{
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  "concept_id": "urn:uuid:8634dc6a-08e3-49e9-941d-590b27f88cfe",
  "labels": {
    "zh-CN": "对称关系",
    "en": "symmetric relation"
  },
  "alternative_labels": [
    {
      "lang": "en",
      "value": "symmetric"
    },
    {
      "lang": "zh-CN",
      "value": "对称"
    }
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  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "4dc136cb4c298f07df987dd9138003fb4580536f5945c713ef0d7d6f589e2876",
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    {
      "concept_id": "urn:uuid:8634dc6a-08e3-49e9-941d-590b27f88cfe",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-01/03-products-and-relations",
      "anchor": "first-760eb7e9150caa9c7ef3-relation-zh",
      "chapter": "1",
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      "source_revision": "45666ab5cdd247b9b5146e4f9df67d1578c145c21402219499435dac061d8141",
      "source_category": "translation",
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      "role": "occurrence",
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      "label": "对称(symmetric)",
      "context": {
        "range": [
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        "quote": "\n> [!definition] 关系的三种性质\n>\n> - <u class=\"concept-term\" data-concept-identity=\"urn:uuid:2396ddfd-f7f2-4e75-8107-4e0be31adab1\" data-concept-route=\"/concept-identities#concept-2396ddfd-f7f2-4e75-8107-4e0be31adab1\" id=\"first-d1aad3541c402ead298d-zh\">自反(reflexive)</u>：对所有 $a\\in S$，有 $aRa$。\n> - <span id=\"first-760eb7e9150caa9c7ef3-zh\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-identity=\"urn:uuid:8634dc6a-08e3-49e9-941d-590b27f88cfe\" data-concept-route=\"/concept-identities#concept-8634dc6a-08e3-49e9-941d-590b27f88cfe\" id=\"first-760eb7e9150caa9c7ef3-relation-zh\">对称(symmetric)</u>：$aRb\\Rightarrow bRa$。\n> - <span id=\"first-16cddd3179afedd4e486-zh\" class=\"block-anchor\"></span><u class=\"concept-term\" data-concept-identity=\"urn:uuid:09554153-3c86-4e74-bed8-77f8ade887be\" data-concept-route=\"/concept-identities#concept-09554153-3c86-4e74-bed8-77f8ade887be\" id=\"first-16cddd3179afedd4e486-relation-zh\">传递(transitive)</u>：$aRb$ 且 $bRc\\Rightarrow aRc$。\n",
        "quote_sha256": "50f271590754697a5991e661f61bc73f617ca7fcb2a68601812cd846e497c4d9",
        "environment": "definition",
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      "section": "1.3",
      "signal": "term-mark",
      "label": "对称",
      "english": "symmetric",
      "offset": 2189
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  "resolved_references": [],
  "reading_order": [
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  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
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    "located_occurrences": 1,
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  "unresolved": [],
  "base_revision": "7d1493737c900efb83bb7ee95e1ef11cd3faa1502ee38332963642dd5afb2c9b",
  "optional_enrichments": [
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      "id": "archived-8634dc6a-08e3-49e9-941d-590b27f88cfe",
      "kind": "archived-composition",
      "actor": {
        "model": "gpt-6-luna",
        "reasoning_effort": "high"
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      "source_status": "current",
      "stale_reasons": [],
      "review_status": {
        "generation": "complete",
        "structure": "validated",
        "semantic_review": "independent-luna-reviewed; human-review-not-performed",
        "translation_review": "not-performed; inherited-source-status"
      },
      "result": {
        "overview_claims": [
          {
            "id": "overview-1",
            "text": "在 Szekeres 第 1.3 节，先把二元关系视为 $S\\times S$ 的子集，并用 $aRb$ 表示 $(a,b)\\in R$；对称性要求任意一对相关元素反向后仍相关：$a R b \\Rightarrow b R a$",
            "evidence_ids": [
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          {
            "id": "overview-2",
            "text": "该性质只表达关系在交换两个输入后保持成立；本节随后把它与自反性、传递性并列介绍，并以实数通常序说明关系可以不对称。",
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            "id": "author-szekeres",
            "book_id": "szekeres",
            "edition_id": "source-snapshot-bc3404156f6e",
            "summary": "本节在一般集合 $S$ 上讨论二元关系，并将反身、对称、传递列为常用性质。对称关系的条件只涉及成对交换，不要求自反或传递。实数上的通常序被用作不对称的例子。",
            "conditions": "$R$ 是 $S$ 上的二元关系，即 $R\\subseteq S\\times S$；对任意 $a,b\\in S$，若 $aRb$，则 $bRa$。",
            "notation": "$S$ 为集合，$R\\subseteq S\\times S$ 为关系；$aRb$ 表示 $(a,b)\\in R$。",
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        "reading_suggestions": [
          {
            "id": "read-szekeres",
            "text": "可把对称性与同节的自反性、传递性对照阅读；本节的实数通常序例子展示了“自反且传递但不对称”。",
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        "assessment": {
          "composition": "complete",
          "key_material": "available",
          "critical_gaps": [],
          "whole_book_coverage": "not-exhausted"
        },
        "gaps": [
          "当前登记的来源摘录尚未经过人工复核；本页只说明这些摘录明确支持的内容。",
          "已收录的章节范围未穷尽全书，其他章节中的用法仍待查。"
        ]
      },
      "evidence": {
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          "route": "zh/chapter-01/03-products-and-relations",
          "anchor": "",
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          "label": "Szekeres · §1.3",
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          "label": "Szekeres · §1.3",
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