# Question 27809: Oversized Steps, Stationary Maxima and Lost Feasibility Block Different Inferences [Return to catalogue page 140](https://ocme.evemisslab.com/en/questions/page/140/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261015-advance-20261119-r03-gradient-descent-foundations/#q-20261015-pulse-20261119-r03-0084) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0054-27809 · q-20261015-pulse-20261119-r03-0084 ## Original question and givens Use mode=oversized_step, complete model={"curvature":4,"point":9,"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":4,"point":9,"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](https://ocme.evemisslab.com/en/mko/mko-gradient-descent/) ## Step-by-step derivation S001 · impliesBefore source roles = [gd-boundary] After derived = [[mode, curvature, point, step_size, next_point, objective_before, objective_after, automatic_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. Step identifiers and dependenciesRule: source_ordered_fields_without_JS · Uses: G001 S002 · calculationBefore GD boundary ORIGINAL upper2 over curvature := div(2, 4) After GD boundary ORIGINAL upper2 over curvature = 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. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S001 S003 · calculationBefore GD boundary ORIGINAL gradient := mul(4, 9) After GD boundary ORIGINAL gradient = 36 Conditions: none Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S002 S004 · calculationBefore GD boundary ORIGINAL alpha gradient := mul(3, 36) After GD boundary ORIGINAL alpha gradient = 108 Conditions: none Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S003 S005 · calculationBefore GD boundary ORIGINAL next := sub(9, 108) After GD boundary ORIGINAL next = -99 Conditions: none Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S004 S006 · calculationBefore GD boundary ORIGINAL before SQUARE := mul(9, 9) After GD boundary ORIGINAL before SQUARE = 81 Conditions: none Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S005 S007 · calculationBefore GD boundary ORIGINAL before diagonal := mul(4, 81) After GD boundary ORIGINAL before diagonal = 324 Conditions: none Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S006 S008 · calculationBefore GD boundary ORIGINAL before half := div(324, 2) After GD boundary ORIGINAL before half = 162 Conditions: none Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S007 S009 · calculationBefore GD boundary ORIGINAL after SQUARE := mul(-99, -99) After GD boundary ORIGINAL after SQUARE = 9801 Conditions: none Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S008 S010 · calculationBefore GD boundary ORIGINAL after diagonal := mul(4, 9801) After GD boundary ORIGINAL after diagonal = 39204 Conditions: none Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S009 S011 · calculationBefore GD boundary ORIGINAL after half := div(39204, 2) After GD boundary ORIGINAL after half = 19602 Conditions: none Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S010 S012 · impliesBefore source roles = [4, 9, 3, 1/2] After derived = [36, -99, 162, 19602, No] Conditions: none x_next=(1-alpha*c)x.With alpha>2/c,|1-alpha*c|>1 and x is nonzero,so the objective actually increases.Equality alpha=2/c is not this strict witness. Step identifiers and dependenciesRule: GD_STRICT_oversized_nonzero_scalar_actual_increase · Uses: G001, S011 ## 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, 4, 9, 3, -99, 162, 19602, 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. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: 2b330f1da90cd915c9e634515e72f633aea2a98aae2610cdd2fafe610f1344ac - candidate record SHA-256: 22fc1b218af5c28ad29f163eb9f3f41f181398c3e53caab66c4875382ca6ebbe - semantic review receipt SHA-256: 0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54 - question-first witness SHA-256: 09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437 - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-pulse-20261119-r03-0084.json)