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R0065-33142 · q-20261006-advance-20261007-r01-matrix-0042
The real matrix M=[[4, 3], [6, 5], [8, 7], [10, 9]] is displayed as nested rows. Using one-based indices, find the entry in row 1, column 2.
G001 — The real matrix M=[[4, 3], [6, 5], [8, 7], [10, 9]] is displayed as nested rows. Using one-based indices, find the entry in row 1, column 2.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-entry, matrix_entry, reals, []]
After
derived = [[integer_STRING]]
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, [[4, 3], [6, 5], [8, 7], [10, 9]]]
After
derived = [4, 2]
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 = [[[4, 3], [6, 5], [8, 7], [10, 9]], 1, 2]
After
derived = [0, 1, 3]
Conditions: none
The SOURCE i/j are ONE-based and must lie within the shape.BEFORE reading the ORIGINAL entry,convert to internal zero-based indices.
Rule: Matrix_ENTRY_ONE_based_typed_indices_to_original_position · 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
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: 37a2fdf36a337b7d1f164f71a5a769587801262e2be4745ac8f9d2be8617bf39candidate record SHA-256: f071b6d937c242e93551d52a74743af5bccd8821c9a049f00af417f259fdb44fsemantic review receipt SHA-256: 92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6question-first witness SHA-256: 012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00Lean: NOT_RUN · human review: NOT_PERFORMED