that the node uses, for example ring: unital.",
      "type": "object",
      "required": [
        "convention",
        "option"
      ],
      "additionalProperties": false,
      "properties": {
        "convention": {
          "description": "The id of the convention in notation/conventions.yaml.",
          "$ref": "#/$defs/slug"
        },
        "option": {
          "description": "The option that this node uses.",
          "type": "string",
          "minLength": 1,
          "maxLength": 200
        },
        "note": {
          "type": "string"
        }
      }
    },
    "symbol": {
      "description": "A symbol that the node introduces: its macro and its meaning (corpus K8.3 and K10.4).",
      "type": "object",
      "required": [
        "macro",
        "meaning"
      ],
      "additionalProperties": false,
      "properties": {
        "macro": {
          "description": "The macro that a body uses for the symbol, for example \\\\totient.",
          "type": "string",
          "pattern": "^\\\\[A-Za-z]+$"
        },
        "meaning": {
          "description": "What the symbol denotes, in one line.",
          "type": "string",
          "minLength": 1,
          "maxLength": 200
        }
      }
    },
    "not_instance_edge": {
      "description": "A non-example: the target is a concept or a definition, and fails gives the numbers of the clauses of the definition that the example does not satisfy (corpus K8.4a).",
      "type": "object",
      "required": [
        "target"
      ],
      "additionalProperties": false,
      "properties": {
        "target": {
          "$ref": "#/$defs/ref"
        },
        "fails": {
          "type": "array",
          "items": {
            "type": "integer",
            "minimum": 1
          },
          "uniqueItems": true,
          "minItems": 1
        },
        "note": {
          "type": "string"
        }
      }
    }
  }
}