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R0070-35751 · q-20260925-triangle-side-set-0021
Triangle LNP has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
G001 — Triangle LNP has explicitly distinct noncollinear vertices. List its three undirected sides 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-side-set, [noncollinear, operation, vertices]]
After
derived = [triangle, side_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 = [[L, N, P], Yes]
After
derived = [[L, N, P], 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 = [L, N]
After
derived = [LN]
Conditions: none
EACH unordered pair of distinct vertices defines ONE side.Endpoint sorting is canonical notation only;do not double-count reversed edges or infer lengths.
Rule: Triangle_EACH_unordered_distinct_endpoint_pair · Uses: G001, S002
Before
source roles = [L, P]
After
derived = [LP]
Conditions: none
EACH unordered pair of distinct vertices defines ONE side.Endpoint sorting is canonical notation only;do not double-count reversed edges or infer lengths.
Rule: Triangle_EACH_unordered_distinct_endpoint_pair · Uses: G001, S003
Before
source roles = [N, P]
After
derived = [NP]
Conditions: none
EACH unordered pair of distinct vertices defines ONE side.Endpoint sorting is canonical notation only;do not double-count reversed edges or infer lengths.
Rule: Triangle_EACH_unordered_distinct_endpoint_pair · Uses: G001, S004
Before
source roles = [[L, N, P], [LN, LP, NP]]
After
derived = [LN, LP, NP]
Conditions: none
Three vertices give EXACTLY three pairs.Use the ORIGINAL comma-separated format without extra braces;omit no edge and invent no diagonal.
Rule: Triangle_ALL_three_sides_source_comma_format · Uses: G001, S005
S006 · 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.S005 · 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.S004 · 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.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.LN, LP, NP
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: 76993f6533e6f4637202be5624a1b3a65ee4e4238d0e77ec85a8004103144668candidate record SHA-256: a61e2de87ecd486b5d37ba3edc0d05f84bc166091fec8db1d84eb71276683029semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dabLean: NOT_RUN · human review: NOT_PERFORMED