# Question 923: Empty Domains, Partial Lists, Ties and Local-Only Witnesses Block Different Claims

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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.

P1000-0923 · q-20261015-pulse-20261119-r07-0098



## Original question and givens

Use mode=incomplete_domain, complete model={"listed_points":["A","B"],"values":[23,46]}. Give (mode, listed_objective_rows, global_certificate_claim, boundary).


- G001 — Use mode=incomplete_domain, complete model={"listed_points":["A","B"],"values":[23,46]}. Give (mode, listed_objective_rows, global_certificate_claim, boundary).





## Definition and scope

An empty set has no optimizer; an unverified partial list supports no global claim; ties are not unique; a local minimum need not be global.


- [mko-optimization-problem](https://ocme.evemisslab.com/en/mko/mko-optimization-problem/)





## Step-by-step derivation

S001 · impliesBefore

mode=incomplete_domain

After

identify the exact missing optimization obligation

Conditions: none

Distinguish nonexistence, unverified completeness, nonuniqueness and merely local optimality.

Step identifiers and dependenciesRule: optimization_scope · Uses: G001





S002 · impliesBefore

only these points are listed

After

[[A, 23], [B, 46]]

Conditions: none

The listed values can be compared exactly, but no certificate says they exhaust the feasible domain.

Step identifiers and dependenciesRule: partial_objective_data · Uses: G001, S001





S003 · impliesBefore

listed minimum=23

After

an unlisted feasible point with value 22 would change the minimum

Conditions: none

This is a possible countermodel to the inference, not a claim that the original task actually contains this extra point.

Step identifiers and dependenciesRule: unlisted_point_countermodel · Uses: G001, S002





S004 · impliesBefore

unverified partial list

After

cannot certify a global claim from these data alone

Conditions: none

The false flag denies certificate sufficiency; it does not prove that a listed candidate is nonoptimal.

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









## Reverse checks


- S004 · premise_and_result_audit — Completeness, neighborhoods, attainment and uniqueness are separate obligations; local data do not license a global conclusion.
- S003 · premise_and_result_audit — Completeness, neighborhoods, attainment and uniqueness are separate obligations; local data do not license a global conclusion.
- S002 · premise_and_result_audit — Completeness, neighborhoods, attainment and uniqueness are separate obligations; local data do not license a global conclusion.
- S001 · premise_and_result_audit — Completeness, neighborhoods, attainment and uniqueness are separate obligations; local data do not license a global conclusion.





## Result

(incomplete_domain, [[A, 23], [B, 46]], No, an_unverified_partial_list_cannot_support_a_global_claim)

The full substitutions and premise audits recover the original answer, retaining its field order and verdict meanings.





## 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: 2c5d5bda5fccd0cac9ebdacce3c5ec2a72010ffa56d4eba33df3256b6ec63187
- candidate record SHA-256: b2f6ece6bb57068e8cc35c7e6898b0e2018ac7414bd3766bffc35a9b55e33410
- semantic review receipt SHA-256: 6c2c6d46aded7582a11ac41a8c0b3bdde2669a53bdb6e796eea2039994a02772
- question-first witness SHA-256: 77e43898df9efdbf8094ad81fe4ab91cf4b4bd82f481eb9b4699b73cb4da612b
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-pulse-20261119-r07-0098.json)