Question 27821: Oversized Steps, Stationary Maxima and Lost Feasibility Block Different Inferences

Original question and givens

Use mode=oversized_step, complete model={"curvature":1,"point":21,"step_size":3}. Give (mode, curvature, point, step_size, next_point, objective_before, objective_after, automatic_descent_claim, boundary).

• G001 — Use mode=oversized_step, complete model={"curvature":1,"point":21,"step_size":3}. Give (mode, curvature, point, step_size, next_point, objective_before, objective_after, automatic_descent_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, curvature, point, step_size, next_point, objective_before, objective_after, automatic_descent_claim, boundary]]

GD boundary ORIGINAL upper2 over curvature := div(2, 1)

GD boundary ORIGINAL upper2 over curvature = 2

GD boundary ORIGINAL gradient := mul(1, 21)

GD boundary ORIGINAL gradient = 21

GD boundary ORIGINAL alpha gradient := mul(3, 21)

GD boundary ORIGINAL alpha gradient = 63

GD boundary ORIGINAL next := sub(21, 63)

GD boundary ORIGINAL next = -42

GD boundary ORIGINAL before SQUARE := mul(21, 21)

GD boundary ORIGINAL before SQUARE = 441

GD boundary ORIGINAL before diagonal := mul(1, 441)

GD boundary ORIGINAL before diagonal = 441

GD boundary ORIGINAL before half := div(441, 2)

GD boundary ORIGINAL before half = 441/2

GD boundary ORIGINAL after SQUARE := mul(-42, -42)

GD boundary ORIGINAL after SQUARE = 1764

GD boundary ORIGINAL after diagonal := mul(1, 1764)

GD boundary ORIGINAL after diagonal = 1764

GD boundary ORIGINAL after half := div(1764, 2)

GD boundary ORIGINAL after half = 882

source roles = [1, 21, 3, 2]

derived = [21, -42, 441/2, 882, No]

Reverse checks

• S012 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
• S011 · premise_and_result_audit — Recompute GD boundary ORIGINAL after half with exact rational arithmetic, not rounded decimals.
• S010 · premise_and_result_audit — Recompute GD boundary ORIGINAL after diagonal with exact rational arithmetic, not rounded decimals.
• S009 · premise_and_result_audit — Recompute GD boundary ORIGINAL after SQUARE with exact rational arithmetic, not rounded decimals.
• S008 · premise_and_result_audit — Recompute GD boundary ORIGINAL before half with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Recompute GD boundary ORIGINAL before diagonal with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Recompute GD boundary ORIGINAL before SQUARE with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute GD boundary ORIGINAL next with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute GD boundary ORIGINAL alpha gradient with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute GD boundary ORIGINAL gradient with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute GD boundary ORIGINAL upper2 over curvature 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.

Result

(oversized_step, 1, 21, 3, -42, 441/2, 882, No, positive_but_oversized_step_can_increase_the_objective)

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.