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Question 26916: Comparison Direction, Nonnegativity and Reference Status Cannot Be Omitted

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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R0052-26916 · q-20261015-advance-20261117-r01-series-comparison-test-0091

Original question and givens

Boundary mode=unknown_reference, positive scale=16. Give (mode, scale, reference_status_scope, comparison_test_claim).

  • G001 — Boundary mode=unknown_reference, positive scale=16. Give (mode, scale, reference_status_scope, comparison_test_claim).

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.

Step-by-step derivation

S001 · implies

Before

source roles = [series-comparison-boundary]

After

derived = [[mode, scale, reference_status, inference]]

Conditions: none

List this operation/mode exact source field order without JavaScript.Keep Boolean,string and null roles distinct;do not pad fields or infer the interface from answer shape.

Step identifiers and dependencies

Rule: source_ordered_fields_without_JS · Uses: G001

S002 · implies

Before

source roles = [unknown_reference, 16]

After

derived = [unknown_reference, 16, comparison_holds_reference_status_not_proved, No]

Conditions: none

finite_sample is a scope statement,not a complete infinite witness.A divergent upper series cannot force a smaller one to diverge,e.g.1/n²<=1/n.Signed terms fail nonnegativity and unknown_reference lacks the reference status.No rejects this inference,not every underlying convergence claim.

Step identifiers and dependencies

Rule: Series_original_comparison_boundary_scope_and_direction · Uses: G001, S001

Reverse checks

  • S002 · premise_and_result_audit — Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems.
  • S001 · premise_and_result_audit — Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems.

Result

(unknown_reference, 16, comparison_holds_reference_status_not_proved, No)

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: 6bbe43ef72b71d29d201b2c2582c1df1af88dc1948c90d76fae2b1fdabd40d23
  • candidate record SHA-256: 1f37ff6bb3db8b3759a3b0a7d5ce3827085879a390ebfd05b4c7763958246033
  • semantic review receipt SHA-256: 729b25cbf6bf5cb1d07a21a511ae216ec5fdd54a4a7aa2f7c21156b81ff37252
  • question-first witness SHA-256: d1ab788770eaad04f986986e65afb0d55791e8a8c0d747e9a2b499f79fe78df2
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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