{
  "$schema": "../../../schemas/mko-v0.4.schema.json",
  "schema_version": "mko-v0.4",
  "id": "mko-dimensional-analysis",
  "semantic_family_id": "sf-dimensional-analysis",
  "type": "concept",
  "version": "0.10.0",
  "language": "zh-Hant",
  "titles": {
    "zh-Hant": "量綱分析"
  },
  "summary": {
    "zh-Hant": "量綱分析用基本量綱指數向量追蹤乘、除與冪，並核對方程兩側量綱是否一致。"
  },
  "statement": {
    "zh-Hant": "相對基本量綱 L、M、T，把物理量 Q 的量綱記為 [Q]=L^a M^b T^c，亦即指數向量 (a,b,c)。乘法相加向量、除法相減、整數冪倍乘；可相等或相加的量必須量綱一致。"
  },
  "formula": {
    "tex": "d(Q)",
    "mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>d</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></math>",
    "semantic_ast": {
      "type": "function_call",
      "callee": {
        "type": "symbol",
        "name": "d",
        "glyph": "d"
      },
      "arguments": [
        {
          "type": "symbol",
          "name": "Q",
          "glyph": "Q"
        }
      ]
    },
    "compiler": {
      "id": "ocme-formula-core",
      "version": "0.4.0",
      "source_sha256": "b2298d8d4d6c95747d025e237c19a0a025319f7f0501b048c2141512a9c3293d"
    }
  },
  "assumptions": [
    {
      "id": "a1",
      "zh-Hant": "題庫只用 L、M、T 三個基本量綱及整數指數。"
    },
    {
      "id": "a2",
      "zh-Hant": "量綱一致是候選物理方程的必要條件，不是充分條件；無因次常數與具量綱常數需由題目明示。"
    }
  ],
  "symbols": [
    {
      "token": "Q",
      "role": "physical_quantity",
      "role_zh": "物理量",
      "scope": "representative_formula"
    },
    {
      "token": "L",
      "role": "length_dimension",
      "role_zh": "長度量綱",
      "scope": "representative_formula"
    },
    {
      "token": "M",
      "role": "mass_dimension",
      "role_zh": "質量量綱",
      "scope": "representative_formula"
    },
    {
      "token": "T",
      "role": "time_dimension",
      "role_zh": "時間量綱",
      "scope": "representative_formula"
    }
  ],
  "dependencies": [
    {
      "id": "mko-ratio-proportion",
      "title_zh": "比與比例",
      "reason_zh": "除法與無因次比值需要比例語義。"
    },
    {
      "id": "mko-arithmetic-operations",
      "title_zh": "四則運算",
      "reason_zh": "指數向量以加減與整數倍運算。"
    },
    {
      "id": "mko-equation",
      "title_zh": "方程式",
      "reason_zh": "方程兩側需作量綱一致核對。"
    }
  ],
  "explanation": {
    "paragraphs_zh": [
      "速度的量綱可由長度除以時間取得，乘積與商則逐基本量綱合併指數。",
      "方程若兩側量綱不同，不能由調整純數常數修正；若一致，仍可能有錯係數、錯方向或錯物理假設。",
      "量綱分析不追蹤單位換算的數值因子，也不替代實驗、邊界條件與模型驗證。"
    ],
    "common_misconception_zh": "把量綱一致當成方程必然正確，或把單位名稱與量綱指數完全等同。"
  },
  "proofs": [],
  "computational_companions": [],
  "verification": {
    "computational_status": "not_evaluated_no_computational_claim",
    "warning_zh": "本輪只核對 L、M、T 指數向量；一致性不升格為物理正確性。",
    "evidence_refs": [],
    "producers": [
      {
        "id": "lean-mathlib",
        "adapter": "formal_system",
        "config_path": "formal/lean/lakefile.toml",
        "status": "configured"
      }
    ]
  },
  "formalization": {
    "status": "not_formalized",
    "target_systems": [
      "Lean 4",
      "Mathlib"
    ],
    "next_obligation_zh": "加入 SI 單位換算、Buckingham Pi 與無因次化。"
  },
  "provenance": {
    "origin": "ocme_local_ai_materialization_candidate",
    "note_zh": "依 research/atlas-dimensional-analysis.md 整理；2026-10-13 脈衝 R05（使用者手動接續 2026-10-20 工作序列；實際日期仍為 2026-10-13），英文及 Lean 依使用者指示延後。",
    "content_license": "CC-BY-SA-4.0",
    "code_license": "MIT",
    "created_at": "2026-10-13"
  }
}