# Question 27812: Oversized Steps, Stationary Maxima and Lost Feasibility Block Different Inferences

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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.

R0054-27812 · q-20261015-pulse-20261119-r03-0087



## Original question and givens

Use mode=constrained_confusion, complete model={"point":0,"gradient":12,"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":12,"step_size":2,"lower":-1,"upper":1}. Give (mode, lower_bound, upper_bound, feasible_point, unconstrained_next_point, constrained_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, 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.

Step identifiers and dependenciesRule: source_ordered_fields_without_JS · Uses: G001





S002 · calculationBefore

GD constrained ORIGINAL alpha supplied gradient := mul(2, 12)

After

GD constrained ORIGINAL alpha supplied gradient = 24

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 constrained ORIGINAL unprojected next := sub(0, 24)

After

GD constrained ORIGINAL unprojected next = -24

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 · impliesBefore

source roles = [-1, 1, 0, 12, 2]

After

derived = [-24, 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.

Step identifiers and dependenciesRule: GD_ACTUAL_loss_of_feasibility_NO_projection_or_unknown_objective · Uses: G001, S003









## Reverse checks


- 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.





## Result

(constrained_confusion, -1, 1, 0, -24, 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.





## 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: cbf83be21dd01ae634ca34c6ccf85c7d5b4091e3f9eafac73627b9ca1c5f6023
- candidate record SHA-256: 9b41db2ba38db7367cf470445a7256f48733881b457f21b5d00d0194d1e134f2
- 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-r03-0087.json)