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R0070-35757 · q-20260925-triangle-vertex-set-0002
Triangle DEF has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
G001 — Triangle DEF has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.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
source roles = [qf-triangle-vertex-set, [noncollinear, operation, vertices]]
After
derived = [triangle, vertex_set, null]
Conditions: none
Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules.
Rule: R70_SOURCE_bank_specific_interface · Uses: G001
Before
source roles = [[D, E, F], Yes]
After
derived = [[D, E, F], Yes, Yes]
Conditions: none
THIS nondegenerate triangle requires DISTINCT vertices AND GIVEN noncollinearity.Repeated points plus asserted noncollinearity is contradictory.Neither letter names nor a sketch proves noncollinearity.
Rule: Triangle_DISTINCT_labels_AND_GIVEN_noncollinearity · Uses: G001, S001
Before
source roles = [[D, E, F]]
After
derived = [[D, E, F], {D, E, F}]Conditions: none
Collect ALL three labels and canonically sort the vertex SET.A permutation is not a new triangle;the ORIGINAL JSON order remains preserved.
Rule: Triangle_VERTEX_set_complete_sorted_labels · Uses: G001, S002
S003 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S002 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.{D, E, F}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: de8b36443dd9ccb742f8c2d495a2356a761612f46000869e92dcde1e65ab980fcandidate record SHA-256: 48f13fecfdf258150971aaac8a0caf6a34cc74f82337423833862e641bac9608semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dabLean: NOT_RUN · human review: NOT_PERFORMED