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R0011-06176 · q-20261009-advance-20261013-r02-integer-0026
Integer start=0, signed steps s1=0, s2=0. Give (endpoint, s1+s2, |s1|+|s2|).
G001 — Integer start=0, signed steps s1=0, s2=0. Give (endpoint, s1+s2, |s1|+|s2|).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.
Before
declared exact integer or rational-representation protocol
After
retain signs,ordered operands and original index order
Conditions: none
Check these finite data with exact integer arithmetic,without floating approximations or a claim to prove all integer-ring axioms.
Rule: integer_arithmetic_scope · Uses: G001
Before
signed net displacement := sum(0, 0)
After
signed net displacement = 0
Conditions: none
Add the two signed steps to obtain net displacement.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
final position := sum(0, 0)
After
final position = 0
Conditions: none
Add net displacement to the start to obtain the endpoint;net displacement alone is not an absolute position.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
steps=(0,0)
After
absolute step lengths=(0,0)
Conditions: none
Step signs encode direction;path length uses each step's absolute value.Do not cancel first and then take an absolute value.
Rule: signed_step_vs_length · Uses: G001, S003
Before
sum of step lengths := sum(0, 0)
After
sum of step lengths = 0
Conditions: none
Add both step lengths;returning to the start may still involve positive travel.
Rule: exact_rational_arithmetic · Uses: G001, S004
S005 · premise_and_result_audit — Recompute sum of step lengths with exact rational arithmetic, not rounded decimals.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 final position with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute signed net displacement 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.(0, 0, 0)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 6d8cfd8864e3f3936bfddb5f108983c7632b1e61088c2f5625136984b4236961candidate record SHA-256: fd1634ae23e6668424bab568ee49134552604c817ef3a5897761fd12274ba79bsemantic review receipt SHA-256: b9bbc1c947f477a9c4bb5a579368ac5265f2da4572ce612c30f3633ecaf4ae80question-first witness SHA-256: 93f720df3ab3af13a792a3e6b443728e3c2a56276df839911f36569333236c55Lean: NOT_RUN · human review: NOT_PERFORMED