Explore related knowledge and questions →
← Question derivation index · Original question batch
R0047-24445 · q-20261015-advance-20261113-r06-gradient-vector-0045
Use dimension=3, raw polynomial terms=[[20, [2, 1, 0]], [21, [0, 1, 1]], [1, [0, 0, 0]]], each [rational coefficient,ordered exponent vector]. Coefficients may be integers or [numerator,denominator]. Exponent/point arities equal the dimension. Combine equal monomials and remove zero coefficients before the canonical symbolic output. Coordinate order and the standard Euclidean basis/metric are fixed. Point=[20/1, 21/2, 22/3]. Give (dimension, canonical_terms, point, coordinate_derivative_polynomials, gradient_values, certificate).
G001 — Use dimension=3, raw polynomial terms=[[20, [2, 1, 0]], [21, [0, 1, 1]], [1, [0, 0, 0]]], each [rational coefficient,ordered exponent vector]. Coefficients may be integers or [numerator,denominator]. Exponent/point arities equal the dimension. Combine equal monomials and remove zero coefficients before the canonical symbolic output. Coordinate order and the standard Euclidean basis/metric are fixed. Point=[20/1, 21/2, 22/3]. Give (dimension, canonical_terms, point, coordinate_derivative_polynomials, gradient_values, certificate).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.
Before
source roles = [gradient-rational-point]
After
derived = [[dimension, canonical_terms, point, coordinate_derivative_polynomials, gradient_values, certificate]]
Conditions: none
List the source field order without JavaScript.Gradient boundary uses its original mode to choose6,8 or7 fields;no padding or answer-derived mode.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
Gradient ORIGINAL monomial coefficient sum0 := sum(0, 20)
After
Gradient ORIGINAL monomial coefficient sum0 = 20
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
source roles = [0, 3, [2, 1, 0], 20]
After
derived = [20]
Conditions: none
Combine only identical ordered exponent vectors;remove zeros after combining and keep fixed Euclidean coordinate order.
Rule: Gradient_original_term_position_and_exponent_arity · Uses: G001, S002
Before
Gradient ORIGINAL monomial coefficient sum1 := sum(0, 21)
After
Gradient ORIGINAL monomial coefficient sum1 = 21
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
source roles = [1, 3, [0, 1, 1], 21]
After
derived = [21]
Conditions: none
Combine only identical ordered exponent vectors;remove zeros after combining and keep fixed Euclidean coordinate order.
Rule: Gradient_original_term_position_and_exponent_arity · Uses: G001, S004
Before
Gradient ORIGINAL monomial coefficient sum2 := sum(0, 1)
After
Gradient ORIGINAL monomial coefficient sum2 = 1
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S005
Before
source roles = [2, 3, [0, 0, 0], 1]
After
derived = [1]
Conditions: none
Combine only identical ordered exponent vectors;remove zeros after combining and keep fixed Euclidean coordinate order.
Rule: Gradient_original_term_position_and_exponent_arity · Uses: G001, S006
Before
source roles = [[[20, [2, 1, 0]], [21, [0, 1, 1]], [1, [0, 0, 0]]]]
After
derived = [3, [[1, [0, 0, 0]], [21, [0, 1, 1]], [20, [2, 1, 0]]]]
Conditions: none
Use source English canonical-exponent order,not numeric tuple order.Complete cancellation may yield an empty canonical list for the zero polynomial.
Rule: Gradient_canonical_nonzero_polynomial_terms_source_order · Uses: G001, S007
Before
source roles = [0, 0, [0, 0, 0], 1]
After
derived = [0]
Conditions: none
Exponent0 means derivative0 in this coordinate,without omitting other coordinates.
Rule: Gradient_constant_in_coordinate_derivative_zero · Uses: G001, S008
Before
source roles = [0, 1, [0, 1, 1], 21]
After
derived = [0]
Conditions: none
Exponent0 means derivative0 in this coordinate,without omitting other coordinates.
Rule: Gradient_constant_in_coordinate_derivative_zero · Uses: G001, S009
Before
Gradient axis0 term2 power-rule coefficient := mul(20, 2)
After
Gradient axis0 term2 power-rule coefficient = 40
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S010
Before
Gradient axis0 derivative combine2 := sum(0, 40)
After
Gradient axis0 derivative combine2 = 40
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S011
Before
source roles = [0, 2, [2, 1, 0], 20, 2]
After
derived = [[1, 1, 0], 40]
Conditions: none
Hold the other variables fixed:the coefficient becomes ck and only this coordinate exponent decreases by1.
Rule: Gradient_coordinate_power_rule_ordered_exponents · Uses: G001, S012
Before
source roles = [1, 0, [0, 0, 0], 1]
After
derived = [0]
Conditions: none
Exponent0 means derivative0 in this coordinate,without omitting other coordinates.
Rule: Gradient_constant_in_coordinate_derivative_zero · Uses: G001, S013
Before
Gradient axis1 term1 power-rule coefficient := mul(21, 1)
After
Gradient axis1 term1 power-rule coefficient = 21
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S014
Before
Gradient axis1 derivative combine1 := sum(0, 21)
After
Gradient axis1 derivative combine1 = 21
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S015
Before
source roles = [1, 1, [0, 1, 1], 21, 1]
After
derived = [[0, 0, 1], 21]
Conditions: none
Hold the other variables fixed:the coefficient becomes ck and only this coordinate exponent decreases by1.
Rule: Gradient_coordinate_power_rule_ordered_exponents · Uses: G001, S016
Before
Gradient axis1 term2 power-rule coefficient := mul(20, 1)
After
Gradient axis1 term2 power-rule coefficient = 20
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S017
Before
Gradient axis1 derivative combine2 := sum(0, 20)
After
Gradient axis1 derivative combine2 = 20
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S018
Before
source roles = [1, 2, [2, 1, 0], 20, 1]
After
derived = [[2, 0, 0], 20]
Conditions: none
Hold the other variables fixed:the coefficient becomes ck and only this coordinate exponent decreases by1.
Rule: Gradient_coordinate_power_rule_ordered_exponents · Uses: G001, S019
Before
source roles = [2, 0, [0, 0, 0], 1]
After
derived = [0]
Conditions: none
Exponent0 means derivative0 in this coordinate,without omitting other coordinates.
Rule: Gradient_constant_in_coordinate_derivative_zero · Uses: G001, S020
Before
Gradient axis2 term1 power-rule coefficient := mul(21, 1)
After
Gradient axis2 term1 power-rule coefficient = 21
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S021
Before
Gradient axis2 derivative combine1 := sum(0, 21)
After
Gradient axis2 derivative combine1 = 21
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S022
Before
source roles = [2, 1, [0, 1, 1], 21, 1]
After
derived = [[0, 1, 0], 21]
Conditions: none
Hold the other variables fixed:the coefficient becomes ck and only this coordinate exponent decreases by1.
Rule: Gradient_coordinate_power_rule_ordered_exponents · Uses: G001, S023
Before
source roles = [2, 2, [2, 1, 0], 20]
After
derived = [0]
Conditions: none
Exponent0 means derivative0 in this coordinate,without omitting other coordinates.
Rule: Gradient_constant_in_coordinate_derivative_zero · Uses: G001, S024
Before
source roles = [3, [[1, [0, 0, 0]], [21, [0, 1, 1]], [20, [2, 1, 0]]]]
After
derived = [[[[40, [1, 1, 0]]], [[21, [0, 0, 1]], [20, [2, 0, 0]]], [[21, [0, 1, 0]]]]]
Conditions: none
The gradient contains all d ordered component polynomials.Polynomial differentiability makes this Euclidean vector represent the differential,not a sampled single direction.
Rule: Gradient_ALL_ordered_coordinate_polynomials · Uses: G001, S025
Before
(20)^1
After
Gradient axis0 term0 coordinate0 power = 20
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S026
Before
Gradient axis0 term0 coordinate0 factor := mul(40, 20)
After
Gradient axis0 term0 coordinate0 factor = 800
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S027
Before
(21/2)^1
After
Gradient axis0 term0 coordinate1 power = 21/2
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S028
Before
Gradient axis0 term0 coordinate1 factor := mul(800, 21/2)
After
Gradient axis0 term0 coordinate1 factor = 8400
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S029
Before
(22/3)^0
After
Gradient axis0 term0 coordinate2 power = 1
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S030
Before
Gradient axis0 term0 coordinate2 factor := mul(8400, 1)
After
Gradient axis0 term0 coordinate2 factor = 8400
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S031
Before
Gradient axis0 cumulative term0 := sum(0, 8400)
After
Gradient axis0 cumulative term0 = 8400
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S032
Before
(20)^0
After
Gradient axis1 term0 coordinate0 power = 1
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S033
Before
Gradient axis1 term0 coordinate0 factor := mul(21, 1)
After
Gradient axis1 term0 coordinate0 factor = 21
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S034
Before
(21/2)^0
After
Gradient axis1 term0 coordinate1 power = 1
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S035
Before
Gradient axis1 term0 coordinate1 factor := mul(21, 1)
After
Gradient axis1 term0 coordinate1 factor = 21
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S036
Before
(22/3)^1
After
Gradient axis1 term0 coordinate2 power = 22/3
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S037
Before
Gradient axis1 term0 coordinate2 factor := mul(21, 22/3)
After
Gradient axis1 term0 coordinate2 factor = 154
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S038
Before
(20)^2
After
Gradient axis1 term1 coordinate0 power = 400
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S039
Before
Gradient axis1 term1 coordinate0 factor := mul(20, 400)
After
Gradient axis1 term1 coordinate0 factor = 8000
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S040
Before
(21/2)^0
After
Gradient axis1 term1 coordinate1 power = 1
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S041
Before
Gradient axis1 term1 coordinate1 factor := mul(8000, 1)
After
Gradient axis1 term1 coordinate1 factor = 8000
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S042
Before
(22/3)^0
After
Gradient axis1 term1 coordinate2 power = 1
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S043
Before
Gradient axis1 term1 coordinate2 factor := mul(8000, 1)
After
Gradient axis1 term1 coordinate2 factor = 8000
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S044
Before
Gradient axis1 cumulative term0 := sum(0, 154)
After
Gradient axis1 cumulative term0 = 154
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S045
Before
Gradient axis1 cumulative term1 := sum(154, 8000)
After
Gradient axis1 cumulative term1 = 8154
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S046
Before
(20)^0
After
Gradient axis2 term0 coordinate0 power = 1
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S047
Before
Gradient axis2 term0 coordinate0 factor := mul(21, 1)
After
Gradient axis2 term0 coordinate0 factor = 21
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S048
Before
(21/2)^1
After
Gradient axis2 term0 coordinate1 power = 21/2
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S049
Before
Gradient axis2 term0 coordinate1 factor := mul(21, 21/2)
After
Gradient axis2 term0 coordinate1 factor = 441/2
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S050
Before
(22/3)^0
After
Gradient axis2 term0 coordinate2 power = 1
Conditions: none
Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity.
Rule: integer_power · Uses: G001, S051
Before
Gradient axis2 term0 coordinate2 factor := mul(441/2, 1)
After
Gradient axis2 term0 coordinate2 factor = 441/2
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S052
Before
Gradient axis2 cumulative term0 := sum(0, 441/2)
After
Gradient axis2 cumulative term0 = 441/2
Conditions: none
Substitute original roles and established intermediates exactly;check nonzero denominators and do not round.
Rule: exact_rational_arithmetic · Uses: G001, S053
Before
source roles = [3, [20, 21/2, 22/3], [[[40, [1, 1, 0]]], [[21, [0, 0, 1]], [20, [2, 0, 0]]], [[21, [0, 1, 0]]]]]
After
derived = [[8400, 8154, 441/2], No, No]
Conditions: none
Evaluate every component at the same point before deciding stationarity.Zero gradient supplies no automatic extremum certificate;No does not deny actual extrema of special cases such as constant functions.
Rule: Gradient_SAME_point_all_coordinates_stationary_not_extremum · Uses: G001, S054
S055 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S054 · premise_and_result_audit — Recompute Gradient axis2 cumulative term0 with exact rational arithmetic, not rounded decimals.S053 · premise_and_result_audit — Recompute Gradient axis2 term0 coordinate2 factor with exact rational arithmetic, not rounded decimals.S052 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S051 · premise_and_result_audit — Recompute Gradient axis2 term0 coordinate1 factor with exact rational arithmetic, not rounded decimals.S050 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S049 · premise_and_result_audit — Recompute Gradient axis2 term0 coordinate0 factor with exact rational arithmetic, not rounded decimals.S048 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S047 · premise_and_result_audit — Recompute Gradient axis1 cumulative term1 with exact rational arithmetic, not rounded decimals.S046 · premise_and_result_audit — Recompute Gradient axis1 cumulative term0 with exact rational arithmetic, not rounded decimals.S045 · premise_and_result_audit — Recompute Gradient axis1 term1 coordinate2 factor with exact rational arithmetic, not rounded decimals.S044 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S043 · premise_and_result_audit — Recompute Gradient axis1 term1 coordinate1 factor with exact rational arithmetic, not rounded decimals.S042 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S041 · premise_and_result_audit — Recompute Gradient axis1 term1 coordinate0 factor with exact rational arithmetic, not rounded decimals.S040 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S039 · premise_and_result_audit — Recompute Gradient axis1 term0 coordinate2 factor with exact rational arithmetic, not rounded decimals.S038 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S037 · premise_and_result_audit — Recompute Gradient axis1 term0 coordinate1 factor with exact rational arithmetic, not rounded decimals.S036 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S035 · premise_and_result_audit — Recompute Gradient axis1 term0 coordinate0 factor with exact rational arithmetic, not rounded decimals.S034 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S033 · premise_and_result_audit — Recompute Gradient axis0 cumulative term0 with exact rational arithmetic, not rounded decimals.S032 · premise_and_result_audit — Recompute Gradient axis0 term0 coordinate2 factor with exact rational arithmetic, not rounded decimals.S031 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S030 · premise_and_result_audit — Recompute Gradient axis0 term0 coordinate1 factor with exact rational arithmetic, not rounded decimals.S029 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S028 · premise_and_result_audit — Recompute Gradient axis0 term0 coordinate0 factor with exact rational arithmetic, not rounded decimals.S027 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S026 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S025 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S024 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S023 · premise_and_result_audit — Recompute Gradient axis2 derivative combine1 with exact rational arithmetic, not rounded decimals.S022 · premise_and_result_audit — Recompute Gradient axis2 term1 power-rule coefficient with exact rational arithmetic, not rounded decimals.S021 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S020 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S019 · premise_and_result_audit — Recompute Gradient axis1 derivative combine2 with exact rational arithmetic, not rounded decimals.S018 · premise_and_result_audit — Recompute Gradient axis1 term2 power-rule coefficient with exact rational arithmetic, not rounded decimals.S017 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S016 · premise_and_result_audit — Recompute Gradient axis1 derivative combine1 with exact rational arithmetic, not rounded decimals.S015 · premise_and_result_audit — Recompute Gradient axis1 term1 power-rule coefficient with exact rational arithmetic, not rounded decimals.S014 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S013 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S012 · premise_and_result_audit — Recompute Gradient axis0 derivative combine2 with exact rational arithmetic, not rounded decimals.S011 · premise_and_result_audit — Recompute Gradient axis0 term2 power-rule coefficient with exact rational arithmetic, not rounded decimals.S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S006 · premise_and_result_audit — Recompute Gradient ORIGINAL monomial coefficient sum2 with exact rational arithmetic, not rounded decimals.S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S004 · premise_and_result_audit — Recompute Gradient ORIGINAL monomial coefficient sum1 with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S002 · premise_and_result_audit — Recompute Gradient ORIGINAL monomial coefficient sum0 with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.(3, [[1, [0, 0, 0]], [21, [0, 1, 1]], [20, [2, 1, 0]]], [20, 21/2, 22/3], [[[40, [1, 1, 0]]], [[21, [0, 0, 1]], [20, [2, 0, 0]]], [[21, [0, 1, 0]]]], [8400, 8154, 441/2], exact_rational_coordinate_evaluation)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 4485bd5fb3f516e726d7dde06be6974cd85cfae1e76965a5b86299e569a03e2ecandidate record SHA-256: 6d9d3bbdfc1b31cd85d3ebc0a501207adfb726dd3e49baa5f3642b7b4ebd6cf5semantic review receipt SHA-256: 9b43b9823e9bd2478d6caa5b57ffed161c2c8956af86974e901d5662ad994386question-first witness SHA-256: eb97596068e2d5648033bab2b8f6ca9b653bbe8cb77c0f8e1d16d0c40e46f50bLean: NOT_RUN · human review: NOT_PERFORMED