{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-14T03:25:52Z",
    "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": 4,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-06T12:00:00Z",
      "ingestedAt": "2026-10-06T07:46:11+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-06T19:52:03+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q980509",
    "registryId": "vr.tr.embedding",
    "name": "embedding",
    "version": "0.2.0-wave.4",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q980509/",
  "model": {
    "registry_id": "vr.tr.embedding",
    "name": "embedding",
    "purpose": "Let an agent explain the notion of embedding, relay its meaning across mathematics and its extension to machine learning from reference sources, distinguish the senses the aliases name, and steer a question to the right sense.",
    "definition": "In mathematics, an embedding is a map that places one structure inside another so that the copy faithfully preserves the original structure; the term applies across geometry, topology and algebra. The registry aliases name several senses, including topological embeddings, elementary embeddings in logic, and, by extension, machine-learning embeddings such as word or graph embeddings that map items into a latent space of vectors. The precise meaning depends on the field, so the sense should be identified before answering.",
    "what_it_is_for": "Placing one structure faithfully inside another.",
    "affordances": [
      "explain the mathematical notion",
      "relay the machine-learning extension",
      "distinguish the senses",
      "steer to the right meaning"
    ],
    "distinguishing_features": [
      "Structure-preserving",
      "Field-dependent meaning",
      "Extended to machine learning",
      "Maps into a larger space"
    ],
    "appearance": "Not a visible object; a map or representation, sometimes pictured as points in a space.",
    "visual_identification": [
      "A structure-preserving placement into a larger space",
      "Topological embedding, elementary embedding, latent space, word and graph embeddings",
      "A general function need not preserve structure; a projection may lose information"
    ],
    "physical_properties": [
      {
        "quantity": "field",
        "typical_range": "mathematics and its extensions",
        "unit": "note",
        "note": ""
      },
      {
        "quantity": "key property",
        "typical_range": "preserves structure",
        "unit": "note",
        "note": ""
      },
      {
        "quantity": "registry parent",
        "typical_range": "function",
        "unit": "note",
        "note": ""
      }
    ],
    "families_and_kinds": [
      "topological embedding",
      "elementary embedding",
      "word embedding",
      "graph embedding"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "function",
        "why": "in registry terms"
      },
      {
        "relation": "is contrasted with",
        "target": "projection",
        "why": ""
      },
      {
        "relation": "is used in",
        "target": "machine learning",
        "why": ""
      },
      {
        "relation": "is related to",
        "target": "representation",
        "why": ""
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "Mathematical definitions per field"
    ],
    "failure_modes_and_hazards": [
      "Mixing the senses",
      "Assuming one field s meaning everywhere",
      "Overstating the analogy to latent spaces"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "Explain what an embedding is in the field the user is working in.",
        "Check whether a given map is injective and structure-preserving.",
        "Distinguish the mathematical sense from machine-learning vector embeddings."
      ],
      "must_not": [
        "Mix senses of embedding from different fields in an argument.",
        "Call a map an embedding when it does not preserve the structure.",
        "Overstate what an embedding preserves.",
        "Present a disputed proof involving embeddings as settled."
      ],
      "requires_human": [
        "Publishing a mathematical claim in someone else's name."
      ]
    },
    "ethics": {
      "considerations": [
        "Precise terms matter; confusing them can invalidate results.",
        "Credit for mathematical work should be accurate."
      ],
      "affected_parties": [
        "Students",
        "Researchers",
        "Readers of mathematical work"
      ]
    },
    "owners": {
      "steward": "Nobody: a mathematical concept held in common.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q980509: embedding",
      "url": "https://www.wikidata.org/wiki/Q980509",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Embedding",
      "url": "https://en.wikipedia.org/wiki/Embedding",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "understand",
        "name": "Understand",
        "description": "What embedding means.",
        "rationale": "Definition.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What does embedding mean in mathematics, and how does it differ from a general function or a projection?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which sense is meant, mathematical or machine-learning?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "senses",
            "name": "Senses",
            "description": "The senses.",
            "findings": [
              {
                "id": "senses-finding",
                "name": "Senses",
                "description": "Senses.",
                "questions": [
                  {
                    "text": "What are topological, elementary and machine-learning embeddings?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits the intended sense?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "math",
        "name": "Math",
        "description": "Mathematics.",
        "rationale": "Sources.",
        "layers": [
          {
            "id": "topology",
            "name": "Topology",
            "description": "Topological embedding.",
            "findings": [
              {
                "id": "topology-finding",
                "name": "Topology",
                "description": "Topology.",
                "questions": [
                  {
                    "text": "What is a topological embedding?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "logic",
            "name": "Logic",
            "description": "Elementary embedding.",
            "findings": [
              {
                "id": "logic-finding",
                "name": "Logic",
                "description": "Logic.",
                "questions": [
                  {
                    "text": "What is an elementary embedding in logic?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "ml",
        "name": "ML",
        "description": "Machine learning.",
        "rationale": "Sources.",
        "layers": [
          {
            "id": "latent",
            "name": "Latent",
            "description": "Latent space.",
            "findings": [
              {
                "id": "latent-finding",
                "name": "Latent",
                "description": "Latent.",
                "questions": [
                  {
                    "text": "What is a machine-learning embedding into a latent space?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Is the analogy to the mathematical sense loose?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "kinds",
            "name": "Kinds",
            "description": "Embedding kinds.",
            "findings": [
              {
                "id": "kinds-finding",
                "name": "Kinds",
                "description": "Kinds.",
                "questions": [
                  {
                    "text": "What are word and graph embeddings?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the specific kind?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "Context.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "preservation",
            "name": "Preservation",
            "description": "What is preserved.",
            "findings": [
              {
                "id": "preservation-finding",
                "name": "Preservation",
                "description": "Preservation.",
                "questions": [
                  {
                    "text": "What structure does an embedding preserve in each field?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "use",
            "name": "Use",
            "description": "Use.",
            "findings": [
              {
                "id": "use-finding",
                "name": "Use",
                "description": "Use.",
                "questions": [
                  {
                    "text": "How are embeddings used in practice?",
                    "kind": "action"
                  },
                  {
                    "text": "Is the sense correctly identified?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should each sense be a separate entry?",
    "How should the machine-learning sense be scoped?",
    "How should the senses be signposted?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}