{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261010-advance-20261014-r06-absolute-value-0090", "pilot_number": "R0059-30265", "number": 30265, "family_id": "qf-density14-absolute-preimage-rational-audit", "title": { "zh-Hant": "第 30265 題：絕對值目標的根與代入", "en": "Question 30265: Absolute-Value Target Roots and Candidate Audit" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261010-advance-20261014-r06-absolute-value-0090", "batch_id": "batch-20261010-advance-20261014-r06-absolute-value-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-absolute-value" ], "title_zh": "絕對值目標的根與代入", "stem_zh": "有理嵌入的絕對值協議；r=13/2，queries=[-13/2, 13/2, 15/2]。依序答 (r非負資格, |x|=r遞增根列表, 三個abs(query), 三個等於r資格)。", "answer": { "kind": "expression", "value": "(是, [-13/2, 13/2], [13/2, 13/2, 15/2], [是, 是, 否])", "explanation_zh": "絕對值目標資格根與代入=(是, [-13/2, 13/2], [13/2, 13/2, 15/2], [是, 是, 否])。負目標無根，零只有0，正目標有正負兩根；再逐一精確代入。有限分段核對非全部實數性質證明。" }, "difficulty": { "band": "lower_secondary", "level": 2, "skills": [ "絕對值目標的根與代入" ] }, "variant": { "family_id": "qf-density14-absolute-preimage-rational-audit", "seed": 202610146090, "parameters": { "r": [ 13, 2 ], "queries": [ [ -13, 2 ], [ 13, 2 ], [ 15, 2 ] ], "domain": "finite_rational_absolute_protocol", "operation": "density14_absolute_preimage_rational_audit", "semantic_template": "qf-density14-absolute-preimage-rational-audit/[\"13/2\",[\"13/2\",\"13/2\",\"15/2\"]]" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_integer_rational_arithmetic", "producer_finite_enumeration", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-10", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261010-advance-20261014-r06-absolute-value-0090", "batch_id": "batch-20261010-advance-20261014-r06-absolute-value-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "5fc4da465b037d2c85ac3855ad27d595e26184857f023ac3a2f5efa97b6a8551", "family_id": "qf-density14-absolute-preimage-rational-audit", "seed": 202610146090, "semantic_template": "qf-density14-absolute-preimage-rational-audit/[\"13/2\",[\"13/2\",\"13/2\",\"15/2\"]]" }, "fields": { "title": "Absolute-Value Target Roots and Candidate Audit", "stem": "Use exact rational absolute values embedded in R; negative representation denominators are normalized before deciding signs. Target r=13/2, ordered queries=[-13/2, 13/2, 15/2]. Give (is r nonnegative?, increasing roots of |x|=r, three absolute query values, three equality-to-r values).", "answer": { "kind": "expression", "value": "(Yes, [-13/2, 13/2], [13/2, 13/2, 15/2], [Yes, Yes, No])", "explanation": "A negative target has no roots, zero has only root zero, and a positive target has two signed roots; substitute each candidate exactly. The exact result, retaining the requested order, is (Yes, [-13/2, 13/2], [13/2, 13/2, 15/2], [Yes, Yes, No])." }, "skills": [ "Absolute-Value Target Roots and Candidate Audit" ], "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": "有理嵌入的絕對值協議；r=13/2，queries=[-13/2, 13/2, 15/2]。依序答 (r非負資格, |x|=r遞增根列表, 三個abs(query), 三個等於r資格)。", "en": "Use exact rational absolute values embedded in R; negative representation denominators are normalized before deciding signs. Target r=13/2, ordered queries=[-13/2, 13/2, 15/2]. Give (is r nonnegative?, increasing roots of |x|=r, three absolute query values, three equality-to-r values)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-density14-absolute-preimage-rational-audit, density14_absolute_preimage_rational_audit, finite_rational_absolute_protocol]", "after": "derived = [[target_nonnegative, ALL_increasing_roots, ALL_absolute_query_values, ALL_equal_target_flags]]", "relation": "implies", "rule_id": "R59_EXACT_family_domain_FULLprefix_operation_and_answer_roles", "conditions": [], "explanation": { "zh-Hant": "保原bank的完整operation前綴、domain及輸出欄序；frame只用orthogonal_equal_unit，角度unit只用degrees。分數整數保/1；不增不存在的參數，不改原中英來源。", "en": "Retain the ORIGINAL bank full operation prefix,domain and ordered answer roles.Use orthogonal_equal_unit only where a frame is declared,and degrees where an angle unit is declared.Integer fractions retain/1.Do not invent parameters or alter original bilingual sources." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [Absolute target r, [13, 2]]", "after": "derived = [13/2, 13, 2]", "relation": "implies", "rule_id": "Absolute_RAW_SAFE_pair_NONZERO_den_normalize_SIGN_and_gcd", "conditions": [], "explanation": { "zh-Hant": "原pair兩數SAFE且den非0；這個bank允許負den，先正分母約分才按值選sign。不套primitive正den或STR22 component cap。", "en": "Require a RAW SAFE pair with nonzero denominator.This bank ALLOWS negative denominators;normalize sign/gcd BEFORE deciding the value sign.Do not import a primitive positive-denominator rule or a STR22 component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [Absolute ORIGINAL queries slot0, [-13, 2]]", "after": "derived = [-13/2, -13, 2]", "relation": "implies", "rule_id": "Absolute_RAW_SAFE_pair_NONZERO_den_normalize_SIGN_and_gcd", "conditions": [], "explanation": { "zh-Hant": "原pair兩數SAFE且den非0；這個bank允許負den，先正分母約分才按值選sign。不套primitive正den或STR22 component cap。", "en": "Require a RAW SAFE pair with nonzero denominator.This bank ALLOWS negative denominators;normalize sign/gcd BEFORE deciding the value sign.Do not import a primitive positive-denominator rule or a STR22 component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [Absolute ORIGINAL queries slot1, [13, 2]]", "after": "derived = [13/2, 13, 2]", "relation": "implies", "rule_id": "Absolute_RAW_SAFE_pair_NONZERO_den_normalize_SIGN_and_gcd", "conditions": [], "explanation": { "zh-Hant": "原pair兩數SAFE且den非0；這個bank允許負den，先正分母約分才按值選sign。不套primitive正den或STR22 component cap。", "en": "Require a RAW SAFE pair with nonzero denominator.This bank ALLOWS negative denominators;normalize sign/gcd BEFORE deciding the value sign.Do not import a primitive positive-denominator rule or a STR22 component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "source roles = [Absolute ORIGINAL queries slot2, [15, 2]]", "after": "derived = [15/2, 15, 2]", "relation": "implies", "rule_id": "Absolute_RAW_SAFE_pair_NONZERO_den_normalize_SIGN_and_gcd", "conditions": [], "explanation": { "zh-Hant": "原pair兩數SAFE且den非0；這個bank允許負den，先正分母約分才按值選sign。不套primitive正den或STR22 component cap。", "en": "Require a RAW SAFE pair with nonzero denominator.This bank ALLOWS negative denominators;normalize sign/gcd BEFORE deciding the value sign.Do not import a primitive positive-denominator rule or a STR22 component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "Absolute ORIGINAL queries slot0 ORIGINAL negative branch negation := sub(0, -13/2)", "after": "Absolute ORIGINAL queries slot0 ORIGINAL negative branch negation = 13/2", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute ORIGINAL queries slot0 ORIGINAL negative branch negation，不以小數近似替代。", "en": "Recompute Absolute ORIGINAL queries slot0 ORIGINAL negative branch negation with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "0", "-13/2" ], "output": "13/2", "label": "Absolute ORIGINAL queries slot0 ORIGINAL negative branch negation" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "source roles = [Absolute ORIGINAL queries slot0, -13/2]", "after": "derived = [否, 13/2]", "relation": "implies", "rule_id": "Absolute_value_normalized_sign_branch_ZERO_is_nonnegative", "conditions": [], "explanation": { "zh-Hant": "以已正規化數值的sign選分段：x>=0保x，x<0取0-x；zero在非負分支，不因raw負分母而誤判。", "en": "Choose the branch by the NORMALIZED value:x>=0 keeps x;for x<0 use0-x.Zero is in the nonnegative branch;do not misclassify a raw negative denominator." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "source roles = [Absolute ORIGINAL queries slot1, 13/2]", "after": "derived = [是, 13/2]", "relation": "implies", "rule_id": "Absolute_value_normalized_sign_branch_ZERO_is_nonnegative", "conditions": [], "explanation": { "zh-Hant": "以已正規化數值的sign選分段：x>=0保x，x<0取0-x；zero在非負分支，不因raw負分母而誤判。", "en": "Choose the branch by the NORMALIZED value:x>=0 keeps x;for x<0 use0-x.Zero is in the nonnegative branch;do not misclassify a raw negative denominator." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "source roles = [Absolute ORIGINAL queries slot2, 15/2]", "after": "derived = [是, 15/2]", "relation": "implies", "rule_id": "Absolute_value_normalized_sign_branch_ZERO_is_nonnegative", "conditions": [], "explanation": { "zh-Hant": "以已正規化數值的sign選分段：x>=0保x，x<0取0-x；zero在非負分支，不因raw負分母而誤判。", "en": "Choose the branch by the NORMALIZED value:x>=0 keeps x;for x<0 use0-x.Zero is in the nonnegative branch;do not misclassify a raw negative denominator." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "Absolute ORIGINAL magnitude minus target slot0 := sub(13/2, 13/2)", "after": "Absolute ORIGINAL magnitude minus target slot0 = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute ORIGINAL magnitude minus target slot0，不以小數近似替代。", "en": "Recompute Absolute ORIGINAL magnitude minus target slot0 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "13/2", "13/2" ], "output": "0", "label": "Absolute ORIGINAL magnitude minus target slot0" } }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "Absolute ORIGINAL magnitude minus target slot1 := sub(13/2, 13/2)", "after": "Absolute ORIGINAL magnitude minus target slot1 = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute ORIGINAL magnitude minus target slot1，不以小數近似替代。", "en": "Recompute Absolute ORIGINAL magnitude minus target slot1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "13/2", "13/2" ], "output": "0", "label": "Absolute ORIGINAL magnitude minus target slot1" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "Absolute ORIGINAL magnitude minus target slot2 := sub(15/2, 13/2)", "after": "Absolute ORIGINAL magnitude minus target slot2 = 1", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原角色精確代值，不作浮點近似；SAFE只驗raw輸入，衍生整數／有理數不截斷，不套其他銀行的component cap。", "en": "Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Absolute ORIGINAL magnitude minus target slot2，不以小數近似替代。", "en": "Recompute Absolute ORIGINAL magnitude minus target slot2 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sub", "inputs": [ "15/2", "13/2" ], "output": "1", "label": "Absolute ORIGINAL magnitude minus target slot2" } }, { "id": "S013", "uses": [ "G001", "S012" ], "before": "source roles = [13/2, [-13/2, 13/2, 15/2]]", "after": "derived = [是, [-13/2, 13/2], [13/2, 13/2, 15/2], [是, 是, 否]]", "relation": "implies", "rule_id": "Absolute_preimage_NEGATIVE_target_LEGAL_EMPTY_roots_ZERO_singleton", "conditions": [], "explanation": { "zh-Hant": "|x|非負，負target是合法No/空根集；target0只有0/1，正target有遞增-r,r。仍算三個原query的abs與代入mask，不拒絕負target或去重query位置。", "en": "Since |x|>=0,a negative target is a LEGAL No with an empty root list.At0 the ONLY root is0/1;a positive target gives increasing-r,r.STILL compute all three ORIGINAL absolute query values and masks;do not reject the negative target or deduplicate query positions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、索引與前提反向代回本步，不聲稱可由結論唯一還原輸入。有限精確核對、獨立審查、形式證明及發布資格分開。", "en": "Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate." } }, "arithmetic": null } ], "math_model": { "result": [ true, [ "-13/2", "13/2" ], [ "13/2", "13/2", "15/2" ], [ true, true, false ] ] }, "conclusion": { "canonical_value": "(是, [-13/2, 13/2], [13/2, 13/2, 15/2], [是, 是, 否])", "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-20261010-advance-20261014-r06-absolute-value-foundations", "batch_path": "public/data/questions/batches/batch-20261010-advance-20261014-r06-absolute-value-foundations/questions.jsonl", "batch_sha256": "6f64d92445cd0622999a4aea7165b9a1bc243bbea1361e5440354586968dac04", "original_line": 90, "original_line_sha256": "c88711f91b361c23a73650f93bb3e69df1f9087bf51fea05f0f1df106f9f8a41", "question_compact_sha256": "5fc4da465b037d2c85ac3855ad27d595e26184857f023ac3a2f5efa97b6a8551", "english_row_compact_sha256": "d36debff854eb0e89e9473039d6e65cc721888ab29a985c5494b39d5fc82b9eb", "english_manifest_path": "public/data/i18n/editions/batch-20261010-advance-20261014-r06-absolute-value-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261010-advance-20261014-r06-absolute-value-foundations.en.jsonl" }, "mko_bindings": { "mko-absolute-value": { "sha256": "7df0aed9ca41a0e67b84a464f450422348753d1171802220b41a103488fb5f95", "english_sha256": "7f191b7dbbd24ac7ec2a252a08d3178f961ef31414f76098c51f5f01d63473f6", "original_path": "public/data/mko/absolute-value.json", "english_path": "public/data/i18n/editions/mko-absolute-value.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "17d593a551933064f195bd9277d5085fe2b6c98e11cbda0c8aa27d11b7b07949", "original_candidate_sha256": "0771d76bab94ed6e9060c69cb781a608afa737f3c295a6ba07a5167eab80e218", "original_candidate_line_sha256": "0771d76bab94ed6e9060c69cb781a608afa737f3c295a6ba07a5167eab80e218" }, "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-20261026-011-p60", "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": "4c93dea3956f58509e20b3b8bbbf716dbc340b424a2a5177bc04aba9e8ea9ec5", "question_first_witness_sha256": "a5e56e0d64d622d7202840cef7019839c5a99244c602694190779155207dafdf" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 13, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "249af15c60bd88804668497150d3aca7a0fe7902353f38450d86538f2841fd20", "arithmetic_steps": 4 }, "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." } }