# Question 2163: Synthetic Response to a Declared Substitution

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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.

R0003-02163 · q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0063



## 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=2, b=1, x=0, response=0. Give (a,b,x,response,a*x+b,match?,rule code).


- 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=2, b=1, x=0, response=0. Give (a,b,x,response,a*x+b,match?,rule code).





## 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.


- [mko-diagnostic-mathematical-assessment](https://ocme.evemisslab.com/en/mko/mko-diagnostic-mathematical-assessment/)





## Step-by-step derivation

S001 · impliesBefore

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 dependenciesRule: synthetic_record_scope · Uses: G001





S002 · calculationBefore

a·x := mul(2, 0)

After

a·x = 0

Conditions: none

Substitute the given input in the multiplicative term.

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





S003 · calculationBefore

a·x+b := sum(0, 1)

After

a·x+b = 1

Conditions: none

Add the constant to obtain the rule-expected value.

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





S004 · impliesBefore

response=0; expected=1

After

match=No

Conditions: none

This records rule agreement for this substitution only,not the cause of an error.

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





S005 · impliesBefore

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 dependenciesRule: diagnostic_rule_code · Uses: G001, S004









## Reverse checks


- S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- 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 — Recompute a·x+b with exact rational arithmetic, not rounded decimals.
- S002 · premise_and_result_audit — Recompute a·x 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

(2, 1, 0, 0, 1, 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: 90b8786ec253330920f0c5dbee35bb2f5660f12df4f7f7441f4d88dd4c2fb19b
- candidate record SHA-256: efea02f2111143ad0402ea0376d48b46638e57e5f71f2fdb8a6de92f56f925d4
- semantic review receipt SHA-256: 5dbc70ebd5f74b23384c93b63a2b1d6519e206c79f22ae16a6c2d7483cea783f
- question-first witness SHA-256: cf121c8dd2fec13aa118b04b049ee39494f1d6d9ecdc13514cafb78c0fc021fa
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0063.json)