# Question 35811: Probability Variance after Scaling [Return to catalogue page 180](https://ocme.evemisslab.com/en/questions/page/180/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261004-advance-20261005-r07-variance-foundations/#q-20261004-advance-20261005-r07-variance-0061) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0070-35811 · q-20261004-advance-20261005-r07-variance-0061 ## Original question and givens The nonempty finite sample space is S={0, 1, 2, 3}, with event family F=𝒫(S). The total function X:S→R has table {(0, 0), (1, 0), (2, 12), (3, 1009)}. In the displayed order of S, the nonnegative probability weights are [1/(18), 12/(18), 5/(18), 0/(18)], summing exactly to one. Put Z=(1)X. Find Var(Z)=E[(Z−E[Z])²] exactly as a reduced positive-denominator fraction. This is probability-distribution variance, not sample variance with an n−1 denominator. - G001 — The nonempty finite sample space is S={0, 1, 2, 3}, with event family F=𝒫(S). The total function X:S→R has table {(0, 0), (1, 0), (2, 12), (3, 1009)}. In the displayed order of S, the nonnegative probability weights are [1/(18), 12/(18), 5/(18), 0/(18)], summing exactly to one. Put Z=(1)X. Find Var(Z)=E[(Z−E[Z])²] exactly as a reduced positive-denominator fraction. This is probability-distribution variance, not sample variance with an n−1 denominator. ## Definition and scope 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. - [mko-variance](https://ocme.evemisslab.com/en/mko/mko-variance/) ## Step-by-step derivation S001 · impliesBefore source roles = [qf-variance-scale, [F, S, denominator, k, operation, values, weights]] After derived = [variance, scale_variance, null] Conditions: none Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules. Step identifiers and dependenciesRule: R70_SOURCE_bank_specific_interface · Uses: G001 S002 · calculationBefore Variance ORIGINAL nonnegative RAW weights sum := sum(1, 12, 5, 0) After Variance ORIGINAL nonnegative RAW weights sum = 18 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S001 S003 · impliesBefore source roles = [[0, 1, 2, 3], powerset(S), [0, 0, 12, 1009], [1, 12, 5, 0], 18, 1, null] After derived = [Yes] Conditions: none Type ALL RAW values/weights EVEN at zero weight.S is nonempty/distinct,F is powerset(S),weights are nonnegative and sum to q>0.Keep values/weights aligned to ORIGINAL S slots;do not sort independently.Type RAW c/k as well. Step identifiers and dependenciesRule: Variance_WHOLE_normalized_model_ORIGINAL_slot_alignment · Uses: G001, S002 S004 · calculationBefore Variance transformed ORIGINAL value i=0 := mul(1, 0) After Variance transformed ORIGINAL value i=0 = 0 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S003 S005 · calculationBefore Variance weight times transformed value i=0 := mul(1, 0) After Variance weight times transformed value i=0 = 0 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S004 S006 · impliesBefore source roles = [0, 0, 0, 1, 1, null] After derived = [0, 1/18] Conditions: none For EACH ORIGINAL slot,set Y=X,X+c or kX while probability remains w/q.Derived values may exceed SAFE and are not recapped as RAW.Zero-weight slots remain in the source but contribute nothing. Step identifiers and dependenciesRule: Variance_EACH_slot_transformation_preserves_probability · Uses: G001, S005 S007 · calculationBefore Variance transformed ORIGINAL value i=1 := mul(1, 0) After Variance transformed ORIGINAL value i=1 = 0 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S006 S008 · calculationBefore Variance weight times transformed value i=1 := mul(12, 0) After Variance weight times transformed value i=1 = 0 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S007 S009 · impliesBefore source roles = [1, 1, 0, 12, 1, null] After derived = [0, 2/3] Conditions: none For EACH ORIGINAL slot,set Y=X,X+c or kX while probability remains w/q.Derived values may exceed SAFE and are not recapped as RAW.Zero-weight slots remain in the source but contribute nothing. Step identifiers and dependenciesRule: Variance_EACH_slot_transformation_preserves_probability · Uses: G001, S008 S010 · calculationBefore Variance transformed ORIGINAL value i=2 := mul(1, 12) After Variance transformed ORIGINAL value i=2 = 12 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S009 S011 · calculationBefore Variance weight times transformed value i=2 := mul(5, 12) After Variance weight times transformed value i=2 = 60 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S010 S012 · impliesBefore source roles = [2, 2, 12, 5, 1, null] After derived = [12, 5/18] Conditions: none For EACH ORIGINAL slot,set Y=X,X+c or kX while probability remains w/q.Derived values may exceed SAFE and are not recapped as RAW.Zero-weight slots remain in the source but contribute nothing. Step identifiers and dependenciesRule: Variance_EACH_slot_transformation_preserves_probability · Uses: G001, S011 S013 · calculationBefore Variance transformed ORIGINAL value i=3 := mul(1, 1009) After Variance transformed ORIGINAL value i=3 = 1009 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S012 S014 · calculationBefore Variance weight times transformed value i=3 := mul(0, 1009) After Variance weight times transformed value i=3 = 0 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S013 S015 · impliesBefore source roles = [3, 3, 1009, 0, 1, null] After derived = [1009, 0] Conditions: none For EACH ORIGINAL slot,set Y=X,X+c or kX while probability remains w/q.Derived values may exceed SAFE and are not recapped as RAW.Zero-weight slots remain in the source but contribute nothing. Step identifiers and dependenciesRule: Variance_EACH_slot_transformation_preserves_probability · Uses: G001, S014 S016 · calculationBefore Variance mean numerator sum wY := sum(0, 0, 60, 0) After Variance mean numerator sum wY = 60 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S015 S017 · calculationBefore Variance exact expectation M over q := div(60, 18) After Variance exact expectation M over q = 10/3 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S016 S018 · calculationBefore Variance i=0 Y times q := mul(0, 18) After Variance i=0 Y times q = 0 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S017 S019 · calculationBefore Variance i=0 centered integer numerator := sub(0, 60) After Variance i=0 centered integer numerator = -60 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S018 S020 · calculationBefore Variance i=0 centered numerator squared := mul(-60, -60) After Variance i=0 centered numerator squared = 3600 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S019 S021 · calculationBefore Variance i=0 weight times squared numerator := mul(1, 3600) After Variance i=0 weight times squared numerator = 3600 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S020 S022 · calculationBefore Variance i=1 Y times q := mul(0, 18) After Variance i=1 Y times q = 0 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S021 S023 · calculationBefore Variance i=1 centered integer numerator := sub(0, 60) After Variance i=1 centered integer numerator = -60 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S022 S024 · calculationBefore Variance i=1 centered numerator squared := mul(-60, -60) After Variance i=1 centered numerator squared = 3600 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S023 S025 · calculationBefore Variance i=1 weight times squared numerator := mul(12, 3600) After Variance i=1 weight times squared numerator = 43200 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S024 S026 · calculationBefore Variance i=2 Y times q := mul(12, 18) After Variance i=2 Y times q = 216 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S025 S027 · calculationBefore Variance i=2 centered integer numerator := sub(216, 60) After Variance i=2 centered integer numerator = 156 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S026 S028 · calculationBefore Variance i=2 centered numerator squared := mul(156, 156) After Variance i=2 centered numerator squared = 24336 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S027 S029 · calculationBefore Variance i=2 weight times squared numerator := mul(5, 24336) After Variance i=2 weight times squared numerator = 121680 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S028 S030 · calculationBefore Variance i=3 Y times q := mul(1009, 18) After Variance i=3 Y times q = 18162 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S029 S031 · calculationBefore Variance i=3 centered integer numerator := sub(18162, 60) After Variance i=3 centered integer numerator = 18102 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S030 S032 · calculationBefore Variance i=3 centered numerator squared := mul(18102, 18102) After Variance i=3 centered numerator squared = 327682404 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S031 S033 · calculationBefore Variance i=3 weight times squared numerator := mul(0, 327682404) After Variance i=3 weight times squared numerator = 0 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S032 S034 · calculationBefore Variance sum ALL weighted squared numerators := sum(3600, 43200, 121680, 0) After Variance sum ALL weighted squared numerators = 168480 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S033 S035 · calculationBefore Variance denominator q squared := mul(18, 18) After Variance denominator q squared = 324 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S034 S036 · calculationBefore Variance denominator q cubed binary second factor := mul(324, 18) After Variance denominator q cubed binary second factor = 5832 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S035 S037 · calculationBefore Variance probability population centered sum over q cubed := div(168480, 5832) After Variance probability population centered sum over q cubed = 260/9 Conditions: none This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S036 S038 · impliesBefore source roles = [[0, 0, 12, 1009], [1, 12, 5, 0], 18, 10/3, 168480, 5832] After derived = [260/9, [0, 12], No] Conditions: none E[Y]=M/q and Var=Σ(w/q)(Y−M/q)²=C/q³.Every term is nonnegative,so the sum is0 exactly when EVERY positive-weight Y equals the mean,equivalently constancy on positive support.Zero-weight values may differ.This is NOT n−1 sample variance. Step identifiers and dependenciesRule: Variance_CENTERED_definition_and_positive_support_zero_equivalence · Uses: G001, S037 S039 · impliesBefore source roles = [scale_variance, 1, null] After derived = [260/9] Conditions: none Under a shift,the mean also shifts by c,leaving deviations unchanged.Under scaling,the mean scales by k and squared deviations by k²,including negative/zero k.The ACTUAL Y values were fully recomputed;the law does not excuse untyped c/k. Step identifiers and dependenciesRule: Variance_SHIFT_SCALE_law_with_conditions · Uses: G001, S038 ## Reverse checks - S039 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S038 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S037 · premise_and_result_audit — Recompute Variance probability population centered sum over q cubed with exact rational arithmetic, not rounded decimals. - S036 · premise_and_result_audit — Recompute Variance denominator q cubed binary second factor with exact rational arithmetic, not rounded decimals. - S035 · premise_and_result_audit — Recompute Variance denominator q squared with exact rational arithmetic, not rounded decimals. - S034 · premise_and_result_audit — Recompute Variance sum ALL weighted squared numerators with exact rational arithmetic, not rounded decimals. - S033 · premise_and_result_audit — Recompute Variance i=3 weight times squared numerator with exact rational arithmetic, not rounded decimals. - S032 · premise_and_result_audit — Recompute Variance i=3 centered numerator squared with exact rational arithmetic, not rounded decimals. - S031 · premise_and_result_audit — Recompute Variance i=3 centered integer numerator with exact rational arithmetic, not rounded decimals. - S030 · premise_and_result_audit — Recompute Variance i=3 Y times q with exact rational arithmetic, not rounded decimals. - S029 · premise_and_result_audit — Recompute Variance i=2 weight times squared numerator with exact rational arithmetic, not rounded decimals. - S028 · premise_and_result_audit — Recompute Variance i=2 centered numerator squared with exact rational arithmetic, not rounded decimals. - S027 · premise_and_result_audit — Recompute Variance i=2 centered integer numerator with exact rational arithmetic, not rounded decimals. - S026 · premise_and_result_audit — Recompute Variance i=2 Y times q with exact rational arithmetic, not rounded decimals. - S025 · premise_and_result_audit — Recompute Variance i=1 weight times squared numerator with exact rational arithmetic, not rounded decimals. - S024 · premise_and_result_audit — Recompute Variance i=1 centered numerator squared with exact rational arithmetic, not rounded decimals. - S023 · premise_and_result_audit — Recompute Variance i=1 centered integer numerator with exact rational arithmetic, not rounded decimals. - S022 · premise_and_result_audit — Recompute Variance i=1 Y times q with exact rational arithmetic, not rounded decimals. - S021 · premise_and_result_audit — Recompute Variance i=0 weight times squared numerator with exact rational arithmetic, not rounded decimals. - S020 · premise_and_result_audit — Recompute Variance i=0 centered numerator squared with exact rational arithmetic, not rounded decimals. - S019 · premise_and_result_audit — Recompute Variance i=0 centered integer numerator with exact rational arithmetic, not rounded decimals. - S018 · premise_and_result_audit — Recompute Variance i=0 Y times q with exact rational arithmetic, not rounded decimals. - S017 · premise_and_result_audit — Recompute Variance exact expectation M over q with exact rational arithmetic, not rounded decimals. - S016 · premise_and_result_audit — Recompute Variance mean numerator sum wY with exact rational arithmetic, not rounded decimals. - S015 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S014 · premise_and_result_audit — Recompute Variance weight times transformed value i=3 with exact rational arithmetic, not rounded decimals. - S013 · premise_and_result_audit — Recompute Variance transformed ORIGINAL value i=3 with exact rational arithmetic, not rounded decimals. - S012 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S011 · premise_and_result_audit — Recompute Variance weight times transformed value i=2 with exact rational arithmetic, not rounded decimals. - S010 · premise_and_result_audit — Recompute Variance transformed ORIGINAL value i=2 with exact rational arithmetic, not rounded decimals. - S009 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S008 · premise_and_result_audit — Recompute Variance weight times transformed value i=1 with exact rational arithmetic, not rounded decimals. - S007 · premise_and_result_audit — Recompute Variance transformed ORIGINAL value i=1 with exact rational arithmetic, not rounded decimals. - S006 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S005 · premise_and_result_audit — Recompute Variance weight times transformed value i=0 with exact rational arithmetic, not rounded decimals. - S004 · premise_and_result_audit — Recompute Variance transformed ORIGINAL value i=0 with exact rational arithmetic, not rounded decimals. - S003 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S002 · premise_and_result_audit — Recompute Variance ORIGINAL nonnegative RAW weights sum with exact rational arithmetic, not rounded decimals. - S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. ## Result 260/9 The full substitutions and premise checks give the original answer; source identity,format and status are unchanged. ## This question review and source binding Review date: 2026-10-26 Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: fd538cd1bba05afcbbdf7353b5504495aa7ca31e52aad07ad15cd2c74d81e29f - candidate record SHA-256: d690b5d34967c0ee7f6a3461feecb446c36f6e09992682a1be3513e77b85520e - semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80 - question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261004-advance-20261005-r07-variance-0061.json)