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R0016-08609 · q-20260917-explicit-collinearity-classification-0009
Explicit data: P9, Q9, R9 are collinear. Are the three points collinear?
G001 — Explicit data: P9, Q9, R9 are collinear. Are the three points collinear?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
explicit typed incidence data;no coordinate or visual premise supplied
After
read the stated predicate;absence of a premise is not its negation
Conditions: none
Read the explicit geometric premise without inferring from appearance.An absent premise is not a negative premise;do not invent coordinates or equations.
Rule: declared_geometry_not_visual_inference · Uses: G001
Before
distinct point labels=[P9, Q9, R9];declared collinear=Yes;explicit negative=No
After
answer=Yes
Conditions: none
Collinearity means lying on one line,and coplanarity lying in one plane.The positive or negative predicate is explicit here,so answer from that premise,not from labels,drawings or missing data.
Rule: declared_same_line_or_plane_predicate · Uses: G001, S001
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.Yes
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: 60a173b4f230277a38cb9958e6649278dd5bfe0522ad21a93fd7e75df29275fccandidate record SHA-256: e8192ea2d79740e06d6d2fe46825f5e8ab481dea2957a8173fd03ea489c1a425semantic review receipt SHA-256: 00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2question-first witness SHA-256: 198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1Lean: NOT_RUN · human review: NOT_PERFORMED