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R0054-27846 · q-20261015-pulse-20261119-r03-0046
Use f(x)=1/2*sum_i d_i*x_i^2+sum_i b_i*x_i, with positive diagonal d=[3, 2], linear b=[-1, -3], and point x=[-2, 3] in fixed standard Euclidean coordinates. Use positive step size alpha=1/4. Give (point, gradient, step_size, next_point, objective_before, objective_after, nonincreasing, step_scope).
G001 — Use f(x)=1/2*sum_i d_i*x_i^2+sum_i b_i*x_i, with positive diagonal d=[3, 2], linear b=[-1, -3], and point x=[-2, 3] in fixed standard Euclidean coordinates. Use positive step size alpha=1/4. Give (point, gradient, step_size, next_point, objective_before, objective_after, nonincreasing, step_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.
Before
source roles = [gd-one-step]
After
derived = [[point, gradient, step_size, next_point, objective_before, objective_after, nonincreasing, step_scope]]
Conditions: none
List the complete operation/mode field order without JavaScript or answer-shape inference;Boolean,string,null and an unclaimed result remain distinct.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
GD ORIGINAL ORIGINAL gradient d*x coordinate0 := mul(3, -2)
After
GD ORIGINAL ORIGINAL gradient d*x coordinate0 = -6
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
GD ORIGINAL ORIGINAL gradient plus b coordinate0 := sum(-6, -1)
After
GD ORIGINAL ORIGINAL gradient plus b coordinate0 = -7
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
GD ORIGINAL ORIGINAL gradient d*x coordinate1 := mul(2, 3)
After
GD ORIGINAL ORIGINAL gradient d*x coordinate1 = 6
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
GD ORIGINAL ORIGINAL gradient plus b coordinate1 := sum(6, -3)
After
GD ORIGINAL ORIGINAL gradient plus b coordinate1 = 3
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S004
Before
GD ORIGINAL ORIGINAL objective SQUARE FIRST coordinate0 := mul(-2, -2)
After
GD ORIGINAL ORIGINAL objective SQUARE FIRST coordinate0 = 4
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S005
Before
GD ORIGINAL ORIGINAL diagonal times square coordinate0 := mul(3, 4)
After
GD ORIGINAL ORIGINAL diagonal times square coordinate0 = 12
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S006
Before
GD ORIGINAL ORIGINAL quadratic divide2 coordinate0 := div(12, 2)
After
GD ORIGINAL ORIGINAL quadratic divide2 coordinate0 = 6
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S007
Before
GD ORIGINAL ORIGINAL linear product coordinate0 := mul(-1, -2)
After
GD ORIGINAL ORIGINAL linear product coordinate0 = 2
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S008
Before
GD ORIGINAL ORIGINAL coordinate objective sum0 := sum(6, 2)
After
GD ORIGINAL ORIGINAL coordinate objective sum0 = 8
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S009
Before
GD ORIGINAL ORIGINAL objective running sum0 := sum(0, 8)
After
GD ORIGINAL ORIGINAL objective running sum0 = 8
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S010
Before
GD ORIGINAL ORIGINAL objective SQUARE FIRST coordinate1 := mul(3, 3)
After
GD ORIGINAL ORIGINAL objective SQUARE FIRST coordinate1 = 9
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S011
Before
GD ORIGINAL ORIGINAL diagonal times square coordinate1 := mul(2, 9)
After
GD ORIGINAL ORIGINAL diagonal times square coordinate1 = 18
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S012
Before
GD ORIGINAL ORIGINAL quadratic divide2 coordinate1 := div(18, 2)
After
GD ORIGINAL ORIGINAL quadratic divide2 coordinate1 = 9
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S013
Before
GD ORIGINAL ORIGINAL linear product coordinate1 := mul(-3, 3)
After
GD ORIGINAL ORIGINAL linear product coordinate1 = -9
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S014
Before
GD ORIGINAL ORIGINAL coordinate objective sum1 := sum(9, -9)
After
GD ORIGINAL ORIGINAL coordinate objective sum1 = 0
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S015
Before
GD ORIGINAL ORIGINAL objective running sum1 := sum(8, 0)
After
GD ORIGINAL ORIGINAL objective running sum1 = 8
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S016
Before
source roles = [GD ORIGINAL, [3, 2], [-1, -3], [-2, 3]]
After
derived = [[3, 2], [-1, -3], [-2, 3], [-7, 3], 8]
Conditions: none
For the WHOLE specified f(x)=1/2 sum d_i x_i²+sum b_i x_i,differentiate each coordinate to d_i x_i+b_i,not2d_i x_i.Compute ALL gradient entries first,then the objective in original order,squaring before multiplying d_i.Qualify positive diagonals,dimensions and coordinate order.
Rule: GD_WHOLE_positive_diagonal_quadratic_ordered_gradient_and_objective · Uses: G001, S017
Before
GD ORIGINAL one step ORIGINAL alpha times gradient0 := mul(1/4, -7)
After
GD ORIGINAL one step ORIGINAL alpha times gradient0 = -7/4
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S018
Before
GD ORIGINAL one step ORIGINAL next coordinate0 := sub(-2, -7/4)
After
GD ORIGINAL one step ORIGINAL next coordinate0 = -1/4
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S019
Before
GD ORIGINAL one step ORIGINAL alpha times gradient1 := mul(1/4, 3)
After
GD ORIGINAL one step ORIGINAL alpha times gradient1 = 3/4
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S020
Before
GD ORIGINAL one step ORIGINAL next coordinate1 := sub(3, 3/4)
After
GD ORIGINAL one step ORIGINAL next coordinate1 = 9/4
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S021
Before
GD ORIGINAL one step next recomputation ORIGINAL gradient d*x coordinate0 := mul(3, -1/4)
After
GD ORIGINAL one step next recomputation ORIGINAL gradient d*x coordinate0 = -3/4
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S022
Before
GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate0 := sum(-3/4, -1)
After
GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate0 = -7/4
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S023
Before
GD ORIGINAL one step next recomputation ORIGINAL gradient d*x coordinate1 := mul(2, 9/4)
After
GD ORIGINAL one step next recomputation ORIGINAL gradient d*x coordinate1 = 9/2
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S024
Before
GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate1 := sum(9/2, -3)
After
GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate1 = 3/2
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S025
Before
GD ORIGINAL one step next recomputation ORIGINAL objective SQUARE FIRST coordinate0 := mul(-1/4, -1/4)
After
GD ORIGINAL one step next recomputation ORIGINAL objective SQUARE FIRST coordinate0 = 1/16
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S026
Before
GD ORIGINAL one step next recomputation ORIGINAL diagonal times square coordinate0 := mul(3, 1/16)
After
GD ORIGINAL one step next recomputation ORIGINAL diagonal times square coordinate0 = 3/16
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S027
Before
GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 coordinate0 := div(3/16, 2)
After
GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 coordinate0 = 3/32
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S028
Before
GD ORIGINAL one step next recomputation ORIGINAL linear product coordinate0 := mul(-1, -1/4)
After
GD ORIGINAL one step next recomputation ORIGINAL linear product coordinate0 = 1/4
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S029
Before
GD ORIGINAL one step next recomputation ORIGINAL coordinate objective sum0 := sum(3/32, 1/4)
After
GD ORIGINAL one step next recomputation ORIGINAL coordinate objective sum0 = 11/32
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S030
Before
GD ORIGINAL one step next recomputation ORIGINAL objective running sum0 := sum(0, 11/32)
After
GD ORIGINAL one step next recomputation ORIGINAL objective running sum0 = 11/32
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S031
Before
GD ORIGINAL one step next recomputation ORIGINAL objective SQUARE FIRST coordinate1 := mul(9/4, 9/4)
After
GD ORIGINAL one step next recomputation ORIGINAL objective SQUARE FIRST coordinate1 = 81/16
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S032
Before
GD ORIGINAL one step next recomputation ORIGINAL diagonal times square coordinate1 := mul(2, 81/16)
After
GD ORIGINAL one step next recomputation ORIGINAL diagonal times square coordinate1 = 81/8
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S033
Before
GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 coordinate1 := div(81/8, 2)
After
GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 coordinate1 = 81/16
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S034
Before
GD ORIGINAL one step next recomputation ORIGINAL linear product coordinate1 := mul(-3, 9/4)
After
GD ORIGINAL one step next recomputation ORIGINAL linear product coordinate1 = -27/4
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S035
Before
GD ORIGINAL one step next recomputation ORIGINAL coordinate objective sum1 := sum(81/16, -27/4)
After
GD ORIGINAL one step next recomputation ORIGINAL coordinate objective sum1 = -27/16
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S036
Before
GD ORIGINAL one step next recomputation ORIGINAL objective running sum1 := sum(11/32, -27/16)
After
GD ORIGINAL one step next recomputation ORIGINAL objective running sum1 = -43/32
Conditions: none
Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.
Rule: exact_rational_arithmetic · Uses: G001, S037
Before
source roles = [GD ORIGINAL one step next recomputation, [[3, 1], [2, 1]], [[-1, 1], [-3, 1]], [[-1, 4], [9, 4]]]
After
derived = [[3, 2], [-1, -3], [-1/4, 9/4], [-7/4, 3/2], -43/32]
Conditions: none
For the WHOLE specified f(x)=1/2 sum d_i x_i²+sum b_i x_i,differentiate each coordinate to d_i x_i+b_i,not2d_i x_i.Compute ALL gradient entries first,then the objective in original order,squaring before multiplying d_i.Qualify positive diagonals,dimensions and coordinate order.
Rule: GD_WHOLE_positive_diagonal_quadratic_ordered_gradient_and_objective · Uses: G001, S038
Before
source roles = [[-2, 3], [-7, 3], 1/4]
After
derived = [[-1/4, 9/4], 8, -43/32, Yes]
Conditions: none
This family requires only a positive step and compares the ACTUAL objectives.The flag can be False.A positive_step description does not imply descent,and no stronger safe-step guard is added.
Rule: GD_one_positive_step_ACTUAL_objective_comparison_not_safe_assumption · Uses: G001, S039
S040 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S039 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S038 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL objective running sum1 with exact rational arithmetic, not rounded decimals.S037 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL coordinate objective sum1 with exact rational arithmetic, not rounded decimals.S036 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL linear product coordinate1 with exact rational arithmetic, not rounded decimals.S035 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 coordinate1 with exact rational arithmetic, not rounded decimals.S034 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL diagonal times square coordinate1 with exact rational arithmetic, not rounded decimals.S033 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL objective SQUARE FIRST coordinate1 with exact rational arithmetic, not rounded decimals.S032 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL objective running sum0 with exact rational arithmetic, not rounded decimals.S031 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL coordinate objective sum0 with exact rational arithmetic, not rounded decimals.S030 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL linear product coordinate0 with exact rational arithmetic, not rounded decimals.S029 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 coordinate0 with exact rational arithmetic, not rounded decimals.S028 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL diagonal times square coordinate0 with exact rational arithmetic, not rounded decimals.S027 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL objective SQUARE FIRST coordinate0 with exact rational arithmetic, not rounded decimals.S026 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate1 with exact rational arithmetic, not rounded decimals.S025 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL gradient d*x coordinate1 with exact rational arithmetic, not rounded decimals.S024 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate0 with exact rational arithmetic, not rounded decimals.S023 · premise_and_result_audit — Recompute GD ORIGINAL one step next recomputation ORIGINAL gradient d*x coordinate0 with exact rational arithmetic, not rounded decimals.S022 · premise_and_result_audit — Recompute GD ORIGINAL one step ORIGINAL next coordinate1 with exact rational arithmetic, not rounded decimals.S021 · premise_and_result_audit — Recompute GD ORIGINAL one step ORIGINAL alpha times gradient1 with exact rational arithmetic, not rounded decimals.S020 · premise_and_result_audit — Recompute GD ORIGINAL one step ORIGINAL next coordinate0 with exact rational arithmetic, not rounded decimals.S019 · premise_and_result_audit — Recompute GD ORIGINAL one step ORIGINAL alpha times gradient0 with exact rational arithmetic, not rounded decimals.S018 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S017 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL objective running sum1 with exact rational arithmetic, not rounded decimals.S016 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL coordinate objective sum1 with exact rational arithmetic, not rounded decimals.S015 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL linear product coordinate1 with exact rational arithmetic, not rounded decimals.S014 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL quadratic divide2 coordinate1 with exact rational arithmetic, not rounded decimals.S013 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL diagonal times square coordinate1 with exact rational arithmetic, not rounded decimals.S012 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL objective SQUARE FIRST coordinate1 with exact rational arithmetic, not rounded decimals.S011 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL objective running sum0 with exact rational arithmetic, not rounded decimals.S010 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL coordinate objective sum0 with exact rational arithmetic, not rounded decimals.S009 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL linear product coordinate0 with exact rational arithmetic, not rounded decimals.S008 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL quadratic divide2 coordinate0 with exact rational arithmetic, not rounded decimals.S007 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL diagonal times square coordinate0 with exact rational arithmetic, not rounded decimals.S006 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL objective SQUARE FIRST coordinate0 with exact rational arithmetic, not rounded decimals.S005 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL gradient plus b coordinate1 with exact rational arithmetic, not rounded decimals.S004 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL gradient d*x coordinate1 with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL gradient plus b coordinate0 with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute GD ORIGINAL ORIGINAL gradient d*x coordinate0 with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.([-2, 3], [-7, 3], 1/4, [-1/4, 9/4], 8, -43/32, Yes, positive_step_alone_does_not_guarantee_descent)
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: af44e2a5072e85843426ae1f64001618405f609600f4d1e22c36db1fdb048de3candidate record SHA-256: 7e07a3bb8985c5c7740213c362c1048ccca7fac5557b5f3c1b2948aeb0288298semantic review receipt SHA-256: 0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54question-first witness SHA-256: 09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437Lean: NOT_RUN · human review: NOT_PERFORMED