{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:7d6e05ef-910c-49a8-aebb-ba22dd99946c",
  "labels": {
    "zh-CN": "向量场的流与指数映射",
    "en": "Flow of a vector field and the exponential map"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "84c51d8b7cdc1dbe3c4aa441e6a598fc5a4b8ada0b80d50de16fb93e1b3a5043",
  "occurrences": [
    {
      "concept_id": "urn:uuid:7d6e05ef-910c-49a8-aebb-ba22dd99946c",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-15/01-vector-fields-and-the-exponential-map",
      "anchor": "first-0fe44bd2f2272996f2fd-zh",
      "chapter": "15",
      "section": "15.1",
      "offset": 1331,
      "range": [
        7963,
        8214
      ],
      "source_revision": "c57ff5b23a72a1078a08e864e3c69ec6184e9757d6c35cd0c024ff54fc3db06b",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "definition",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-15/01-vector-fields-and-the-exponential-map",
          "lang": "zh-CN",
          "section": "15.1",
          "signal": "named-definition",
          "label": "向量场的流与指数映射",
          "english": "",
          "offset": 1261
        }
      },
      "label": "> [!definition] 定义（向量场的流与指数映射）",
      "context": {
        "range": [
          7963,
          8214
        ],
        "quote": "\n\n> [!definition] 定义（向量场的流与指数映射）\n> 域 $M$ 上向量场 $X$ 的流是映射\n>\n> $$\n> \\Phi_ {X}: (t, m) \\in \\mathbf {R} \\times M \\to \\Phi_ {X} (t, m) \\in M\n> $$\n>\n> 满足\n>\n> $$\n> \\frac {d}{d t} \\Phi_ {X} (t, m) = X (\\Phi_ {X} (t, m))\n> $$\n>\n> $$\n> \\Phi_ {X} (0, m) = m\n> $$\n",
        "quote_sha256": "65cbf7ffbcee7013a0225a5d3738261c765c14c3eca59375a9bea8cff7dcff94",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-15/01-vector-fields-and-the-exponential-map",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-7aba60ad58e7735109b26a6a"
    },
    {
      "concept_id": "urn:uuid:7d6e05ef-910c-49a8-aebb-ba22dd99946c",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-15/01-vector-fields-and-the-exponential-map",
      "anchor": "first-6c37c0ee3dabd3ed9eb6-en",
      "chapter": "15",
      "section": "15.1",
      "offset": 2458,
      "range": [
        8250,
        8462
      ],
      "source_revision": "b65b18fddad8e04514902cc932a915604c49f0ed68f96b72980d8cb0a453bec5",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "theorem",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-15/01-vector-fields-and-the-exponential-map",
          "lang": "en",
          "section": "15.1",
          "signal": "named-theorem",
          "label": "Flow of a vector field and the exponential map",
          "english": "Flow of a vector field and the exponential map",
          "offset": 2388
        }
      },
      "label": "> [!theorem] Definition (Flow of a vector field and the exponential map)",
      "context": {
        "range": [
          8250,
          8462
        ],
        "quote": "\n\n> [!theorem] Definition (Flow of a vector field and the exponential map)\n> The flow of the vector field $X$ on $M$ is the map\n>\n> $$\n> \\Phi_ {X}: (t, m) \\in \\mathbf {R} \\times M \\to \\Phi_ {X} (t, m) \\in M\n> $$\n",
        "quote_sha256": "3fc5ff9c3c10eee6f0facf0c9191d40f0b1d2167f364015b87057da7d70db71d",
        "environment": "theorem",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-15/01-vector-fields-and-the-exponential-map",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-4bd20c5cb377a0d1f92f4f21"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-15/01-vector-fields-and-the-exponential-map",
      "lang": "en",
      "section": "15.1",
      "signal": "named-theorem",
      "label": "Flow of a vector field and the exponential map",
      "english": "Flow of a vector field and the exponential map",
      "offset": 2388
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-15/01-vector-fields-and-the-exponential-map",
      "lang": "zh-CN",
      "section": "15.1",
      "signal": "named-definition",
      "label": "向量场的流与指数映射",
      "english": "",
      "offset": 1261
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-7aba60ad58e7735109b26a6a",
    "occ-4bd20c5cb377a0d1f92f4f21"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "bd82b6fb51ce3e640650981c721d3f44577bb936abb474199fad773e8a4c1184",
  "optional_enrichments": []
}
