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Question 28152: Quadratic Reference Error Is Not a General Quadrature Error Theorem

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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R0055-28152 · q-20261015-pulse-20261119-r02-0077

Original question and givens

Use mode=nonincreasing_partition, complete model={"nodes":[0,0,2],"values":[1,2,3]}. Give (mode, nodes, endpoint_values, aligned, strictly_increasing, partition_qualification_claim, boundary).

  • G001 — Use mode=nonincreasing_partition, complete model={"nodes":[0,0,2],"values":[1,2,3]}. Give (mode, nodes, endpoint_values, aligned, strictly_increasing, partition_qualification_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.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-mod50-trap-error-boundary, trap-error-boundary]

After

derived = [[mode, nodes, endpoint_values, aligned, strictly_increasing, partition_qualification_claim, boundary]]

Conditions: none

List this scalar/label/set/point answer role or mode-specific ordered fields,not an imposed universal tuple.Retain legacy domain/underscore operation and integer fractions with/1;original bilingual snapshots stay unchanged.

Step identifiers and dependencies

Rule: source_answer_roles_or_ordered_fields_without_JS · Uses: G001

S002 · implies

Before

source roles = [[0, 0, 2], [1, 2, 3]]

After

derived = [Yes, No, No]

Conditions: none

This boundary requires an actually aligned nonincreasing witness.Do not repair it by sorting,import the normal24-node cap or calculate an unqualified quadrature.

Step identifiers and dependencies

Rule: Trapezoid_ACTUAL_aligned_nonincreasing_partition_not_repaired_by_sort · Uses: G001, S001

Reverse checks

  • S002 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.
  • S001 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.

Result

(nonincreasing_partition, [0, 0, 2], [1, 2, 3], Yes, No, No, partition_must_be_strictly_increasing)

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: cf44dec35d441fba1ce2aef1833499d176eeaa68675f5d0ee6fb67e7b526663c
  • candidate record SHA-256: 3d7f68fca16e3e761d740bb4cabf64f042b2c8ca29ee8403a2901b982aeb30ed
  • semantic review receipt SHA-256: 6af367dae24a584f3596525c4953bbc2115343efd68cc9083693eb5c1ef2e683
  • question-first witness SHA-256: 611eb69f3716404b968296a8b0d7d8c61b5ca18129d406f1ff9c7c11e10ffb4e
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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