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R0065-33116 · q-20261006-advance-20261007-r01-matrix-0066
Over R, A=[[3], [5], [7], [9]] and B=[[-3], [-5], [-7], [-9]] have the same dimensions. Find A+B as a nested list of rows.
G001 — Over R, A=[[3], [5], [7], [9]] and B=[[-3], [-5], [-7], [-9]] have the same dimensions. Find A+B as a nested list of rows.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-addition, matrix_addition, reals, []]
After
derived = [[nested_ROW_matrix]]
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 = [A ORIGINAL, [[3], [5], [7], [9]]]
After
derived = [4, 1]
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 = [B ORIGINAL, [[-3], [-5], [-7], [-9]]]
After
derived = [4, 1]
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, S002
Before
Matrix sum ORIGINAL entry0,0 := sum(3, -3)
After
Matrix sum ORIGINAL entry0,0 = 0
Conditions: none
Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
Matrix sum ORIGINAL entry1,0 := sum(5, -5)
After
Matrix sum ORIGINAL entry1,0 = 0
Conditions: none
Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations.
Rule: exact_rational_arithmetic · Uses: G001, S004
Before
Matrix sum ORIGINAL entry2,0 := sum(7, -7)
After
Matrix sum ORIGINAL entry2,0 = 0
Conditions: none
Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations.
Rule: exact_rational_arithmetic · Uses: G001, S005
Before
Matrix sum ORIGINAL entry3,0 := sum(9, -9)
After
Matrix sum ORIGINAL entry3,0 = 0
Conditions: none
Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations.
Rule: exact_rational_arithmetic · Uses: G001, S006
Before
source roles = [[[3], [5], [7], [9]], [[-3], [-5], [-7], [-9]]]
After
derived = [[[0], [0], [0], [0]]]
Conditions: none
Add EVERY corresponding entry ONLY at equal shapes.Derived sums may exceed SAFE;do not reparse as a RAW matrix.No zero-padding or broadcasting.
Rule: Matrix_ADDITION_all_corresponding_entries_NO_padding_or_raw_recap · Uses: G001, S007
S008 · 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.S007 · premise_and_result_audit — Recompute Matrix sum ORIGINAL entry3,0 with exact rational arithmetic, not rounded decimals.S006 · premise_and_result_audit — Recompute Matrix sum ORIGINAL entry2,0 with exact rational arithmetic, not rounded decimals.S005 · premise_and_result_audit — Recompute Matrix sum ORIGINAL entry1,0 with exact rational arithmetic, not rounded decimals.S004 · premise_and_result_audit — Recompute Matrix sum ORIGINAL entry0,0 with exact rational arithmetic, not rounded decimals.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.[[0], [0], [0], [0]]
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: 4912a1ab22a0f72b65287f8d1723d8cc7761e8c7d49fdeebc41815799160283acandidate record SHA-256: d2b0bc8740c3a1a8cac7f78c8249499dbfa558ea1b195e5afccb6fd35e84e061semantic review receipt SHA-256: 92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6question-first witness SHA-256: 012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00Lean: NOT_RUN · human review: NOT_PERFORMED