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R0054-27808 · q-20261015-pulse-20261119-r03-0083
Use mode=constrained_confusion, complete model={"point":0,"gradient":8,"step_size":2,"lower":-1,"upper":1}. Give (mode, lower_bound, upper_bound, feasible_point, unconstrained_next_point, constrained_descent_claim, boundary).
G001 — Use mode=constrained_confusion, complete model={"point":0,"gradient":8,"step_size":2,"lower":-1,"upper":1}. Give (mode, lower_bound, upper_bound, feasible_point, unconstrained_next_point, constrained_descent_claim, boundary).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-boundary]
After
derived = [[mode, lower_bound, upper_bound, feasible_point, unconstrained_next_point, constrained_descent_claim, boundary]]
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 constrained ORIGINAL alpha supplied gradient := mul(2, 8)
After
GD constrained ORIGINAL alpha supplied gradient = 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, S001
Before
GD constrained ORIGINAL unprojected next := sub(0, 16)
After
GD constrained ORIGINAL unprojected next = -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, S002
Before
source roles = [-1, 1, 0, 8, 2]
After
derived = [-16, No]
Conditions: none
The gradient scalar is given,not verified from an unprovided objective.The original point is in the CLOSED interval but the unprojected update is strictly outside.Do not silently clamp and call it the same step or constrained descent.
Rule: GD_ACTUAL_loss_of_feasibility_NO_projection_or_unknown_objective · Uses: G001, S003
S004 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S003 · premise_and_result_audit — Recompute GD constrained ORIGINAL unprojected next with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute GD constrained ORIGINAL alpha supplied gradient 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.(constrained_confusion, -1, 1, 0, -16, No, unconstrained_gradient_step_is_not_projected_or_constrained_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: ef178341a4e9afb2fee345209fbe35cb347c279c179af977a180158538e0b1c4candidate record SHA-256: f334cfe9e47efd8153e360e87d35e343556a051cca72812358901087f75fa637semantic review receipt SHA-256: 0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54question-first witness SHA-256: 09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437Lean: NOT_RUN · human review: NOT_PERFORMED