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Question 905: Empty Domains, Partial Lists, Ties and Local-Only Witnesses Block Different Claims

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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P1000-0905 · q-20261015-pulse-20261119-r07-0080

Original question and givens

Use mode=incomplete_domain, complete model={"listed_points":["A","B"],"values":[5,10]}. Give (mode, listed_objective_rows, global_certificate_claim, boundary).

  • G001 — Use mode=incomplete_domain, complete model={"listed_points":["A","B"],"values":[5,10]}. 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.

Step-by-step derivation

S001 · implies

Before

mode=incomplete_domain

After

identify the exact missing optimization obligation

Conditions: none

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

Step identifiers and dependencies

Rule: optimization_scope · Uses: G001

S002 · implies

Before

only these points are listed

After

[[A, 5], [B, 10]]

Conditions: none

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

Step identifiers and dependencies

Rule: partial_objective_data · Uses: G001, S001

S003 · implies

Before

listed minimum=5

After

an unlisted feasible point with value 4 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 dependencies

Rule: unlisted_point_countermodel · Uses: G001, S002

S004 · implies

Before

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 dependencies

Rule: 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, 5], [B, 10]], 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: d6a61865a72b4272dca285e271a2b95fe7752ee3765743eeb43bd84f13dad239
  • candidate record SHA-256: 264c855c024dbebac34e38ba7c6226866026be2f72a1d472fb7520aac0ddb092
  • semantic review receipt SHA-256: 6c2c6d46aded7582a11ac41a8c0b3bdde2669a53bdb6e796eea2039994a02772
  • question-first witness SHA-256: 77e43898df9efdbf8094ad81fe4ab91cf4b4bd82f481eb9b4699b73cb4da612b
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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