{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:a51762fe-b5fc-5c7f-8802-7a6c7fec4299",
  "labels": {
    "zh-CN": "路径的连接",
    "en": "path concatenation"
  },
  "alternative_labels": [],
  "scope_note": "Nakahara Definition 4.2：路径的连接。完整条件以所列原文节点为准；不将同框中作为前提提及的概念视为被定义。这是端点相容路径的连接，不是一般代数乘积。",
  "identity_status": "active",
  "identity_revision": "fc9a45ac4c56829afe37891b78af0bd8facaeb3cac4fec22c20c518cff7244f8",
  "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:a51762fe-b5fc-5c7f-8802-7a6c7fec4299",
      "definition_id": "urn:uuid:5b4c4ab7-847a-51d0-9c25-5c1d9d990446",
      "definition_group": "definition-4-2",
      "path": "library/concepts/source-evidence/mcp/77e162f665707482d402228214c52f61eb6ecaaed4eba9027fd5b3ecbe289f50.txt",
      "range": [
        0,
        193
      ],
      "quote": "Definition 4.2. Let  $\\alpha, \\beta: I \\to X$  be paths such that  $\\alpha(1) = \\beta(0)$ . The product of  $\\alpha$  and  $\\beta$ , denoted by  $\\alpha * \\beta$ , is a path in  $X$  defined by",
      "document_sha256": "77e162f665707482d402228214c52f61eb6ecaaed4eba9027fd5b3ecbe289f50",
      "quote_sha256": "77e162f665707482d402228214c52f61eb6ecaaed4eba9027fd5b3ecbe289f50",
      "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": "4.1.2",
      "pdf_page_index": 140,
      "node": "a-597945b12490d42d3b89a4b6",
      "source_node_sha256": "77e162f665707482d402228214c52f61eb6ecaaed4eba9027fd5b3ecbe289f50",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/18ef3f319c123ea89a053e7371dd3b564d5658400e75658ac9b2ab61e2a19021.json",
        "document_sha256": "18ef3f319c123ea89a053e7371dd3b564d5658400e75658ac9b2ab61e2a19021",
        "node_id": "a-597945b12490d42d3b89a4b6",
        "node_source_sha256": "77e162f665707482d402228214c52f61eb6ecaaed4eba9027fd5b3ecbe289f50"
      },
      "conditions": "Nakahara Definition 4.2：路径的连接。完整条件以所列原文节点为准；不将同框中作为前提提及的概念视为被定义。这是端点相容路径的连接，不是一般代数乘积。",
      "review_status": "librarian-original-source-reviewed",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml",
        "sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-597945b12490d42d3b89a4b6",
          "a-2f94b25fb7e10d8aeb7e566d",
          "a-0358cb3c952224657b07d0e4"
        ],
        "node_hashes": {
          "a-597945b12490d42d3b89a4b6": "77e162f665707482d402228214c52f61eb6ecaaed4eba9027fd5b3ecbe289f50",
          "a-2f94b25fb7e10d8aeb7e566d": "051038209b0b136716441c5ca8b2a31177df1a9810db59efcc05243f0f5d3ce5",
          "a-0358cb3c952224657b07d0e4": "87c1d3614141f5c74e0bd2b73c8f7eaaf8961a6844618ec09ab845e366dcd7ef"
        },
        "environment": "definition-4-2"
      },
      "environment_basis": {
        "path": "library/concepts/source-evidence/environment-basis/686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb.yaml.txt",
        "document_sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "source_path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml"
      },
      "role": "definition",
      "first_in_book": "not-established",
      "evidence_origin": "explicit-reviewed-source-manifest",
      "definition_part": "definition-environment",
      "definition_part_basis": "original-environment-range",
      "reading_links": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-04/01-section-4-1",
          "anchor": "node-a-597945b12490d42d3b89a4b6",
          "lang": "en",
          "basis": "explicit-source-anchor"
        },
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/01-section-4-1",
          "anchor": "node-a-597945b12490d42d3b89a4b6",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    },
    {
      "concept_id": "urn:uuid:a51762fe-b5fc-5c7f-8802-7a6c7fec4299",
      "definition_id": "urn:uuid:5b4c4ab7-847a-51d0-9c25-5c1d9d990446",
      "definition_group": "definition-4-2",
      "path": "library/concepts/source-evidence/mcp/051038209b0b136716441c5ca8b2a31177df1a9810db59efcc05243f0f5d3ce5.txt",
      "range": [
        0,
        176
      ],
      "quote": "\n$$\n\\alpha * \\beta (s) = \\left\\{ \\begin{array}{l l} \\alpha (2 s) & 0 \\leq s \\leq \\frac {1}{2} \\\\ \\beta (2 s - 1) & \\frac {1}{2} \\leq s \\leq 1 \\end{array} \\right. \\tag {4.1}\n$$\n",
      "document_sha256": "051038209b0b136716441c5ca8b2a31177df1a9810db59efcc05243f0f5d3ce5",
      "quote_sha256": "051038209b0b136716441c5ca8b2a31177df1a9810db59efcc05243f0f5d3ce5",
      "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": "4.1.2",
      "pdf_page_index": 140,
      "node": "a-2f94b25fb7e10d8aeb7e566d",
      "source_node_sha256": "051038209b0b136716441c5ca8b2a31177df1a9810db59efcc05243f0f5d3ce5",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/18ef3f319c123ea89a053e7371dd3b564d5658400e75658ac9b2ab61e2a19021.json",
        "document_sha256": "18ef3f319c123ea89a053e7371dd3b564d5658400e75658ac9b2ab61e2a19021",
        "node_id": "a-2f94b25fb7e10d8aeb7e566d",
        "node_source_sha256": "051038209b0b136716441c5ca8b2a31177df1a9810db59efcc05243f0f5d3ce5"
      },
      "conditions": "Nakahara Definition 4.2：路径的连接。完整条件以所列原文节点为准；不将同框中作为前提提及的概念视为被定义。这是端点相容路径的连接，不是一般代数乘积。",
      "review_status": "librarian-original-source-reviewed",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml",
        "sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-597945b12490d42d3b89a4b6",
          "a-2f94b25fb7e10d8aeb7e566d",
          "a-0358cb3c952224657b07d0e4"
        ],
        "node_hashes": {
          "a-597945b12490d42d3b89a4b6": "77e162f665707482d402228214c52f61eb6ecaaed4eba9027fd5b3ecbe289f50",
          "a-2f94b25fb7e10d8aeb7e566d": "051038209b0b136716441c5ca8b2a31177df1a9810db59efcc05243f0f5d3ce5",
          "a-0358cb3c952224657b07d0e4": "87c1d3614141f5c74e0bd2b73c8f7eaaf8961a6844618ec09ab845e366dcd7ef"
        },
        "environment": "definition-4-2"
      },
      "environment_basis": {
        "path": "library/concepts/source-evidence/environment-basis/686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb.yaml.txt",
        "document_sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "source_path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml"
      },
      "role": "definition",
      "first_in_book": "not-established",
      "evidence_origin": "explicit-reviewed-source-manifest",
      "definition_part": "definition-environment",
      "definition_part_basis": "original-environment-range",
      "reading_links": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-04/01-section-4-1",
          "anchor": "node-a-2f94b25fb7e10d8aeb7e566d",
          "lang": "en",
          "basis": "explicit-source-anchor"
        },
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/01-section-4-1",
          "anchor": "node-a-2f94b25fb7e10d8aeb7e566d",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    },
    {
      "concept_id": "urn:uuid:a51762fe-b5fc-5c7f-8802-7a6c7fec4299",
      "definition_id": "urn:uuid:5b4c4ab7-847a-51d0-9c25-5c1d9d990446",
      "definition_group": "definition-4-2",
      "path": "library/concepts/source-evidence/mcp/87c1d3614141f5c74e0bd2b73c8f7eaaf8961a6844618ec09ab845e366dcd7ef.txt",
      "range": [
        0,
        301
      ],
      "quote": "see figure 4.2. Since  $\\alpha(1) = \\beta(0)$ ,  $\\alpha * \\beta$  is a continuous map from  $I$  to  $X$ . [Geometrically,  $\\alpha * \\beta$  corresponds to traversing the image  $\\alpha(I)$ , in the first half, then followed by  $\\beta(I)$  in the remaining half. Note that the velocity is doubled.]",
      "document_sha256": "87c1d3614141f5c74e0bd2b73c8f7eaaf8961a6844618ec09ab845e366dcd7ef",
      "quote_sha256": "87c1d3614141f5c74e0bd2b73c8f7eaaf8961a6844618ec09ab845e366dcd7ef",
      "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": "4.1.2",
      "pdf_page_index": 140,
      "node": "a-0358cb3c952224657b07d0e4",
      "source_node_sha256": "87c1d3614141f5c74e0bd2b73c8f7eaaf8961a6844618ec09ab845e366dcd7ef",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/18ef3f319c123ea89a053e7371dd3b564d5658400e75658ac9b2ab61e2a19021.json",
        "document_sha256": "18ef3f319c123ea89a053e7371dd3b564d5658400e75658ac9b2ab61e2a19021",
        "node_id": "a-0358cb3c952224657b07d0e4",
        "node_source_sha256": "87c1d3614141f5c74e0bd2b73c8f7eaaf8961a6844618ec09ab845e366dcd7ef"
      },
      "conditions": "Nakahara Definition 4.2：路径的连接。完整条件以所列原文节点为准；不将同框中作为前提提及的概念视为被定义。这是端点相容路径的连接，不是一般代数乘积。",
      "review_status": "librarian-original-source-reviewed",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml",
        "sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-597945b12490d42d3b89a4b6",
          "a-2f94b25fb7e10d8aeb7e566d",
          "a-0358cb3c952224657b07d0e4"
        ],
        "node_hashes": {
          "a-597945b12490d42d3b89a4b6": "77e162f665707482d402228214c52f61eb6ecaaed4eba9027fd5b3ecbe289f50",
          "a-2f94b25fb7e10d8aeb7e566d": "051038209b0b136716441c5ca8b2a31177df1a9810db59efcc05243f0f5d3ce5",
          "a-0358cb3c952224657b07d0e4": "87c1d3614141f5c74e0bd2b73c8f7eaaf8961a6844618ec09ab845e366dcd7ef"
        },
        "environment": "definition-4-2"
      },
      "environment_basis": {
        "path": "library/concepts/source-evidence/environment-basis/686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb.yaml.txt",
        "document_sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "source_path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml"
      },
      "role": "definition",
      "first_in_book": "not-established",
      "evidence_origin": "explicit-reviewed-source-manifest",
      "definition_part": "definition-environment",
      "definition_part_basis": "original-environment-range",
      "reading_links": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-04/01-section-4-1",
          "anchor": "node-a-0358cb3c952224657b07d0e4",
          "lang": "en",
          "basis": "explicit-source-anchor"
        },
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/01-section-4-1",
          "anchor": "node-a-0358cb3c952224657b07d0e4",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    }
  ],
  "part_of_speech": "noun",
  "base_revision": "310adc1b88fabb48ff13df520aac92dc2053f8d4bf5efde5b208bcca310bc9a2",
  "optional_enrichments": []
}
