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Question 34424: Fixed-Factor Proportion Check

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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R0067-34424 · q-20260930-r02-proportion-fixed-factor-0024

Original question and givens

In the rational setting, the fixed factor is k=11. Does the explicit point (x,y)=(-1,-10) satisfy y=kx? Check only this point.

  • G001 — In the rational setting, the fixed factor is k=11. Does the explicit point (x,y)=(-1,-10) satisfy y=kx? Check only this point.

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-proportion-fixed-factor, [k, operation, x, y]]

After

derived = [fixed_factor, no-invented-domain]

Conditions: none

Check THIS bank’s keys/operation/domain:legacy table underscores,MOD50 local hyphens;permissive BASE data acquires no unknown-field restriction.Keep Number.isInteger and SAFE source guards distinct,while preserving ORIGINAL JSON number representations.

Step identifiers and dependencies

Rule: R67_SOURCE_specific_keys_operation_domain_and_numeric_bank · Uses: G001

S002 · calculation

Before

Proportion ORIGINAL fixed factor times point x := mul(11, -1)

After

Proportion ORIGINAL fixed factor times point x = -11

Conditions: none

Calculate exactly from ORIGINAL ordered operands.Legacy derived integers are not recapped at the RAW SAFE bound;MOD50 rationals separately retain the NAIVE pre-reduction source envelope.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S001

S003 · implies

Before

source roles = [11, -1, -10]

After

derived = [-11, No]

Conditions: none

Check ONLY THIS point against y=kx.Zero k or x is allowed.One passing point does not establish proportionality for other inputs,nor does x=0 determine a unique factor.

Step identifiers and dependencies

Rule: Proportion_FIXED_factor_THIS_point_ONLY_zero_allowed · Uses: G001, S002

Reverse checks

  • S003 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
  • S002 · premise_and_result_audit — Recompute Proportion ORIGINAL fixed factor times point x with exact rational arithmetic, not rounded decimals.
  • S001 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.

Result

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: 6f77ed7bba7e6801cbe5ba0b8ee61f70f80c99fa64e00a3dd50df9775bd1c3b2
  • candidate record SHA-256: a182437d215552b9928daa302aaa6ffbe23f7b5c90deaac23f5a1a4c9ebbffbf
  • semantic review receipt SHA-256: c89efa383b67bb2cf25bcf16160b9f5f614bbe5e5e791f4d7f58234d17a3371c
  • question-first witness SHA-256: 12766d451c5375842b4fc2843ae94807ec55f15763a916558026912a13873d57
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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