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R0014-07674 · q-20261012-advance-20261016-r02-matrix-0074
Use complete nonempty integer matrices with 1–5 rows and columns and 1-based external indices. Transposition is not inversion or reversal of element order. M=[[11, 10, 9, 8], [12, 11, 10, 9], [13, 12, 11, 10], [14, 13, 12, 11], [15, 14, 13, 12]], ordered (i,j) candidates=[[1, 1], [5, 4], [0, 1]]. Give (shape of M, three index-eligibility values, three entries or invalid-index). Do not read an invalid entry.
G001 — Use complete nonempty integer matrices with 1–5 rows and columns and 1-based external indices. Transposition is not inversion or reversal of element order. M=[[11, 10, 9, 8], [12, 11, 10, 9], [13, 12, 11, 10], [14, 13, 12, 11], [15, 14, 13, 12]], ordered (i,j) candidates=[[1, 1], [5, 4], [0, 1]]. Give (shape of M, three index-eligibility values, three entries or invalid-index). Do not read an invalid entry.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
M=[[11, 10, 9, 8], [12, 11, 10, 9], [13, 12, 11, 10], [14, 13, 12, 11], [15, 14, 13, 12]];shape=[5, 4]
After
external indices start at1;transpose is not inverse
Conditions: none
First confirm a nonempty rectangular shape and complete integer entries.Transposition is defined for rectangular matrices without invertibility and is not matrix inversion.
Rule: rectangular_matrix_scope · Uses: G001
Before
query0=(1,1);shape=[5, 4]
After
qualified=Yes;value/status=11
Conditions: none
Both external indices must lie from1 through the corresponding size before reading the internal(i−1,j−1) position.Do not fill an invalid query using negative or wrapping indices.
Rule: matrix_index_eligibility_before_read · Uses: G001, S001
Before
query1=(5,4);shape=[5, 4]
After
qualified=Yes;value/status=12
Conditions: none
Both external indices must lie from1 through the corresponding size before reading the internal(i−1,j−1) position.Do not fill an invalid query using negative or wrapping indices.
Rule: matrix_index_eligibility_before_read · Uses: G001, S002
Before
query2=(0,1);shape=[5, 4]
After
qualified=No;value/status=invalid index
Conditions: none
Both external indices must lie from1 through the corresponding size before reading the internal(i−1,j−1) position.Do not fill an invalid query using negative or wrapping indices.
Rule: matrix_index_eligibility_before_read · Uses: G001, S003
S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.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.([5, 4], [Yes, Yes, No], [11, 12, invalid-index])
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: 6194eabd9e9a54d68a635d035e2266f36cdead8ecee4be573db151f3a5999d7dcandidate record SHA-256: 6e0f05251af6861ab196e07c60bb69fde1ee50c5ae070912b20e9194c990d052semantic review receipt SHA-256: 23ba8196e85a09c03add0a87f96bec5d67a00dc648d1d68eef89101525b41a77question-first witness SHA-256: 17d59afc327b7cb8b6e588686d6dc1abbccd384d8ba32b8c046652f96821d705Lean: NOT_RUN · human review: NOT_PERFORMED