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R0065-33163 · q-20261006-advance-20261007-r01-matrix-0013
The real matrix M=[[0, -1, -2], [2, 1, 0], [4, 3, 2]] is displayed as nested rows. Each dimension is from one through five. Give (number of rows, number of columns).
G001 — The real matrix M=[[0, -1, -2], [2, 1, 0], [4, 3, 2]] is displayed as nested rows. Each dimension is from one through five. Give (number of rows, number of columns).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-matrix-shape, matrix_shape, reals, []]
After
derived = [[rows_columns_NUMBER_pair]]
Conditions: none
MOD25 uses LOCAL hyphens/named domains,legacy matrices underscores/reals;BASE logic acquires no domain/op.Output tuples,matrices,numeric fields and fraction texts follow THIS source,not a universal/1 rule.Retain originals/English/AST/status.
Rule: R65_SOURCE_bank_keys_operation_domain_ordered_output_roles · Uses: G001
Before
source roles = [M ORIGINAL, [[0, -1, -2], [2, 1, 0], [4, 3, 2]]]
After
derived = [3, 3]
Conditions: none
THIS bank allows1..5 by1..5 matrices,not the R64 2×2 restriction.Type EVERY raw SAFE cell,including unused shape/entry cells.Keep original row order.
Rule: Matrix_RAW_rectangular_1to5_ALL_SAFE_entries_even_unused · Uses: G001, S001
Before
source roles = [[[0, -1, -2], [2, 1, 0], [4, 3, 2]]]
After
derived = [3, 3, 9]
Conditions: none
Count rows FIRST,then columns per row.Shape is(m,n),not(n,m)or total entries.
Rule: Matrix_SHAPE_rows_THEN_columns_NOT_total_entries · Uses: G001, S002
S003 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.S002 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.S001 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.(3, 3)
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: eff19a10e9ec6bf7f5512e95cabea538ce77fcac5bb17d6b463187e27ce2cc82candidate record SHA-256: ad79656c6543c6881c2947826024f5551506d5d0fb8737c6f272820ed2f1b47fsemantic review receipt SHA-256: 92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6question-first witness SHA-256: 012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00Lean: NOT_RUN · human review: NOT_PERFORMED