{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261015-pulse-20261119-r03-0088",
  "pilot_number": "R0054-27813",
  "number": 27813,
  "family_id": "qf-mod50-gd-boundary",
  "title": {
    "zh-Hant": "第 27813 題：梯度下降",
    "en": "Question 27813: Oversized Steps, Stationary Maxima and Lost Feasibility Block Different Inferences"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261015-pulse-20261119-r03-0088",
    "batch_id": "batch-20261015-advance-20261119-r03-gradient-descent-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-gradient-descent"
    ],
    "title_zh": "梯度下降",
    "stem_zh": "standard Euclidean coordinate order、正步長與完整gradient update。操作=gd-boundary；明示資料={\"mode\":\"oversized_step\",\"model\":{\"curvature\":3,\"point\":13,\"step_size\":3}}；請依 exact_ordered_tuple_declared_by_interface 回答。",
    "answer": {
      "kind": "expression",
      "value": "(oversized_step, 3, 13, 3, -104, 507/2, 16224, 否, positive_but_oversized_step_can_increase_the_objective)",
      "explanation_zh": "Wave6第十三層核對=(oversized_step, 3, 13, 3, -104, 507/2, 16224, 否, positive_but_oversized_step_can_increase_the_objective)；依完整明示資料精確重算；x_next=x-alpha*gradient逐座標精確重算；safe trace另核0<alpha<2/L；positive alpha、zero gradient或finite trace不自動給descent、minimum、global optimum或convergence；不冒充projected descent。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "梯度下降"
      ]
    },
    "variant": {
      "family_id": "qf-mod50-gd-boundary",
      "seed": 202611193088,
      "parameters": {
        "mode": "oversized_step",
        "model": {
          "curvature": 3,
          "point": 13,
          "step_size": 3
        },
        "domain": "Exact_diagonal_quadratic_gradient_descent",
        "operation": "gd-boundary",
        "semantic_template": "gd-boundary|{\"mode\":\"oversized_step\",\"model\":{\"curvature\":[3,1],\"point\":[13,1],\"step_size\":[3,1]}}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_contract_recomputation",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "GPT-5.6 Terra",
      "generated_at": "2026-10-15",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261015-pulse-20261119-r03-0088",
    "batch_id": "batch-20261015-advance-20261119-r03-gradient-descent-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "eec6ab51dcfcc31b42a95c777fa874a2e14d7369e5afdc52feac4c43f0577c56",
      "family_id": "qf-mod50-gd-boundary",
      "seed": 202611193088,
      "semantic_template": "gd-boundary|{\"mode\":\"oversized_step\",\"model\":{\"curvature\":[3,1],\"point\":[13,1],\"step_size\":[3,1]}}"
    },
    "fields": {
      "title": "Oversized Steps, Stationary Maxima and Lost Feasibility Block Different Inferences",
      "stem": "Use mode=oversized_step, complete model={\"curvature\":3,\"point\":13,\"step_size\":3}. Give (mode, curvature, point, step_size, next_point, objective_before, objective_after, automatic_descent_claim, boundary).",
      "answer": {
        "kind": "expression",
        "value": "(oversized_step, 3, 13, 3, -104, 507/2, 16224, No, positive_but_oversized_step_can_increase_the_objective)",
        "explanation": "A strictly oversized positive step can increase a scalar quadratic objective. A zero gradient may be a strict maximum. A finite trajectory does not certify a limit or global optimum. An unconstrained step leaving the feasible interval is not a projected or constrained gradient update. Keep each actual witness and branch-specific field order. The exact result, retaining the requested order, is (oversized_step, 3, 13, 3, -104, 507/2, 16224, No, positive_but_oversized_step_can_increase_the_objective)."
      },
      "skills": [
        "Oversized Steps, Stationary Maxima and Lost Feasibility Block Different Inferences"
      ],
      "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."
    }
  },
  "givens": [
    {
      "id": "G001",
      "text": {
        "zh-Hant": "standard Euclidean coordinate order、正步長與完整gradient update。操作=gd-boundary；明示資料={\"mode\":\"oversized_step\",\"model\":{\"curvature\":3,\"point\":13,\"step_size\":3}}；請依 exact_ordered_tuple_declared_by_interface 回答。",
        "en": "Use mode=oversized_step, complete model={\"curvature\":3,\"point\":13,\"step_size\":3}. Give (mode, curvature, point, step_size, next_point, objective_before, objective_after, automatic_descent_claim, boundary)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [gd-boundary]",
      "after": "derived = [[mode, curvature, point, step_size, next_point, objective_before, objective_after, automatic_descent_claim, boundary]]",
      "relation": "implies",
      "rule_id": "source_ordered_fields_without_JS",
      "conditions": [],
      "explanation": {
        "zh-Hant": "直接明列此操作與mode完整欄序，不依JavaScript、不由答案形狀猜角色；布林、字串、null與未作聲稱保持不同。",
        "en": "List the complete operation/mode field order without JavaScript or answer-shape inference;Boolean,string,null and an unclaimed result remain distinct."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。",
          "en": "Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "GD boundary ORIGINAL upper2 over curvature := div(2, 3)",
      "after": "GD boundary ORIGINAL upper2 over curvature = 2/3",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL upper2 over curvature，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL upper2 over curvature with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "2",
          "3"
        ],
        "output": "2/3",
        "label": "GD boundary ORIGINAL upper2 over curvature"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "GD boundary ORIGINAL gradient := mul(3, 13)",
      "after": "GD boundary ORIGINAL gradient = 39",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL gradient，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL gradient with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "3",
          "13"
        ],
        "output": "39",
        "label": "GD boundary ORIGINAL gradient"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "GD boundary ORIGINAL alpha gradient := mul(3, 39)",
      "after": "GD boundary ORIGINAL alpha gradient = 117",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL alpha gradient，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL alpha gradient with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "3",
          "39"
        ],
        "output": "117",
        "label": "GD boundary ORIGINAL alpha gradient"
      }
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "GD boundary ORIGINAL next := sub(13, 117)",
      "after": "GD boundary ORIGINAL next = -104",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL next，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL next with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "13",
          "117"
        ],
        "output": "-104",
        "label": "GD boundary ORIGINAL next"
      }
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "GD boundary ORIGINAL before SQUARE := mul(13, 13)",
      "after": "GD boundary ORIGINAL before SQUARE = 169",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL before SQUARE，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL before SQUARE with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "13",
          "13"
        ],
        "output": "169",
        "label": "GD boundary ORIGINAL before SQUARE"
      }
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "GD boundary ORIGINAL before diagonal := mul(3, 169)",
      "after": "GD boundary ORIGINAL before diagonal = 507",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL before diagonal，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL before diagonal with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "3",
          "169"
        ],
        "output": "507",
        "label": "GD boundary ORIGINAL before diagonal"
      }
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "GD boundary ORIGINAL before half := div(507, 2)",
      "after": "GD boundary ORIGINAL before half = 507/2",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL before half，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL before half with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "507",
          "2"
        ],
        "output": "507/2",
        "label": "GD boundary ORIGINAL before half"
      }
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "GD boundary ORIGINAL after SQUARE := mul(-104, -104)",
      "after": "GD boundary ORIGINAL after SQUARE = 10816",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL after SQUARE，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL after SQUARE with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "-104",
          "-104"
        ],
        "output": "10816",
        "label": "GD boundary ORIGINAL after SQUARE"
      }
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "GD boundary ORIGINAL after diagonal := mul(3, 10816)",
      "after": "GD boundary ORIGINAL after diagonal = 32448",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL after diagonal，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL after diagonal with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "mul",
        "inputs": [
          "3",
          "10816"
        ],
        "output": "32448",
        "label": "GD boundary ORIGINAL after diagonal"
      }
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "GD boundary ORIGINAL after half := div(32448, 2)",
      "after": "GD boundary ORIGINAL after half = 16224",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "以原始角色與已證中間量精確代值，不用近似或自洽但換過的操作數；額外教學代數不另縮來源域。",
        "en": "Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 GD boundary ORIGINAL after half，不以小數近似替代。",
          "en": "Recompute GD boundary ORIGINAL after half with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "div",
        "inputs": [
          "32448",
          "2"
        ],
        "output": "16224",
        "label": "GD boundary ORIGINAL after half"
      }
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "source roles = [3, 13, 3, 2/3]",
      "after": "derived = [39, -104, 507/2, 16224, 否]",
      "relation": "implies",
      "rule_id": "GD_STRICT_oversized_nonzero_scalar_actual_increase",
      "conditions": [],
      "explanation": {
        "zh-Hant": "x_next=(1-alpha*c)x；alpha>2/c使|1-alpha*c|>1，且x非零，所以objective實際增加。alpha=2/c只是等值邊界，不是這個strict witness。",
        "en": "x_next=(1-alpha*c)x.With alpha>2/c,|1-alpha*c|>1 and x is nonzero,so the objective actually increases.Equality alpha=2/c is not this strict witness."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。",
          "en": "Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      "oversized_step",
      "3",
      "13",
      "3",
      "-104",
      "507/2",
      "16224",
      false,
      "positive_but_oversized_step_can_increase_the_objective"
    ]
  },
  "conclusion": {
    "canonical_value": "(oversized_step, 3, 13, 3, -104, 507/2, 16224, 否, positive_but_oversized_step_can_increase_the_objective)",
    "explanation": {
      "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。",
      "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged."
    }
  },
  "definition_note": {
    "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。",
    "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate."
  },
  "source": {
    "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db",
    "question_binding": {
      "batch_id": "batch-20261015-advance-20261119-r03-gradient-descent-foundations",
      "batch_path": "public/data/questions/batches/batch-20261015-advance-20261119-r03-gradient-descent-foundations/questions.jsonl",
      "batch_sha256": "ab1c07c8672115b16a6477b3ab604a2116f08a2db6bf163d8cbf723885ab4189",
      "original_line": 88,
      "original_line_sha256": "f60d352890685ba798dbb964ef3763430d237432d2d4faaf6b8cddd00c860c93",
      "question_compact_sha256": "eec6ab51dcfcc31b42a95c777fa874a2e14d7369e5afdc52feac4c43f0577c56",
      "english_row_compact_sha256": "6a918115ceae8d043ef0be827f5fe731b4a31cbfc5ad35288c03a9b71d1a804e",
      "english_manifest_path": "public/data/i18n/editions/batch-20261015-advance-20261119-r03-gradient-descent-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261015-advance-20261119-r03-gradient-descent-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-gradient-descent": {
        "sha256": "b886e6f39050667744f8b88cc6e5d065b39d33d9bbcaf87612a4129ae035973b",
        "english_sha256": "0e010c35c5db93d7d0e7c33c6218d6f9ae774248a498ad97fc98c2be454a1fef",
        "original_path": "public/data/mko/gradient-descent.json",
        "english_path": "public/data/i18n/editions/mko-gradient-descent.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "ad40cc18f9292c43924a7679f3af46574a5284aa5447f5f7f78a0de98840acb8",
    "original_candidate_sha256": "45e8d9d96b5845ee5dc3200c3c285177a62f2471627d5567128e1cc7151ff783",
    "original_candidate_line_sha256": "45e8d9d96b5845ee5dc3200c3c285177a62f2471627d5567128e1cc7151ff783"
  },
  "historical_source_state": {
    "review_state": {
      "derivation": "candidate_authored_and_locally_checked",
      "source_question_state": "candidate",
      "independent_AI_or_human_review": "NOT_PERFORMED",
      "formalization": "not_formalized",
      "Lean": "NOT_RUN"
    },
    "scope_note": {
      "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。",
      "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged."
    },
    "label": "Frozen producer metadata; current per-question review is separate below."
  },
  "revision": {
    "id": "review-20261026-010-p55",
    "review_date": "2026-10-26",
    "owner_authorized_reader_publication": true,
    "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.",
    "review_receipts": {
      "semantic_review_sha256": "0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54",
      "question_first_witness_sha256": "09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 12,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "441df565134bc213c009a5ae40abb6dc8f77c26b9eb3c9d19fe95dbe77826f6e",
      "arithmetic_steps": 10
    },
    "uses_answer_as_premise": false,
    "human_review": "NOT_PERFORMED",
    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
  }
}