{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:cc566ee3-c318-49a8-9e0f-353b0ab878d5",
  "labels": {
    "zh-CN": "真面",
    "en": "proper face"
  },
  "alternative_labels": [],
  "scope_note": "相对于给定几何单纯形σ_r的面σ_q，且σ_q≠σ_r，记σ_q<σ_r；Nakahara约定0-单纯形没有真面。真面是面的严格子类，不是face的无条件异名；不声称首次出现。",
  "identity_status": "active",
  "identity_revision": "3ad80c4d7669747d6cd216e56e3ea864025d3ca8ead4111dff9c79f0af1cf913",
  "occurrences": [],
  "registered_positions": [],
  "statements": [],
  "resolved_references": [],
  "reading_order": [],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 0,
    "located_occurrences": 0,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "reviewed_definitions": [
    {
      "concept_id": "urn:uuid:cc566ee3-c318-49a8-9e0f-353b0ab878d5",
      "definition_id": "urn:uuid:9a064101-56c2-58b6-8052-cf6d030b8f37",
      "definition_group": null,
      "path": "library/concepts/source-evidence/mcp/3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04.txt",
      "range": [
        0,
        356
      ],
      "quote": "Let  $q$  be an integer such that  $0 \\leq q \\leq r$ . If we choose  $q + 1$  points  $p_{i_0}, \\ldots, p_{i_q}$  out of  $p_0, \\ldots, p_r$ , these  $q + 1$  points define a  $q$ -simplex  $\\sigma_q = \\langle p_{i_0}, \\ldots, p_{i_q} \\rangle$ , which is called a  $q$ -face of  $\\sigma_r$ . We write  $\\sigma_q \\leq \\sigma_r$  if  $\\sigma_q$  is a face of",
      "document_sha256": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
      "quote_sha256": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
      "book_id": "nakahara-geometry-topology-physics",
      "edition_id": "second-edition-local",
      "scope": {
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "source_id": "nakahara-mineru-bd76b709"
      },
      "section": "3.2.1",
      "pdf_page_index": 116,
      "node": "a-5710caf8a35ba2f371380cb5",
      "source_node_sha256": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/7e806ec362bb6dbe6a39978b1ed1ec6f6c652d160fcc1d3f64e7081928bd30e4.json",
        "document_sha256": "7e806ec362bb6dbe6a39978b1ed1ec6f6c652d160fcc1d3f64e7081928bd30e4",
        "node_id": "a-5710caf8a35ba2f371380cb5",
        "node_source_sha256": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04"
      },
      "conditions": "相对于给定几何单纯形σ_r的面σ_q，且σ_q≠σ_r，记σ_q<σ_r；Nakahara约定0-单纯形没有真面。真面是面的严格子类，不是face的无条件异名；不声称首次出现。",
      "review_status": "librarian-original-source-reviewed",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/nakahara-3.yaml",
        "sha256": "1137336a1bbcf6d3274c8bd062156bb543e6df779c66ba604b8742621862b485",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-5710caf8a35ba2f371380cb5",
          "a-3292539252c47d51e151c0da"
        ],
        "node_hashes": {
          "a-5710caf8a35ba2f371380cb5": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
          "a-3292539252c47d51e151c0da": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c"
        }
      },
      "role": "definition",
      "first_in_book": "not-established",
      "evidence_origin": "explicit-reviewed-source-manifest",
      "reading_links": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-03/02-section-3-2",
          "anchor": "node-a-5710caf8a35ba2f371380cb5",
          "lang": "en",
          "basis": "explicit-source-anchor"
        },
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/02-section-3-2",
          "anchor": "node-a-5710caf8a35ba2f371380cb5",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    },
    {
      "concept_id": "urn:uuid:cc566ee3-c318-49a8-9e0f-353b0ab878d5",
      "definition_id": "urn:uuid:9a064101-56c2-58b6-8052-cf6d030b8f37",
      "definition_group": null,
      "path": "library/concepts/source-evidence/mcp/7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c.txt",
      "range": [
        0,
        472
      ],
      "quote": "$\\sigma_r$ . If  $\\sigma_q \\neq \\sigma_r$ , we say  $\\sigma_q$  is a proper face of  $\\sigma_r$ , denoted as  $\\sigma_q < \\sigma_r$ . Figure 3.3 shows a 0-face  $p_0$  and a 2-face  $\\langle p_1p_2p_3\\rangle$  of a 3-simplex  $\\langle p_0p_1p_2p_3\\rangle$ . There are one 3-face, four 2-faces, six 1-faces and four 0-faces. The reader should verify that the number of  $q$ -faces in an  $r$ -simplex is  $\\binom{r+1}{q+1}$ . A 0-simplex is defined to have no proper faces.",
      "document_sha256": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c",
      "quote_sha256": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c",
      "book_id": "nakahara-geometry-topology-physics",
      "edition_id": "second-edition-local",
      "scope": {
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "source_id": "nakahara-mineru-bd76b709"
      },
      "section": "3.2.1",
      "pdf_page_index": 117,
      "node": "a-3292539252c47d51e151c0da",
      "source_node_sha256": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/7e806ec362bb6dbe6a39978b1ed1ec6f6c652d160fcc1d3f64e7081928bd30e4.json",
        "document_sha256": "7e806ec362bb6dbe6a39978b1ed1ec6f6c652d160fcc1d3f64e7081928bd30e4",
        "node_id": "a-3292539252c47d51e151c0da",
        "node_source_sha256": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c"
      },
      "conditions": "相对于给定几何单纯形σ_r的面σ_q，且σ_q≠σ_r，记σ_q<σ_r；Nakahara约定0-单纯形没有真面。真面是面的严格子类，不是face的无条件异名；不声称首次出现。",
      "review_status": "librarian-original-source-reviewed",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/nakahara-3.yaml",
        "sha256": "1137336a1bbcf6d3274c8bd062156bb543e6df779c66ba604b8742621862b485",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-5710caf8a35ba2f371380cb5",
          "a-3292539252c47d51e151c0da"
        ],
        "node_hashes": {
          "a-5710caf8a35ba2f371380cb5": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
          "a-3292539252c47d51e151c0da": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c"
        }
      },
      "role": "definition",
      "first_in_book": "not-established",
      "evidence_origin": "explicit-reviewed-source-manifest",
      "reading_links": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-03/02-section-3-2",
          "anchor": "node-a-3292539252c47d51e151c0da",
          "lang": "en",
          "basis": "explicit-source-anchor"
        },
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/02-section-3-2",
          "anchor": "node-a-3292539252c47d51e151c0da",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    }
  ],
  "reviewed_mentions": [
    {
      "concept_id": "urn:uuid:cc566ee3-c318-49a8-9e0f-353b0ab878d5",
      "path": "library/concepts/source-evidence/mcp/3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04.txt",
      "range": [
        0,
        356
      ],
      "quote": "Let  $q$  be an integer such that  $0 \\leq q \\leq r$ . If we choose  $q + 1$  points  $p_{i_0}, \\ldots, p_{i_q}$  out of  $p_0, \\ldots, p_r$ , these  $q + 1$  points define a  $q$ -simplex  $\\sigma_q = \\langle p_{i_0}, \\ldots, p_{i_q} \\rangle$ , which is called a  $q$ -face of  $\\sigma_r$ . We write  $\\sigma_q \\leq \\sigma_r$  if  $\\sigma_q$  is a face of",
      "document_sha256": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
      "quote_sha256": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
      "scope": {
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "source_id": "nakahara-mineru-bd76b709"
      },
      "book_id": "nakahara-geometry-topology-physics",
      "edition_id": "second-edition-local",
      "section": "3.2.1",
      "pdf_page_index": 116,
      "node": "a-5710caf8a35ba2f371380cb5",
      "source_node_sha256": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/nakahara-3.yaml",
        "sha256": "1137336a1bbcf6d3274c8bd062156bb543e6df779c66ba604b8742621862b485",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-5710caf8a35ba2f371380cb5",
          "a-3292539252c47d51e151c0da"
        ],
        "node_hashes": {
          "a-5710caf8a35ba2f371380cb5": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
          "a-3292539252c47d51e151c0da": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c"
        }
      },
      "conditions": "用户指出“nakahara3.2提到一个真面的概念，似乎没入库”；管理员回查§3.2.1英文两段定义，确认proper face增加严格不等条件，独立登记并关联broader=面，保留历史混合条目，不自动合并。",
      "review_status": "librarian-original-source-mention-reviewed",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/7e806ec362bb6dbe6a39978b1ed1ec6f6c652d160fcc1d3f64e7081928bd30e4.json",
        "document_sha256": "7e806ec362bb6dbe6a39978b1ed1ec6f6c652d160fcc1d3f64e7081928bd30e4",
        "node_id": "a-5710caf8a35ba2f371380cb5",
        "node_source_sha256": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04"
      },
      "role": "mention",
      "first_in_book": "not-established",
      "evidence_origin": "explicit-reviewed-source-manifest",
      "reading_links": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-03/02-section-3-2",
          "anchor": "node-a-5710caf8a35ba2f371380cb5",
          "lang": "en",
          "basis": "explicit-source-anchor"
        },
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/02-section-3-2",
          "anchor": "node-a-5710caf8a35ba2f371380cb5",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    },
    {
      "concept_id": "urn:uuid:cc566ee3-c318-49a8-9e0f-353b0ab878d5",
      "path": "library/concepts/source-evidence/mcp/7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c.txt",
      "range": [
        0,
        472
      ],
      "quote": "$\\sigma_r$ . If  $\\sigma_q \\neq \\sigma_r$ , we say  $\\sigma_q$  is a proper face of  $\\sigma_r$ , denoted as  $\\sigma_q < \\sigma_r$ . Figure 3.3 shows a 0-face  $p_0$  and a 2-face  $\\langle p_1p_2p_3\\rangle$  of a 3-simplex  $\\langle p_0p_1p_2p_3\\rangle$ . There are one 3-face, four 2-faces, six 1-faces and four 0-faces. The reader should verify that the number of  $q$ -faces in an  $r$ -simplex is  $\\binom{r+1}{q+1}$ . A 0-simplex is defined to have no proper faces.",
      "document_sha256": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c",
      "quote_sha256": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c",
      "scope": {
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "source_id": "nakahara-mineru-bd76b709"
      },
      "book_id": "nakahara-geometry-topology-physics",
      "edition_id": "second-edition-local",
      "section": "3.2.1",
      "pdf_page_index": 117,
      "node": "a-3292539252c47d51e151c0da",
      "source_node_sha256": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/nakahara-3.yaml",
        "sha256": "1137336a1bbcf6d3274c8bd062156bb543e6df779c66ba604b8742621862b485",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-5710caf8a35ba2f371380cb5",
          "a-3292539252c47d51e151c0da"
        ],
        "node_hashes": {
          "a-5710caf8a35ba2f371380cb5": "3fde633b231274130188116000a18690e27f1ab0e6406e18a72b01f8cedc4c04",
          "a-3292539252c47d51e151c0da": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c"
        }
      },
      "conditions": "用户指出“nakahara3.2提到一个真面的概念，似乎没入库”；管理员回查§3.2.1英文两段定义，确认proper face增加严格不等条件，独立登记并关联broader=面，保留历史混合条目，不自动合并。",
      "review_status": "librarian-original-source-mention-reviewed",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/7e806ec362bb6dbe6a39978b1ed1ec6f6c652d160fcc1d3f64e7081928bd30e4.json",
        "document_sha256": "7e806ec362bb6dbe6a39978b1ed1ec6f6c652d160fcc1d3f64e7081928bd30e4",
        "node_id": "a-3292539252c47d51e151c0da",
        "node_source_sha256": "7e82f42b659231b92db5da99832e1ec612c7d2256982c65b9c5ef1e7c000aa1c"
      },
      "role": "mention",
      "first_in_book": "not-established",
      "evidence_origin": "explicit-reviewed-source-manifest",
      "reading_links": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-03/02-section-3-2",
          "anchor": "node-a-3292539252c47d51e151c0da",
          "lang": "en",
          "basis": "explicit-source-anchor"
        },
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/02-section-3-2",
          "anchor": "node-a-3292539252c47d51e151c0da",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    }
  ],
  "relation_metadata": [
    {
      "predicate": "broader",
      "target": "urn:uuid:83c6cbb2-d720-4dd5-8186-1ceb458dfe53",
      "taxonomy_kind": "generic",
      "reason": "原书先定义σ_q≤σ_r为面，再以σ_q≠σ_r定义proper face，故真面是面的一种。",
      "evidence": [
        "library/concepts/reviewed-relations.json#edge-a76145df2ea2539e0e4f"
      ]
    }
  ],
  "part_of_speech": "noun",
  "semantic_relations": {
    "broader": [
      {
        "concept_id": "urn:uuid:83c6cbb2-d720-4dd5-8186-1ceb458dfe53",
        "labels": {
          "zh-CN": "面",
          "en": "face"
        },
        "route": "concepts/by-id/83c6cbb2-d720-4dd5-8186-1ceb458dfe53"
      }
    ],
    "narrower": [],
    "related": []
  },
  "base_revision": "6296f107c0f9ab6c302856299563757e29490e12df4152f68582e4ebe9b40d54",
  "optional_enrichments": []
}
