{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:1d69ceb7-ab2c-4a69-9c03-48429733f60b",
  "labels": {
    "zh-CN": "重心坐标",
    "en": "barycentric coordinate"
  },
  "alternative_labels": [],
  "scope_note": "单纯形中x=Σc_i p_i、c_i≥0且Σc_i=1的系数；完整假设和公式3.11。管理员核对的原书定义/陈述；不声明首次出现，不把Theorem环境伪作Definition编号。",
  "identity_status": "active",
  "identity_revision": "200c529e082f6c2cd9479b98a7c9d7f2409232371918ec1b59ed5940443afc92",
  "occurrences": [
    {
      "concept_id": "urn:uuid:1d69ceb7-ab2c-4a69-9c03-48429733f60b",
      "book_id": "nakahara-geometry-topology-physics",
      "edition_id": "second-edition-local",
      "lang": "zh-CN",
      "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/02-section-3-2",
      "anchor": "bound-first-e0877327a2d4400632bcb700",
      "chapter": "3",
      "section": "3.2",
      "offset": 11140,
      "range": [
        20677,
        21171
      ],
      "source_revision": "6f0e0f628b7ef0f848e0af306c84637f4ddbe3beb9e56b944915cac61c290004",
      "source_category": "machine_draft",
      "review_status": "unreviewed",
      "role": "first-mention",
      "role_basis": {
        "kind": "explicit-source-uuid-marker",
        "source_bound_role": "first-mention",
        "first_mention": true,
        "source_node": "a-ccb87619f8f28e2869d4cc7c",
        "source_sidecar": {
          "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/provenance/chapter-03/concept-annotations.json",
          "sha256": "6cea3dacb311fa37962312627466368359a7e6a27a452b3c1e498fb373af3a2a",
          "page": "3.2",
          "annotation_count": 28,
          "policy": "explicit-source-bound-UUIDs; no string-based identity allocation",
          "rendered_annotation_count": 17,
          "plain_mention_count": 11,
          "display_policy": "clickable-only"
        }
      },
      "label": "重心坐标(barycentric coordinate)",
      "context": {
        "range": [
          20471,
          22159
        ],
        "quote": null,
        "quote_sha256": "7a5d3dc0c94aa15644dda7af45719efa123c8a947852785a822b6d9e4e3bed0d",
        "environment": null,
        "excerpt_omitted": true
      },
      "parallel_readings": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-03/02-section-3-2",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-ed91769a512f60780c84355b"
    }
  ],
  "registered_positions": [],
  "statements": [],
  "resolved_references": [
    {
      "raw": "href=\"../chapter-02/03-section-2-3.md#bound-definition-80a17683205f5c86c62d0b66\"",
      "href": "../chapter-02/03-section-2-3.md#bound-definition-80a17683205f5c86c62d0b66",
      "range": [
        21247,
        21327
      ],
      "relation": "references",
      "target_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-02/03-section-2-3",
      "target_anchor": "bound-definition-80a17683205f5c86c62d0b66",
      "resolved": true,
      "reason": null,
      "source_revision": "6f0e0f628b7ef0f848e0af306c84637f4ddbe3beb9e56b944915cac61c290004",
      "source_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/02-section-3-2",
      "occurrence_id": "occ-ed91769a512f60780c84355b"
    }
  ],
  "reading_order": [
    "occ-ed91769a512f60780c84355b"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 0,
    "located_occurrences": 1,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "reviewed_definitions": [
    {
      "concept_id": "urn:uuid:1d69ceb7-ab2c-4a69-9c03-48429733f60b",
      "definition_id": "urn:uuid:78c0314c-243a-5398-ad89-e4a45b9ee454",
      "definition_group": null,
      "path": "library/concepts/source-evidence/mcp/522b2915644688bdbc97e0272f30f1baffe1d72c19734fa6cd515271c68f6e3b.txt",
      "range": [
        0,
        154
      ],
      "quote": "$(c_0, \\ldots, c_r)$  is called the barycentric coordinate of  $x$ . Since  $\\sigma_r$  is a bounded and closed subset of  $\\mathbb{R}^m$ , it is compact.",
      "document_sha256": "522b2915644688bdbc97e0272f30f1baffe1d72c19734fa6cd515271c68f6e3b",
      "quote_sha256": "522b2915644688bdbc97e0272f30f1baffe1d72c19734fa6cd515271c68f6e3b",
      "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-ccb87619f8f28e2869d4cc7c",
      "source_node_sha256": "522b2915644688bdbc97e0272f30f1baffe1d72c19734fa6cd515271c68f6e3b",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/00b7ac53ccecfffa6596982c3e013cc9692851ae3da4424be3d9fe4614967e9b.json",
        "document_sha256": "00b7ac53ccecfffa6596982c3e013cc9692851ae3da4424be3d9fe4614967e9b",
        "node_id": "a-ccb87619f8f28e2869d4cc7c",
        "node_source_sha256": "522b2915644688bdbc97e0272f30f1baffe1d72c19734fa6cd515271c68f6e3b"
      },
      "conditions": "单纯形中x=Σc_i p_i、c_i≥0且Σc_i=1的系数；完整假设和公式3.11。管理员核对的原书定义/陈述；不声明首次出现，不把Theorem环境伪作Definition编号。",
      "review_status": "librarian-original-source-reviewed",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/nakahara-3.yaml",
        "sha256": "e2ce8c10e8b2dce6ebc05d605511f1bfd7a53799e562eb681ec7c2c381fa00c4",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-ccb87619f8f28e2869d4cc7c"
        ],
        "node_hashes": {
          "a-ccb87619f8f28e2869d4cc7c": "522b2915644688bdbc97e0272f30f1baffe1d72c19734fa6cd515271c68f6e3b"
        }
      },
      "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-ccb87619f8f28e2869d4cc7c",
          "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-ccb87619f8f28e2869d4cc7c",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    }
  ],
  "part_of_speech": "noun",
  "base_revision": "926ec2821f0f04c09eab450f287bfe400f4483d639f35bd8b65fcc848f1d55bf",
  "optional_enrichments": []
}
