Use mode=inclusive_tolerance, complete model={"error":[10,2],"tolerance":[10,2]}. Give (mode, absolute_error, tolerance, inclusive_test_result, equality_convention).
G001 — Use mode=inclusive_tolerance, complete model={"error":[10,2],"tolerance":[10,2]}. Give (mode, absolute_error, tolerance, inclusive_test_result, equality_convention).
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.
THIS source uses LOCAL-hyphen operations with exact keys/domain.Keep source field order and numeric/Boolean/string roles;integer rational texts omit/1.Original questions,English,MKOs,ASTs and statuses remain unchanged.
source roles = [tolerance ORIGINAL error, 100000000, 10, 2]
After
derived = [[5, 1], 5]
Conditions: none
Bound the SOURCE PRE-reduction numerator/denominator and require a nonzero denominator BEFORE sign/gcd normalization.MOD50 uses100million with NAIVE operations,not prior cross-cancellation;this Wave4 mean uses one million.Out-of-envelope is a source-slice hold,not mathematical falsity.
tolerance ORIGINAL error ORIGINAL numerator over denominator := div(10, 2)
After
tolerance ORIGINAL error ORIGINAL numerator over denominator = 5
Conditions: none
Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank.
source roles = [tolerance ORIGINAL threshold, 100000000, 10, 2]
After
derived = [[5, 1], 5]
Conditions: none
Bound the SOURCE PRE-reduction numerator/denominator and require a nonzero denominator BEFORE sign/gcd normalization.MOD50 uses100million with NAIVE operations,not prior cross-cancellation;this Wave4 mean uses one million.Out-of-envelope is a source-slice hold,not mathematical falsity.
tolerance ORIGINAL threshold ORIGINAL numerator over denominator := div(10, 2)
After
tolerance ORIGINAL threshold ORIGINAL numerator over denominator = 5
Conditions: none
Calculate exactly from THIS step’s ORIGINAL ordered operands.Retain the SOURCE rational pre-reduction envelope separately;do not use floating values or silently widen a different bank.
FIRST qualify nonnegative error/tolerance and THIS equality boundary.Inclusive uses≤ and is true;strict uses< and is false.Equal tuple arity does not allow dropping the mode or swapping results.
S006 · premise_and_result_audit — Reverse-audit THIS step against its ORIGINAL ordered roles and complete premises.Accept the conclusion only under these conditions;do not invert a one-way implication or call a finite check a general formal proof.
S005 · premise_and_result_audit — Recompute tolerance ORIGINAL threshold ORIGINAL numerator over denominator with exact rational arithmetic, not rounded decimals.
S004 · premise_and_result_audit — Reverse-audit THIS step against its ORIGINAL ordered roles and complete premises.Accept the conclusion only under these conditions;do not invert a one-way implication or call a finite check a general formal proof.
S003 · premise_and_result_audit — Recompute tolerance ORIGINAL error ORIGINAL numerator over denominator with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Reverse-audit THIS step against its ORIGINAL ordered roles and complete premises.Accept the conclusion only under these conditions;do not invert a one-way implication or call a finite check a general formal proof.
S001 · premise_and_result_audit — Reverse-audit THIS step against its ORIGINAL ordered roles and complete premises.Accept the conclusion only under these conditions;do not invert a one-way implication or call a finite check a general formal proof.
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.