{
  "$schema": "../../../schemas/mko-v0.4.schema.json",
  "schema_version": "mko-v0.4",
  "id": "mko-finite-sufficient-statistic",
  "semantic_family_id": "sf-finite-sufficient-statistic",
  "type": "definition",
  "version": "0.10.0",
  "language": "zh-Hant",
  "titles": {
    "zh-Hant": "有限模型充分統計量"
  },
  "summary": {
    "zh-Hant": "finite model中，給定statistic value後sample conditional law不依theta時，T對theta充分。"
  },
  "statement": {
    "zh-Hant": "statistic須是sample carrier上的total map，完整fibers形成partition。對每個(theta,t)先算P_theta(T=t)；只在正質量cell定義並exact計算fiber conditional law。跨所有有效theta逐t核對conditional-law invariance；zero-mass cell保持undefined。nonsufficient witness、identity statistic與constant statistic邊界分開；不提前使用factorization theorem或宣稱估計品質。"
  },
  "formula": {
    "tex": "S(T,t)=b",
    "mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><mi>S</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>b</mi></mrow></math>",
    "semantic_ast": {
      "type": "equation",
      "lhs": {
        "type": "function_call",
        "callee": {
          "type": "symbol",
          "name": "S",
          "glyph": "S"
        },
        "arguments": [
          {
            "type": "symbol",
            "name": "T",
            "glyph": "T"
          },
          {
            "type": "symbol",
            "name": "t",
            "glyph": "t"
          }
        ]
      },
      "rhs": {
        "type": "symbol",
        "name": "b",
        "glyph": "b"
      }
    },
    "compiler": {
      "id": "ocme-formula-core",
      "version": "0.4.0",
      "source_sha256": "d65b391fb992f3739c1d1e8bdcb938c7dd52d6db263d90939ec996ce7638e9fd"
    }
  },
  "assumptions": [
    {
      "id": "a1",
      "zh-Hant": "完整finite parametric sampling laws逐theta normalized。"
    },
    {
      "id": "a2",
      "zh-Hant": "statistic total且fibers完整。"
    }
  ],
  "symbols": [
    {
      "token": "S",
      "role": "sufficiency_predicate",
      "role_zh": "充分性述詞",
      "scope": "representative_formula"
    },
    {
      "token": "T",
      "role": "finite_statistic",
      "role_zh": "有限統計量",
      "scope": "representative_formula"
    },
    {
      "token": "t",
      "role": "statistic_value",
      "role_zh": "統計量值",
      "scope": "representative_formula"
    },
    {
      "token": "b",
      "role": "sufficiency_boolean",
      "role_zh": "充分性布林值",
      "scope": "representative_formula"
    }
  ],
  "dependencies": [
    {
      "id": "mko-parametric-statistical-model",
      "title_zh": "參數統計模型",
      "reason_zh": "theta-indexed laws。"
    },
    {
      "id": "mko-statistical-estimator",
      "title_zh": "統計估計量",
      "reason_zh": "statistic mapping。"
    },
    {
      "id": "mko-sampling-distribution",
      "title_zh": "抽樣分布",
      "reason_zh": "T distribution與fibers。"
    },
    {
      "id": "mko-conditional-probability",
      "title_zh": "條件機率",
      "reason_zh": "conditional law。"
    }
  ],
  "explanation": {
    "paragraphs_zh": [
      "total statistic與fibers partition先核對。",
      "positive-mass conditional tables完整計算。",
      "theta invariance、nonsufficient與zero-mass分界。"
    ],
    "common_misconception_zh": "為zero-mass condition填造分布，或從data reduction推估計品質。"
  },
  "proofs": [],
  "computational_companions": [],
  "verification": {
    "computational_status": "not_evaluated_no_computational_claim",
    "warning_zh": "本輪不用factorization theorem，有限表只證指定model。",
    "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factorization criterion。"
  },
  "provenance": {
    "origin": "ocme_local_ai_materialization_candidate",
    "note_zh": "依 research/atlas-finite-sufficient-statistic.md 整理；2026-10-15 脈衝 R05（使用者手動接續 2026-11-16 工作序列；實際日期仍為 2026-10-15），英文及 Lean 依使用者指示延後。",
    "content_license": "CC-BY-SA-4.0",
    "code_license": "MIT",
    "created_at": "2026-10-15"
  }
}