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Question 2129: Synthetic Integer-Sum Response and Its Rule Code

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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R0003-02129 · q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0004

Original question and givens

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-9, b=-3, response=-11. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

  • G001 — Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-9, b=-3, response=-11. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

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

synthetic response record and a declared mathematical rule

After

check rule agreement,not a learner diagnosis

Conditions: none

These are synthetic records;one response does not diagnose a real learner's ability,psychology or learning outcome.

Step identifiers and dependencies

Rule: synthetic_record_scope · Uses: G001

S002 · calculation

Before

rule-expected sum := sum(-9, -3)

After

rule-expected sum = -12

Conditions: none

Compute the rule-expected sum instead of copying the response.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S001

S003 · implies

Before

response=-11; rule expected=-12

After

match=No

Conditions: none

Compare the response with the rule result,not the two inputs with one another.

Step identifiers and dependencies

Rule: response_vs_expected · Uses: G001, S002

S004 · implies

Before

rule agreement=No

After

record code=differs_from_rule_expected

Conditions: none

The code records agreement with the stated rule,not a person-level score or general learning diagnosis.

Step identifiers and dependencies

Rule: diagnostic_rule_code · Uses: G001, S003

Reverse checks

  • S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S002 · premise_and_result_audit — Recompute rule-expected sum with exact rational arithmetic, not rounded decimals.
  • S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(-9, -3, -11, -12, No, differs_from_rule_expected)

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: 54a2baf840eb0797bab33d2c270579928dfaea4f0f49abc46469de4f4cbf7f37
  • candidate record SHA-256: 5468bd8d4d814d28ca402732ff9a7675d006d072297ee88d9ab2920031e95feb
  • semantic review receipt SHA-256: 5dbc70ebd5f74b23384c93b63a2b1d6519e206c79f22ae16a6c2d7483cea783f
  • question-first witness SHA-256: cf121c8dd2fec13aa118b04b049ee39494f1d6d9ecdc13514cafb78c0fc021fa
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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