Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=100. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.
G001 — Use exact degrees for nondirected angles in [0,180], not a directed rotation or a measurement from a sketch. total=90, candidate first=100. Give (is first in [0,total]?, total−first). For an outside candidate still compute the signed arithmetic remainder, without claiming a constructed angle.
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.
Retain the ORIGINAL bank full operation prefix,domain and ordered answer roles.Use orthogonal_equal_unit only where a frame is declared,and degrees where an angle unit is declared.Integer fractions retain/1.Do not invent parameters or alter original bilingual sources.
Angle ORIGINAL SIGNED total minus first := sub(90, 100)
After
Angle ORIGINAL SIGNED total minus first = -10
Conditions: none
Substitute exact ORIGINAL roles,without floating approximation.SAFE bounds raw inputs only;derived integers/rationals are unbounded and do not inherit another bank component cap.
The first candidate may be negative or exceed total;STILL return No and SIGNED total-first.Only a qualified candidate admits an angle-split interpretation.Do not clip or pre-reject it.
S003 · premise_and_result_audit — Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate.
S002 · premise_and_result_audit — Recompute Angle ORIGINAL SIGNED total minus first with exact rational arithmetic, not rounded decimals.
S001 · premise_and_result_audit — Reverse-check this step against the ORIGINAL data,indices and premises,without claiming the conclusion uniquely recovers the inputs.Finite exact checking,independent review,formal proof and publication clearance remain separate.
Result
(No, -10)
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.