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R0054-27833 · q-20261015-pulse-20261119-r03-0033
Use f(x)=1/2*sum_i d_i*x_i^2+sum_i b_i*x_i, with positive diagonal d=[2, 5], linear b=[1, -2], and point x=[0, -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=[2, 5], linear b=[1, -2], and point x=[0, -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(2, 0)
After
GD ORIGINAL ORIGINAL gradient d*x coordinate0 = 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, S001
Before
GD ORIGINAL ORIGINAL gradient plus b coordinate0 := sum(0, 1)
After
GD ORIGINAL ORIGINAL gradient plus b coordinate0 = 1
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(5, -3)
After
GD ORIGINAL ORIGINAL gradient d*x coordinate1 = -15
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(-15, -2)
After
GD ORIGINAL ORIGINAL gradient plus b coordinate1 = -17
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(0, 0)
After
GD ORIGINAL ORIGINAL objective SQUARE FIRST coordinate0 = 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, S005
Before
GD ORIGINAL ORIGINAL diagonal times square coordinate0 := mul(2, 0)
After
GD ORIGINAL ORIGINAL diagonal times square coordinate0 = 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, S006
Before
GD ORIGINAL ORIGINAL quadratic divide2 coordinate0 := div(0, 2)
After
GD ORIGINAL ORIGINAL quadratic divide2 coordinate0 = 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, S007
Before
GD ORIGINAL ORIGINAL linear product coordinate0 := mul(1, 0)
After
GD ORIGINAL ORIGINAL linear product coordinate0 = 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, S008
Before
GD ORIGINAL ORIGINAL coordinate objective sum0 := sum(0, 0)
After
GD ORIGINAL ORIGINAL coordinate objective sum0 = 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, S009
Before
GD ORIGINAL ORIGINAL objective running sum0 := sum(0, 0)
After
GD ORIGINAL ORIGINAL objective running sum0 = 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, 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(5, 9)
After
GD ORIGINAL ORIGINAL diagonal times square coordinate1 = 45
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(45, 2)
After
GD ORIGINAL ORIGINAL quadratic divide2 coordinate1 = 45/2
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, S013
Before
GD ORIGINAL ORIGINAL linear product coordinate1 := mul(-2, -3)
After
GD ORIGINAL ORIGINAL linear product 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, S014
Before
GD ORIGINAL ORIGINAL coordinate objective sum1 := sum(45/2, 6)
After
GD ORIGINAL ORIGINAL coordinate objective sum1 = 57/2
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, S015
Before
GD ORIGINAL ORIGINAL objective running sum1 := sum(0, 57/2)
After
GD ORIGINAL ORIGINAL objective running sum1 = 57/2
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, S016
Before
source roles = [GD ORIGINAL, [2, 5], [1, -2], [0, -3]]
After
derived = [[2, 5], [1, -2], [0, -3], [1, -17], 57/2]
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, 1)
After
GD ORIGINAL one step ORIGINAL alpha times gradient0 = 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, S018
Before
GD ORIGINAL one step ORIGINAL next coordinate0 := sub(0, 1/4)
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, -17)
After
GD ORIGINAL one step ORIGINAL alpha times gradient1 = -17/4
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, -17/4)
After
GD ORIGINAL one step ORIGINAL next coordinate1 = 5/4
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(2, -1/4)
After
GD ORIGINAL one step next recomputation ORIGINAL gradient d*x coordinate0 = -1/2
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, S022
Before
GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate0 := sum(-1/2, 1)
After
GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate0 = 1/2
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, S023
Before
GD ORIGINAL one step next recomputation ORIGINAL gradient d*x coordinate1 := mul(5, 5/4)
After
GD ORIGINAL one step next recomputation ORIGINAL gradient d*x coordinate1 = 25/4
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, S024
Before
GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate1 := sum(25/4, -2)
After
GD ORIGINAL one step next recomputation ORIGINAL gradient plus b coordinate1 = 17/4
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, 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(2, 1/16)
After
GD ORIGINAL one step next recomputation ORIGINAL diagonal times square coordinate0 = 1/8
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, S027
Before
GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 coordinate0 := div(1/8, 2)
After
GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 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, 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(1/16, -1/4)
After
GD ORIGINAL one step next recomputation ORIGINAL coordinate objective sum0 = -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, S030
Before
GD ORIGINAL one step next recomputation ORIGINAL objective running sum0 := sum(0, -3/16)
After
GD ORIGINAL one step next recomputation ORIGINAL objective running sum0 = -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, S031
Before
GD ORIGINAL one step next recomputation ORIGINAL objective SQUARE FIRST coordinate1 := mul(5/4, 5/4)
After
GD ORIGINAL one step next recomputation ORIGINAL objective SQUARE FIRST coordinate1 = 25/16
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(5, 25/16)
After
GD ORIGINAL one step next recomputation ORIGINAL diagonal times square coordinate1 = 125/16
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, S033
Before
GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 coordinate1 := div(125/16, 2)
After
GD ORIGINAL one step next recomputation ORIGINAL quadratic divide2 coordinate1 = 125/32
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, S034
Before
GD ORIGINAL one step next recomputation ORIGINAL linear product coordinate1 := mul(-2, 5/4)
After
GD ORIGINAL one step next recomputation ORIGINAL linear product coordinate1 = -5/2
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, S035
Before
GD ORIGINAL one step next recomputation ORIGINAL coordinate objective sum1 := sum(125/32, -5/2)
After
GD ORIGINAL one step next recomputation ORIGINAL coordinate objective sum1 = 45/32
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, S036
Before
GD ORIGINAL one step next recomputation ORIGINAL objective running sum1 := sum(-3/16, 45/32)
After
GD ORIGINAL one step next recomputation ORIGINAL objective running sum1 = 39/32
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, [[2, 1], [5, 1]], [[1, 1], [-2, 1]], [[-1, 4], [5, 4]]]
After
derived = [[2, 5], [1, -2], [-1/4, 5/4], [1/2, 17/4], 39/32]
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 = [[0, -3], [1, -17], 1/4]
After
derived = [[-1/4, 5/4], 57/2, 39/32, 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.([0, -3], [1, -17], 1/4, [-1/4, 5/4], 57/2, 39/32, 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: 49633ed1861bc1baa4acc5a746a9775e99b2e014479ef667eafb58ff0d70993acandidate record SHA-256: 865033cec6eb6414263f79e4d33c20eba115d52a28ce4a9802f128d9962ff5b5semantic review receipt SHA-256: 0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54question-first witness SHA-256: 09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437Lean: NOT_RUN · human review: NOT_PERFORMED