Question 27802: Oversized Steps, Stationary Maxima and Lost Feasibility Block Different Inferences

Original question and givens

Use mode=zero_gradient_nonminimum, complete model={"scale":2}. Give (mode, objective_description, stationary_point, gradient_statement, actual_point_status, minimum_claim, boundary).

• G001 — Use mode=zero_gradient_nonminimum, complete model={"scale":2}. Give (mode, objective_description, stationary_point, gradient_statement, actual_point_status, minimum_claim, boundary).

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-gradient-descent

Step-by-step derivation

source roles = [gd-boundary]

derived = [[mode, objective_description, stationary_point, gradient_statement, actual_point_status, minimum_claim, boundary]]

source roles = [2]

derived = [zero_gradient_nonminimum, f(x)=-2*x^2, x=0, gradient=0, strict_local_maximum, No, zero_gradient_is_stationary_not_a_minimum_certificate]

Reverse checks

• S002 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S001 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.

Result

(zero_gradient_nonminimum, f(x)=-2*x^2, x=0, gradient=0, strict_local_maximum, No, zero_gradient_is_stationary_not_a_minimum_certificate)

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.