{"assistant":{"explanations":[{"calculationRefs":["report"],"text":"Три преобразования строк приводят матрицу к треугольному виду, решение единственно."},{"calculationRefs":["multiplier"],"text":"Множитель читается из исходного снимка: отношение элемента под ведущим к самому ведущему."},{"calculationRefs":["solution"],"text":"Обратная подстановка даёт x₃ = −1."},{"calculationRefs":["determinant"],"text":"Определитель равен произведению ведущих элементов и сходится с разложением Лейбница."}],"origin":"assistant","summary":"Прямой ход даёт три преобразования строк, обратная подстановка — решение x = (2, 3, −1), определитель равен −1. Вычисления идут точными дробями, без плавающей запятой: первый множитель равен −3/2, второй ведущий элемент 1/2, и произведение ведущих 2 · (1/2) · (−1) сходится с разложением Лейбница. 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Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. 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ведущей до r включительно нулевые"}],"name":"zero_below","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#zero_below/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#zero_below/arg/k","labels":[],"name":"k","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#zero_below/arg/col","labels":[],"name":"col","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#zero_below/arg/r","labels":[],"name":"r","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"}],"tables":[]},"provenance":{"acts":[{"contributed":true,"fragmentCount":0,"fragments":[],"jurisdiction":"none","namespace":"urn:law:calc:matrix-small","package":"calc-matrix-small","title":"calc.matrix_small — ОБЩИЙ ВЫЧИСЛИТЕЛЬ, НЕ АКТ: пошаговое исключение Гаусса для квадратной системы A·x = b размера 1..6 с точными рациональными коэффициентами (DECISION-0123). Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. Проверен сценариями §267, байтовый differential lawc/lawref."}],"caseHash":"sha256:99c4a6ce02773120535097d5e699d7625b6d8796527f2e2807d4c9376de44cdc","codeHash":"sha256:9bcca6a33805c1c364ca1bc8e9d39d6a9c51ba44203c0406bafbf397b96be699","jurisdiction":"вне юрисдикции государства","legalTime":"2026-09-06","mode":"audit","programHash":"sha256:a6548d14de8d5440db779f685fb65fcd8be651dff6da586720f1ba5a46b19e93","resultHash":"sha256:46c3f130742cd9021282f50baf2c500e0dd72a85bc5ff3142677afd0c3fb4981","rustCodeHash":"sha256:d368cafc7162ed7a6563df5e5c943a57be26fa8aeb3179b530fe3bdd67fe9be4","timezone":"Asia/Qyzylorda"},"request":{"args":["urn:calc:matrix:dense"],"facts":[{"args":["urn:calc:matrix:dense",3,10],"predicate":"system"},{"args":["urn:calc:matrix:dense",1,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-3/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"8/1"}],"predicate":"constant"},{"args":["urn:calc:matrix:dense",2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-11/1"}],"predicate":"constant"},{"args":["urn:calc:matrix:dense",3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-3/1"}],"predicate":"constant"}],"kind":"truth","legalTime":"2026-09-06","package":"calc-matrix-small","predicate":"report","proof":true},"sources":[],"text":"report: **TRUE_ONLY** — установлено\nВыведено правом: admissible(urn:calc:matrix:dense, 3, 10); cell(urn:calc:matrix:dense, 0, 2, 2, -1/1); cell(urn:calc:matrix:dense, 0, 2, 1, -3/1); cell(urn:calc:matrix:dense, 0, 3, 2, 1/1); cell(urn:calc:matrix:dense, 0, 1, 1, 2/1); cell(urn:calc:matrix:dense, 0, 1, 2, 1/1); cell(urn:calc:matrix:dense, 0, 3, 1, -2/1); cell(urn:calc:matrix:dense, 0, 3, 3, 2/1); cell(urn:calc:matrix:dense, 0, 1, 3, -1/1); cell(urn:calc:matrix:dense, 0, 2, 3, 2/1); cell(urn:calc:matrix:dense, 0, 3, 4, -3/1); cell(urn:calc:matrix:dense, 0, 1, 4, 8/1); cell(urn:calc:matrix:dense, 0, 2, 4, -11/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 4, -11/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 1, -3/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 2, -1/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 1, -2/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 4, -3/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 2, 1/1); state_complete(urn:calc:matrix:dense, 0); phase(urn:calc:matrix:dense, 0, 1, 1, 1); zero_below(urn:calc:matrix:dense, 0, 1, 0); pivot(urn:calc:matrix:dense, 0, 1, 1, 2/1); pivot_column(urn:calc:matrix:dense, 1); elim(urn:calc:matrix:dense, 0, 1, 1, 2, 1); row_op(urn:calc:matrix:dense, 0, 1, 1, 2, -3/2); cell(urn:calc:matrix:dense, 1, 3, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 2, 1/1); cell(urn:calc:matrix:dense, 1, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 3, -1/1); cell(urn:calc:matrix:dense, 1, 3, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 3, 2/1); cell(urn:calc:matrix:dense, 1, 3, 4, -3/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 4, -3/1); cell(urn:calc:matrix:dense, 1, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 4, 8/1); cell(urn:calc:matrix:dense, 1, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 2, 1/1); cell(urn:calc:matrix:dense, 1, 3, 1, -2/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 1, -2/1); cell(urn:calc:matrix:dense, 1, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 1, 2/1); cell(urn:calc:matrix:dense, 1, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 1, 2, 2, 1/2); cell(urn:calc:matrix:dense, 1, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 1, 2, 3, 1/2); cell(urn:calc:matrix:dense, 1, 2, 1, 0/1); cell(urn:calc:matrix:dense, 1, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 2, 4, 1/1); state_complete(urn:calc:matrix:dense, 1); elim(urn:calc:matrix:dense, 1, 1, 1, 3, 1); row_op(urn:calc:matrix:dense, 1, 1, 1, 3, -1/1); cell(urn:calc:matrix:dense, 2, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 2, 1/1); cell(urn:calc:matrix:dense, 2, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 1, 2/1); cell(urn:calc:matrix:dense, 2, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 4, 8/1); cell(urn:calc:matrix:dense, 2, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 2, 4, 1/1); cell(urn:calc:matrix:dense, 2, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 3, -1/1); cell(urn:calc:matrix:dense, 2, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 2, 2, 2, 1/2); cell(urn:calc:matrix:dense, 2, 2, 1, 0/1); cell(urn:calc:matrix:dense, 2, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 2, 2, 3, 1/2); cell(urn:calc:matrix:dense, 2, 3, 1, 0/1); cell(urn:calc:matrix:dense, 2, 3, 2, 2/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 2, 2/1); cell(urn:calc:matrix:dense, 2, 3, 3, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 3, 1/1); cell(urn:calc:matrix:dense, 2, 3, 4, 5/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 4, 5/1); state_complete(urn:calc:matrix:dense, 2); elim(urn:calc:matrix:dense, 2, 1, 1, 4, 1); phase(urn:calc:matrix:dense, 2, 2, 2, 1); zero_below(urn:calc:matrix:dense, 2, 2, 1); pivot(urn:calc:matrix:dense, 2, 2, 2, 1/2); pivot_column(urn:calc:matrix:dense, 2); elim(urn:calc:matrix:dense, 2, 2, 2, 3, 1); row_op(urn:calc:matrix:dense, 2, 2, 2, 3, 4/1); cell(urn:calc:matrix:dense, 3, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 2, 1/1); cell(urn:calc:matrix:dense, 3, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 4, 8/1); cell(urn:calc:matrix:dense, 3, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 3, -1/1); cell(urn:calc:matrix:dense, 3, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 3, 2, 2, 1/2); cell(urn:calc:matrix:dense, 3, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 3, 2, 3, 1/2); cell(urn:calc:matrix:dense, 3, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 1, 2/1); cell(urn:calc:matrix:dense, 3, 2, 1, 0/1); cell(urn:calc:matrix:dense, 3, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 2, 4, 1/1); cell(urn:calc:matrix:dense, 3, 3, 1, 0/1); cell(urn:calc:matrix:dense, 3, 3, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 3, 3, 3, -1/1); cell(urn:calc:matrix:dense, 3, 3, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 3, 4, 1/1); cell(urn:calc:matrix:dense, 3, 3, 2, 0/1); state_complete(urn:calc:matrix:dense, 3); elim(urn:calc:matrix:dense, 3, 2, 2, 4, 1); phase(urn:calc:matrix:dense, 3, 3, 3, 1); zero_below(urn:calc:matrix:dense, 3, 3, 2); pivot(urn:calc:matrix:dense, 3, 3, 3, -1/1); pivot_column(urn:calc:matrix:dense, 3); elim(urn:calc:matrix:dense, 3, 3, 3, 4, 1); phase(urn:calc:matrix:dense, 3, 4, 4, 1); forward_done(urn:calc:matrix:dense, 3, 3, 1); diagonal_product(urn:calc:matrix:dense, 0, 1/1); final_cell(urn:calc:matrix:dense, 3, 1, 0/1); final_cell(urn:calc:matrix:dense, 2, 2, 1/2); final_cell(urn:calc:matrix:dense, 1, 4, 8/1); final_cell(urn:calc:matrix:dense, 1, 2, 1/1); final_cell(urn:calc:matrix:dense, 2, 4, 1/1); final_cell(urn:calc:matrix:dense, 1, 1, 2/1); diagonal_product(urn:calc:matrix:dense, 1, 2/1); diagonal_product(urn:calc:matrix:dense, 2, 1/1); final_cell(urn:calc:matrix:dense, 3, 4, 1/1); final_cell(urn:calc:matrix:dense, 3, 3, -1/1); diagonal_product(urn:calc:matrix:dense, 3, -1/1); determinant(urn:calc:matrix:dense, -1/1); final_cell(urn:calc:matrix:dense, 3, 2, 0/1); final_cell(urn:calc:matrix:dense, 2, 3, 1/2); final_cell(urn:calc:matrix:dense, 1, 3, -1/1); final_cell(urn:calc:matrix:dense, 2, 1, 0/1); rank(urn:calc:matrix:dense, 3); consistent(urn:calc:matrix:dense); augmented_rank(urn:calc:matrix:dense, 3); outcome(urn:calc:matrix:dense, UNIQUE); back_partial(urn:calc:matrix:dense, 2, 3, 1/1); back_partial(urn:calc:matrix:dense, 3, 3, 1/1); back_partial(urn:calc:matrix:dense, 1, 3, 8/1); check_partial(urn:calc:matrix:dense, 1, 0, 0/1); check_partial(urn:calc:matrix:dense, 2, 0, 0/1); check_partial(urn:calc:matrix:dense, 3, 0, 0/1); solution(urn:calc:matrix:dense, 3, -1/1); back_partial(urn:calc:matrix:dense, 1, 2, 7/1); back_partial(urn:calc:matrix:dense, 2, 2, 3/2); solution(urn:calc:matrix:dense, 2, 3/1); back_partial(urn:calc:matrix:dense, 1, 1, 4/1); solution(urn:calc:matrix:dense, 1, 2/1); check_partial(urn:calc:matrix:dense, 2, 1, -6/1); check_partial(urn:calc:matrix:dense, 1, 1, 4/1); check_partial(urn:calc:matrix:dense, 3, 1, -4/1); check_partial(urn:calc:matrix:dense, 2, 2, -9/1); check_partial(urn:calc:matrix:dense, 2, 3, -11/1); check_partial(urn:calc:matrix:dense, 3, 2, -1/1); check_partial(urn:calc:matrix:dense, 3, 3, -3/1); check_partial(urn:calc:matrix:dense, 1, 2, 7/1); check_partial(urn:calc:matrix:dense, 1, 3, 8/1); row_verified(urn:calc:matrix:dense, 2); row_verified(urn:calc:matrix:dense, 1); row_verified(urn:calc:matrix:dense, 3); solution_verified(urn:calc:matrix:dense); report(urn:calc:matrix:dense)\nПрименены правила: AdmissibleInput, AfterRowOp, BackStart, BackStep, CheckStart, CheckStep, ChoosePivot, ColumnDone, Consistent, ConsistentRank, DeterminantFullRank, DiagonalStart, DiagonalStep, EliminateRow, FinalCell, ForwardDone, InitialCoefficient, InitialConstant, NonzeroNegative, NonzeroPositive, PivotColumn, RankOfA, RowOpCopy, RowOpTransform, RowVerified, SolutionVerified, Solve, Start, StartElimination, StateComplete, UniqueClass, UniqueReport, ZeroBelowStart\nОтвет поражаем правилом «недопустимый вход явно препятствует отчёту» — оно отменило бы вывод, будь установлено: input_error(urn:calc:matrix:dense, v1)\n(поражающее правило не сработало из-за неустановленных фактов — подайте их в facts, если они есть в деле)\nПраво (вне юрисдикции государства): calc.matrix_small — ОБЩИЙ ВЫЧИСЛИТЕЛЬ, НЕ АКТ: пошаговое исключение Гаусса для квадратной системы A·x = b размера 1..6 с точными рациональными коэффициентами (DECISION-0123). Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. Проверен сценариями §267, байтовый differential lawc/lawref. (programHash sha256:a6548d14de8d…)\nproof-граф: 187 узлов — поле evaluation готово для law_explain"},{"answer":{"answer":{"evaluationStatus":"COMPUTED","kind":"TRUTH","meaning":"установлено","missingInputs":[],"truthStatus":"TRUE_ONLY"},"closedEditionRules":[],"derived":["admissible(urn:calc:matrix:dense, 3, 10)","cell(urn:calc:matrix:dense, 0, 2, 2, -1/1)","cell(urn:calc:matrix:dense, 0, 2, 1, -3/1)","cell(urn:calc:matrix:dense, 0, 3, 2, 1/1)","cell(urn:calc:matrix:dense, 0, 1, 1, 2/1)","cell(urn:calc:matrix:dense, 0, 1, 2, 1/1)","cell(urn:calc:matrix:dense, 0, 3, 1, -2/1)","cell(urn:calc:matrix:dense, 0, 3, 3, 2/1)","cell(urn:calc:matrix:dense, 0, 1, 3, -1/1)","cell(urn:calc:matrix:dense, 0, 2, 3, 2/1)","cell(urn:calc:matrix:dense, 0, 3, 4, -3/1)","cell(urn:calc:matrix:dense, 0, 1, 4, 8/1)","cell(urn:calc:matrix:dense, 0, 2, 4, -11/1)","nonzero_cell(urn:calc:matrix:dense, 0, 2, 4, -11/1)","nonzero_cell(urn:calc:matrix:dense, 0, 2, 1, -3/1)","nonzero_cell(urn:calc:matrix:dense, 0, 1, 3, -1/1)","nonzero_cell(urn:calc:matrix:dense, 0, 2, 2, -1/1)","nonzero_cell(urn:calc:matrix:dense, 0, 3, 1, -2/1)","nonzero_cell(urn:calc:matrix:dense, 0, 3, 4, -3/1)","nonzero_cell(urn:calc:matrix:dense, 0, 3, 3, 2/1)","nonzero_cell(urn:calc:matrix:dense, 0, 2, 3, 2/1)","nonzero_cell(urn:calc:matrix:dense, 0, 1, 1, 2/1)","nonzero_cell(urn:calc:matrix:dense, 0, 3, 2, 1/1)","nonzero_cell(urn:calc:matrix:dense, 0, 1, 4, 8/1)","nonzero_cell(urn:calc:matrix:dense, 0, 1, 2, 1/1)","state_complete(urn:calc:matrix:dense, 0)","phase(urn:calc:matrix:dense, 0, 1, 1, 1)","zero_below(urn:calc:matrix:dense, 0, 1, 0)","pivot(urn:calc:matrix:dense, 0, 1, 1, 2/1)","pivot_column(urn:calc:matrix:dense, 1)","elim(urn:calc:matrix:dense, 0, 1, 1, 2, 1)","row_op(urn:calc:matrix:dense, 0, 1, 1, 2, -3/2)","cell(urn:calc:matrix:dense, 1, 3, 2, 1/1)","nonzero_cell(urn:calc:matrix:dense, 1, 3, 2, 1/1)","cell(urn:calc:matrix:dense, 1, 1, 3, -1/1)","nonzero_cell(urn:calc:matrix:dense, 1, 1, 3, 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— ОБЩИЙ ВЫЧИСЛИТЕЛЬ, НЕ АКТ: пошаговое исключение Гаусса для квадратной системы A·x = b размера 1..6 с точными рациональными коэффициентами (DECISION-0123). Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. 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решением"}],"name":"row_verified","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#row_verified/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#row_verified/arg/i","labels":[],"name":"i","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#solution","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"значение j-й неизвестной"}],"name":"solution","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#solution/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#solution/arg/j","labels":[],"name":"j","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#solution/arg/x","labels":[],"name":"x","type":{"name":"urn:law:std#Rational"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#solution_verified","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"решение проверено подстановкой во все исходные уравнения"}],"name":"solution_verified","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#solution_verified/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#state_complete","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"снимок k получил все n·(n+1) ячеек"}],"name":"state_complete","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#state_complete/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#state_complete/arg/k","labels":[],"name":"k","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#step","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"конечный домен номеров снимков: 0..40"}],"name":"step","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#step/arg/k","labels":[],"name":"k","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#system","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"предъявлена система из n уравнений с n неизвестными и бюджет преобразований"}],"name":"system","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#system/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#system/arg/n","labels":[],"name":"n","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#system/arg/budget","labels":[],"name":"budget","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#zero_below","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"в столбце col строки от ведущей до r включительно нулевые"}],"name":"zero_below","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#zero_below/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#zero_below/arg/k","labels":[],"name":"k","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#zero_below/arg/col","labels":[],"name":"col","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#zero_below/arg/r","labels":[],"name":"r","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"}],"tables":[]},"provenance":{"acts":[{"contributed":true,"fragmentCount":0,"fragments":[],"jurisdiction":"none","namespace":"urn:law:calc:matrix-small","package":"calc-matrix-small","title":"calc.matrix_small — ОБЩИЙ ВЫЧИСЛИТЕЛЬ, НЕ АКТ: пошаговое исключение Гаусса для квадратной системы A·x = b размера 1..6 с точными рациональными коэффициентами (DECISION-0123). Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. Проверен сценариями §267, байтовый differential lawc/lawref."}],"caseHash":"sha256:99c4a6ce02773120535097d5e699d7625b6d8796527f2e2807d4c9376de44cdc","codeHash":"sha256:9bcca6a33805c1c364ca1bc8e9d39d6a9c51ba44203c0406bafbf397b96be699","jurisdiction":"вне юрисдикции государства","legalTime":"2026-09-06","mode":"audit","programHash":"sha256:a6548d14de8d5440db779f685fb65fcd8be651dff6da586720f1ba5a46b19e93","resultHash":"sha256:d5f367a027119a368c896f168ee13c8e7269e08ccffd487e79bb64358629e702","rustCodeHash":"sha256:d368cafc7162ed7a6563df5e5c943a57be26fa8aeb3179b530fe3bdd67fe9be4","timezone":"Asia/Qyzylorda"},"request":{"args":["urn:calc:matrix:dense",0,1,1,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-3/2"}],"facts":[{"args":["urn:calc:matrix:dense",3,10],"predicate":"system"},{"args":["urn:calc:matrix:dense",1,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-3/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"8/1"}],"predicate":"constant"},{"args":["urn:calc:matrix:dense",2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-11/1"}],"predicate":"constant"},{"args":["urn:calc:matrix:dense",3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-3/1"}],"predicate":"constant"}],"kind":"truth","legalTime":"2026-09-06","package":"calc-matrix-small","predicate":"row_op","proof":true},"sources":[],"text":"row_op: **TRUE_ONLY** — установлено\nВыведено правом: admissible(urn:calc:matrix:dense, 3, 10); cell(urn:calc:matrix:dense, 0, 2, 2, -1/1); cell(urn:calc:matrix:dense, 0, 2, 1, -3/1); cell(urn:calc:matrix:dense, 0, 3, 2, 1/1); cell(urn:calc:matrix:dense, 0, 1, 1, 2/1); cell(urn:calc:matrix:dense, 0, 1, 2, 1/1); cell(urn:calc:matrix:dense, 0, 3, 1, -2/1); cell(urn:calc:matrix:dense, 0, 3, 3, 2/1); cell(urn:calc:matrix:dense, 0, 1, 3, -1/1); cell(urn:calc:matrix:dense, 0, 2, 3, 2/1); cell(urn:calc:matrix:dense, 0, 3, 4, -3/1); cell(urn:calc:matrix:dense, 0, 1, 4, 8/1); cell(urn:calc:matrix:dense, 0, 2, 4, -11/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 4, -11/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 1, -3/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 2, -1/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 1, -2/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 4, -3/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 2, 1/1); state_complete(urn:calc:matrix:dense, 0); phase(urn:calc:matrix:dense, 0, 1, 1, 1); zero_below(urn:calc:matrix:dense, 0, 1, 0); pivot(urn:calc:matrix:dense, 0, 1, 1, 2/1); pivot_column(urn:calc:matrix:dense, 1); elim(urn:calc:matrix:dense, 0, 1, 1, 2, 1); row_op(urn:calc:matrix:dense, 0, 1, 1, 2, -3/2); cell(urn:calc:matrix:dense, 1, 3, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 2, 1/1); cell(urn:calc:matrix:dense, 1, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 3, -1/1); cell(urn:calc:matrix:dense, 1, 3, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 3, 2/1); cell(urn:calc:matrix:dense, 1, 3, 4, -3/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 4, -3/1); cell(urn:calc:matrix:dense, 1, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 4, 8/1); cell(urn:calc:matrix:dense, 1, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 2, 1/1); cell(urn:calc:matrix:dense, 1, 3, 1, -2/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 1, -2/1); cell(urn:calc:matrix:dense, 1, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 1, 2/1); cell(urn:calc:matrix:dense, 1, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 1, 2, 2, 1/2); cell(urn:calc:matrix:dense, 1, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 1, 2, 3, 1/2); cell(urn:calc:matrix:dense, 1, 2, 1, 0/1); cell(urn:calc:matrix:dense, 1, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 2, 4, 1/1); state_complete(urn:calc:matrix:dense, 1); elim(urn:calc:matrix:dense, 1, 1, 1, 3, 1); row_op(urn:calc:matrix:dense, 1, 1, 1, 3, -1/1); cell(urn:calc:matrix:dense, 2, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 2, 1/1); cell(urn:calc:matrix:dense, 2, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 1, 2/1); cell(urn:calc:matrix:dense, 2, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 4, 8/1); cell(urn:calc:matrix:dense, 2, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 2, 4, 1/1); cell(urn:calc:matrix:dense, 2, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 3, -1/1); cell(urn:calc:matrix:dense, 2, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 2, 2, 2, 1/2); cell(urn:calc:matrix:dense, 2, 2, 1, 0/1); cell(urn:calc:matrix:dense, 2, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 2, 2, 3, 1/2); cell(urn:calc:matrix:dense, 2, 3, 1, 0/1); cell(urn:calc:matrix:dense, 2, 3, 2, 2/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 2, 2/1); cell(urn:calc:matrix:dense, 2, 3, 3, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 3, 1/1); cell(urn:calc:matrix:dense, 2, 3, 4, 5/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 4, 5/1); state_complete(urn:calc:matrix:dense, 2); elim(urn:calc:matrix:dense, 2, 1, 1, 4, 1); phase(urn:calc:matrix:dense, 2, 2, 2, 1); zero_below(urn:calc:matrix:dense, 2, 2, 1); pivot(urn:calc:matrix:dense, 2, 2, 2, 1/2); pivot_column(urn:calc:matrix:dense, 2); elim(urn:calc:matrix:dense, 2, 2, 2, 3, 1); row_op(urn:calc:matrix:dense, 2, 2, 2, 3, 4/1); cell(urn:calc:matrix:dense, 3, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 2, 1/1); cell(urn:calc:matrix:dense, 3, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 4, 8/1); cell(urn:calc:matrix:dense, 3, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 3, -1/1); cell(urn:calc:matrix:dense, 3, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 3, 2, 2, 1/2); cell(urn:calc:matrix:dense, 3, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 3, 2, 3, 1/2); cell(urn:calc:matrix:dense, 3, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 1, 2/1); cell(urn:calc:matrix:dense, 3, 2, 1, 0/1); cell(urn:calc:matrix:dense, 3, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 2, 4, 1/1); cell(urn:calc:matrix:dense, 3, 3, 1, 0/1); cell(urn:calc:matrix:dense, 3, 3, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 3, 3, 3, -1/1); cell(urn:calc:matrix:dense, 3, 3, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 3, 4, 1/1); cell(urn:calc:matrix:dense, 3, 3, 2, 0/1); state_complete(urn:calc:matrix:dense, 3); elim(urn:calc:matrix:dense, 3, 2, 2, 4, 1); phase(urn:calc:matrix:dense, 3, 3, 3, 1); zero_below(urn:calc:matrix:dense, 3, 3, 2); pivot(urn:calc:matrix:dense, 3, 3, 3, -1/1); pivot_column(urn:calc:matrix:dense, 3); elim(urn:calc:matrix:dense, 3, 3, 3, 4, 1); phase(urn:calc:matrix:dense, 3, 4, 4, 1); forward_done(urn:calc:matrix:dense, 3, 3, 1); diagonal_product(urn:calc:matrix:dense, 0, 1/1); final_cell(urn:calc:matrix:dense, 3, 1, 0/1); final_cell(urn:calc:matrix:dense, 2, 2, 1/2); final_cell(urn:calc:matrix:dense, 1, 4, 8/1); final_cell(urn:calc:matrix:dense, 1, 2, 1/1); final_cell(urn:calc:matrix:dense, 2, 4, 1/1); final_cell(urn:calc:matrix:dense, 1, 1, 2/1); diagonal_product(urn:calc:matrix:dense, 1, 2/1); diagonal_product(urn:calc:matrix:dense, 2, 1/1); final_cell(urn:calc:matrix:dense, 3, 4, 1/1); final_cell(urn:calc:matrix:dense, 3, 3, -1/1); diagonal_product(urn:calc:matrix:dense, 3, -1/1); determinant(urn:calc:matrix:dense, -1/1); final_cell(urn:calc:matrix:dense, 3, 2, 0/1); final_cell(urn:calc:matrix:dense, 2, 3, 1/2); final_cell(urn:calc:matrix:dense, 1, 3, -1/1); final_cell(urn:calc:matrix:dense, 2, 1, 0/1); rank(urn:calc:matrix:dense, 3); consistent(urn:calc:matrix:dense); augmented_rank(urn:calc:matrix:dense, 3); outcome(urn:calc:matrix:dense, UNIQUE); back_partial(urn:calc:matrix:dense, 2, 3, 1/1); back_partial(urn:calc:matrix:dense, 3, 3, 1/1); back_partial(urn:calc:matrix:dense, 1, 3, 8/1); check_partial(urn:calc:matrix:dense, 1, 0, 0/1); check_partial(urn:calc:matrix:dense, 2, 0, 0/1); check_partial(urn:calc:matrix:dense, 3, 0, 0/1); solution(urn:calc:matrix:dense, 3, -1/1); back_partial(urn:calc:matrix:dense, 1, 2, 7/1); back_partial(urn:calc:matrix:dense, 2, 2, 3/2); solution(urn:calc:matrix:dense, 2, 3/1); back_partial(urn:calc:matrix:dense, 1, 1, 4/1); solution(urn:calc:matrix:dense, 1, 2/1); check_partial(urn:calc:matrix:dense, 2, 1, -6/1); check_partial(urn:calc:matrix:dense, 1, 1, 4/1); check_partial(urn:calc:matrix:dense, 3, 1, -4/1); check_partial(urn:calc:matrix:dense, 2, 2, -9/1); check_partial(urn:calc:matrix:dense, 2, 3, -11/1); check_partial(urn:calc:matrix:dense, 3, 2, -1/1); check_partial(urn:calc:matrix:dense, 3, 3, -3/1); check_partial(urn:calc:matrix:dense, 1, 2, 7/1); check_partial(urn:calc:matrix:dense, 1, 3, 8/1); row_verified(urn:calc:matrix:dense, 2); row_verified(urn:calc:matrix:dense, 1); row_verified(urn:calc:matrix:dense, 3); solution_verified(urn:calc:matrix:dense); report(urn:calc:matrix:dense)\nПрименены правила: AdmissibleInput, AfterRowOp, BackStart, BackStep, CheckStart, CheckStep, ChoosePivot, ColumnDone, Consistent, ConsistentRank, DeterminantFullRank, DiagonalStart, DiagonalStep, EliminateRow, FinalCell, ForwardDone, InitialCoefficient, InitialConstant, NonzeroNegative, NonzeroPositive, PivotColumn, RankOfA, RowOpCopy, RowOpTransform, RowVerified, SolutionVerified, Solve, Start, StartElimination, StateComplete, UniqueClass, UniqueReport, ZeroBelowStart\nОтвет поражаем правилом «недопустимый вход явно препятствует отчёту» — оно отменило бы вывод, будь установлено: input_error(urn:calc:matrix:dense, v1)\n(поражающее правило не сработало из-за неустановленных фактов — подайте их в facts, если они есть в деле)\nПраво (вне юрисдикции государства): calc.matrix_small — ОБЩИЙ ВЫЧИСЛИТЕЛЬ, НЕ АКТ: пошаговое исключение Гаусса для квадратной системы A·x = b размера 1..6 с точными рациональными коэффициентами (DECISION-0123). Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. Проверен сценариями §267, байтовый differential lawc/lawref. 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Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. 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Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. Проверен сценариями §267, байтовый differential lawc/lawref."}],"caseHash":"sha256:99c4a6ce02773120535097d5e699d7625b6d8796527f2e2807d4c9376de44cdc","codeHash":"sha256:9bcca6a33805c1c364ca1bc8e9d39d6a9c51ba44203c0406bafbf397b96be699","jurisdiction":"вне юрисдикции государства","legalTime":"2026-09-06","mode":"audit","programHash":"sha256:a6548d14de8d5440db779f685fb65fcd8be651dff6da586720f1ba5a46b19e93","resultHash":"sha256:9ba8ab280e83a2cb2998d717f6e7e104c14aad711e6ab6d108ef3a8449c51af1","rustCodeHash":"sha256:d368cafc7162ed7a6563df5e5c943a57be26fa8aeb3179b530fe3bdd67fe9be4","timezone":"Asia/Qyzylorda"},"request":{"args":["urn:calc:matrix:dense",3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"facts":[{"args":["urn:calc:matrix:dense",3,10],"predicate":"system"},{"args":["urn:calc:matrix:dense",1,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-3/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"8/1"}],"predicate":"constant"},{"args":["urn:calc:matrix:dense",2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-11/1"}],"predicate":"constant"},{"args":["urn:calc:matrix:dense",3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-3/1"}],"predicate":"constant"}],"kind":"truth","legalTime":"2026-09-06","package":"calc-matrix-small","predicate":"solution","proof":true},"sources":[],"text":"solution: **TRUE_ONLY** — установлено\nВыведено правом: admissible(urn:calc:matrix:dense, 3, 10); cell(urn:calc:matrix:dense, 0, 2, 2, -1/1); cell(urn:calc:matrix:dense, 0, 2, 1, -3/1); cell(urn:calc:matrix:dense, 0, 3, 2, 1/1); cell(urn:calc:matrix:dense, 0, 1, 1, 2/1); cell(urn:calc:matrix:dense, 0, 1, 2, 1/1); cell(urn:calc:matrix:dense, 0, 3, 1, -2/1); cell(urn:calc:matrix:dense, 0, 3, 3, 2/1); cell(urn:calc:matrix:dense, 0, 1, 3, -1/1); cell(urn:calc:matrix:dense, 0, 2, 3, 2/1); cell(urn:calc:matrix:dense, 0, 3, 4, -3/1); cell(urn:calc:matrix:dense, 0, 1, 4, 8/1); cell(urn:calc:matrix:dense, 0, 2, 4, -11/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 4, -11/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 1, -3/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 2, -1/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 1, -2/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 4, -3/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 2, 1/1); state_complete(urn:calc:matrix:dense, 0); phase(urn:calc:matrix:dense, 0, 1, 1, 1); zero_below(urn:calc:matrix:dense, 0, 1, 0); pivot(urn:calc:matrix:dense, 0, 1, 1, 2/1); pivot_column(urn:calc:matrix:dense, 1); elim(urn:calc:matrix:dense, 0, 1, 1, 2, 1); row_op(urn:calc:matrix:dense, 0, 1, 1, 2, -3/2); cell(urn:calc:matrix:dense, 1, 3, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 2, 1/1); cell(urn:calc:matrix:dense, 1, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 3, -1/1); cell(urn:calc:matrix:dense, 1, 3, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 3, 2/1); cell(urn:calc:matrix:dense, 1, 3, 4, -3/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 4, -3/1); cell(urn:calc:matrix:dense, 1, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 4, 8/1); cell(urn:calc:matrix:dense, 1, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 2, 1/1); cell(urn:calc:matrix:dense, 1, 3, 1, -2/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 1, -2/1); cell(urn:calc:matrix:dense, 1, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 1, 2/1); cell(urn:calc:matrix:dense, 1, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 1, 2, 2, 1/2); cell(urn:calc:matrix:dense, 1, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 1, 2, 3, 1/2); cell(urn:calc:matrix:dense, 1, 2, 1, 0/1); cell(urn:calc:matrix:dense, 1, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 2, 4, 1/1); state_complete(urn:calc:matrix:dense, 1); elim(urn:calc:matrix:dense, 1, 1, 1, 3, 1); row_op(urn:calc:matrix:dense, 1, 1, 1, 3, -1/1); cell(urn:calc:matrix:dense, 2, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 2, 1/1); cell(urn:calc:matrix:dense, 2, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 1, 2/1); cell(urn:calc:matrix:dense, 2, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 4, 8/1); cell(urn:calc:matrix:dense, 2, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 2, 4, 1/1); cell(urn:calc:matrix:dense, 2, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 3, -1/1); cell(urn:calc:matrix:dense, 2, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 2, 2, 2, 1/2); cell(urn:calc:matrix:dense, 2, 2, 1, 0/1); cell(urn:calc:matrix:dense, 2, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 2, 2, 3, 1/2); cell(urn:calc:matrix:dense, 2, 3, 1, 0/1); cell(urn:calc:matrix:dense, 2, 3, 2, 2/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 2, 2/1); cell(urn:calc:matrix:dense, 2, 3, 3, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 3, 1/1); cell(urn:calc:matrix:dense, 2, 3, 4, 5/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 4, 5/1); state_complete(urn:calc:matrix:dense, 2); elim(urn:calc:matrix:dense, 2, 1, 1, 4, 1); phase(urn:calc:matrix:dense, 2, 2, 2, 1); zero_below(urn:calc:matrix:dense, 2, 2, 1); pivot(urn:calc:matrix:dense, 2, 2, 2, 1/2); pivot_column(urn:calc:matrix:dense, 2); elim(urn:calc:matrix:dense, 2, 2, 2, 3, 1); row_op(urn:calc:matrix:dense, 2, 2, 2, 3, 4/1); cell(urn:calc:matrix:dense, 3, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 2, 1/1); cell(urn:calc:matrix:dense, 3, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 4, 8/1); cell(urn:calc:matrix:dense, 3, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 3, -1/1); cell(urn:calc:matrix:dense, 3, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 3, 2, 2, 1/2); cell(urn:calc:matrix:dense, 3, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 3, 2, 3, 1/2); cell(urn:calc:matrix:dense, 3, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 1, 2/1); cell(urn:calc:matrix:dense, 3, 2, 1, 0/1); cell(urn:calc:matrix:dense, 3, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 2, 4, 1/1); cell(urn:calc:matrix:dense, 3, 3, 1, 0/1); cell(urn:calc:matrix:dense, 3, 3, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 3, 3, 3, -1/1); cell(urn:calc:matrix:dense, 3, 3, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 3, 4, 1/1); cell(urn:calc:matrix:dense, 3, 3, 2, 0/1); state_complete(urn:calc:matrix:dense, 3); elim(urn:calc:matrix:dense, 3, 2, 2, 4, 1); phase(urn:calc:matrix:dense, 3, 3, 3, 1); zero_below(urn:calc:matrix:dense, 3, 3, 2); pivot(urn:calc:matrix:dense, 3, 3, 3, -1/1); pivot_column(urn:calc:matrix:dense, 3); elim(urn:calc:matrix:dense, 3, 3, 3, 4, 1); phase(urn:calc:matrix:dense, 3, 4, 4, 1); forward_done(urn:calc:matrix:dense, 3, 3, 1); diagonal_product(urn:calc:matrix:dense, 0, 1/1); final_cell(urn:calc:matrix:dense, 3, 1, 0/1); final_cell(urn:calc:matrix:dense, 2, 2, 1/2); final_cell(urn:calc:matrix:dense, 1, 4, 8/1); final_cell(urn:calc:matrix:dense, 1, 2, 1/1); final_cell(urn:calc:matrix:dense, 2, 4, 1/1); final_cell(urn:calc:matrix:dense, 1, 1, 2/1); diagonal_product(urn:calc:matrix:dense, 1, 2/1); diagonal_product(urn:calc:matrix:dense, 2, 1/1); final_cell(urn:calc:matrix:dense, 3, 4, 1/1); final_cell(urn:calc:matrix:dense, 3, 3, -1/1); diagonal_product(urn:calc:matrix:dense, 3, -1/1); determinant(urn:calc:matrix:dense, -1/1); final_cell(urn:calc:matrix:dense, 3, 2, 0/1); final_cell(urn:calc:matrix:dense, 2, 3, 1/2); final_cell(urn:calc:matrix:dense, 1, 3, -1/1); final_cell(urn:calc:matrix:dense, 2, 1, 0/1); rank(urn:calc:matrix:dense, 3); consistent(urn:calc:matrix:dense); augmented_rank(urn:calc:matrix:dense, 3); outcome(urn:calc:matrix:dense, UNIQUE); back_partial(urn:calc:matrix:dense, 2, 3, 1/1); back_partial(urn:calc:matrix:dense, 3, 3, 1/1); back_partial(urn:calc:matrix:dense, 1, 3, 8/1); check_partial(urn:calc:matrix:dense, 1, 0, 0/1); check_partial(urn:calc:matrix:dense, 2, 0, 0/1); check_partial(urn:calc:matrix:dense, 3, 0, 0/1); solution(urn:calc:matrix:dense, 3, -1/1); back_partial(urn:calc:matrix:dense, 1, 2, 7/1); back_partial(urn:calc:matrix:dense, 2, 2, 3/2); solution(urn:calc:matrix:dense, 2, 3/1); back_partial(urn:calc:matrix:dense, 1, 1, 4/1); solution(urn:calc:matrix:dense, 1, 2/1); check_partial(urn:calc:matrix:dense, 2, 1, -6/1); check_partial(urn:calc:matrix:dense, 1, 1, 4/1); check_partial(urn:calc:matrix:dense, 3, 1, -4/1); check_partial(urn:calc:matrix:dense, 2, 2, -9/1); check_partial(urn:calc:matrix:dense, 2, 3, -11/1); check_partial(urn:calc:matrix:dense, 3, 2, -1/1); check_partial(urn:calc:matrix:dense, 3, 3, -3/1); check_partial(urn:calc:matrix:dense, 1, 2, 7/1); check_partial(urn:calc:matrix:dense, 1, 3, 8/1); row_verified(urn:calc:matrix:dense, 2); row_verified(urn:calc:matrix:dense, 1); row_verified(urn:calc:matrix:dense, 3); solution_verified(urn:calc:matrix:dense); report(urn:calc:matrix:dense)\nПрименены правила: AdmissibleInput, AfterRowOp, BackStart, BackStep, CheckStart, CheckStep, ChoosePivot, ColumnDone, Consistent, ConsistentRank, DeterminantFullRank, DiagonalStart, DiagonalStep, EliminateRow, FinalCell, ForwardDone, InitialCoefficient, InitialConstant, NonzeroNegative, NonzeroPositive, PivotColumn, RankOfA, RowOpCopy, RowOpTransform, RowVerified, SolutionVerified, Solve, Start, StartElimination, StateComplete, UniqueClass, UniqueReport, ZeroBelowStart\nОтвет поражаем правилом «недопустимый вход явно препятствует отчёту» — оно отменило бы вывод, будь установлено: input_error(urn:calc:matrix:dense, v1)\n(поражающее правило не сработало из-за неустановленных фактов — подайте их в facts, если они есть в деле)\nПраво (вне юрисдикции государства): calc.matrix_small — ОБЩИЙ ВЫЧИСЛИТЕЛЬ, НЕ АКТ: пошаговое исключение Гаусса для квадратной системы A·x = b размера 1..6 с точными рациональными коэффициентами (DECISION-0123). Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. Проверен сценариями §267, байтовый differential lawc/lawref. (programHash sha256:a6548d14de8d…)\nproof-граф: 187 узлов — поле evaluation готово для law_explain"},{"answer":{"answer":{"evaluationStatus":"COMPUTED","kind":"TRUTH","meaning":"установлено","missingInputs":[],"truthStatus":"TRUE_ONLY"},"closedEditionRules":[],"derived":["admissible(urn:calc:matrix:dense, 3, 10)","cell(urn:calc:matrix:dense, 0, 2, 2, -1/1)","cell(urn:calc:matrix:dense, 0, 2, 1, -3/1)","cell(urn:calc:matrix:dense, 0, 3, 2, 1/1)","cell(urn:calc:matrix:dense, 0, 1, 1, 2/1)","cell(urn:calc:matrix:dense, 0, 1, 2, 1/1)","cell(urn:calc:matrix:dense, 0, 3, 1, -2/1)","cell(urn:calc:matrix:dense, 0, 3, 3, 2/1)","cell(urn:calc:matrix:dense, 0, 1, 3, -1/1)","cell(urn:calc:matrix:dense, 0, 2, 3, 2/1)","cell(urn:calc:matrix:dense, 0, 3, 4, -3/1)","cell(urn:calc:matrix:dense, 0, 1, 4, 8/1)","cell(urn:calc:matrix:dense, 0, 2, 4, -11/1)","nonzero_cell(urn:calc:matrix:dense, 0, 2, 4, -11/1)","nonzero_cell(urn:calc:matrix:dense, 0, 2, 1, -3/1)","nonzero_cell(urn:calc:matrix:dense, 0, 1, 3, -1/1)","nonzero_cell(urn:calc:matrix:dense, 0, 2, 2, -1/1)","nonzero_cell(urn:calc:matrix:dense, 0, 3, 1, -2/1)","nonzero_cell(urn:calc:matrix:dense, 0, 3, 4, -3/1)","nonzero_cell(urn:calc:matrix:dense, 0, 3, 3, 2/1)","nonzero_cell(urn:calc:matrix:dense, 0, 2, 3, 2/1)","nonzero_cell(urn:calc:matrix:dense, 0, 1, 1, 2/1)","nonzero_cell(urn:calc:matrix:dense, 0, 3, 2, 1/1)","nonzero_cell(urn:calc:matrix:dense, 0, 1, 4, 8/1)","nonzero_cell(urn:calc:matrix:dense, 0, 1, 2, 1/1)","state_complete(urn:calc:matrix:dense, 0)","phase(urn:calc:matrix:dense, 0, 1, 1, 1)","zero_below(urn:calc:matrix:dense, 0, 1, 0)","pivot(urn:calc:matrix:dense, 0, 1, 1, 2/1)","pivot_column(urn:calc:matrix:dense, 1)","elim(urn:calc:matrix:dense, 0, 1, 1, 2, 1)","row_op(urn:calc:matrix:dense, 0, 1, 1, 2, -3/2)","cell(urn:calc:matrix:dense, 1, 3, 2, 1/1)","nonzero_cell(urn:calc:matrix:dense, 1, 3, 2, 1/1)","cell(urn:calc:matrix:dense, 1, 1, 3, -1/1)","nonzero_cell(urn:calc:matrix:dense, 1, 1, 3, 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— ОБЩИЙ ВЫЧИСЛИТЕЛЬ, НЕ АКТ: пошаговое исключение Гаусса для квадратной системы A·x = b размера 1..6 с точными рациональными коэффициентами (DECISION-0123). Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. 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k+1"}],"name":"row_op","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#row_op/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#row_op/arg/k","labels":[],"name":"k","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#row_op/arg/col","labels":[],"name":"col","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#row_op/arg/prow","labels":[],"name":"prow","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#row_op/arg/row","labels":[],"name":"row","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#row_op/arg/m","labels":[],"name":"m","type":{"name":"urn:law:std#Rational"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#row_verified","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"исходное уравнение i выполнено найденным решением"}],"name":"row_verified","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#row_verified/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#row_verified/arg/i","labels":[],"name":"i","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#solution","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"значение j-й неизвестной"}],"name":"solution","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#solution/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#solution/arg/j","labels":[],"name":"j","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#solution/arg/x","labels":[],"name":"x","type":{"name":"urn:law:std#Rational"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#solution_verified","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"решение проверено подстановкой во все исходные уравнения"}],"name":"solution_verified","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#solution_verified/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#state_complete","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"снимок k получил все n·(n+1) ячеек"}],"name":"state_complete","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#state_complete/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#state_complete/arg/k","labels":[],"name":"k","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#step","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"конечный домен номеров снимков: 0..40"}],"name":"step","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#step/arg/k","labels":[],"name":"k","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#system","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"предъявлена система из n уравнений с n неизвестными и бюджет преобразований"}],"name":"system","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#system/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#system/arg/n","labels":[],"name":"n","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#system/arg/budget","labels":[],"name":"budget","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"},{"id":"urn:law:calc:matrix-small#zero_below","kind":"symbol_decl","labels":[{"language":"ru","status":"unofficial","text":"в столбце col строки от ведущей до r включительно нулевые"}],"name":"zero_below","package":"urn:law:calc:matrix-small","parameters":[{"id":"urn:law:calc:matrix-small#zero_below/arg/c","labels":[],"name":"c","type":{"name":"urn:law:calc:matrix-small#Calc"}},{"id":"urn:law:calc:matrix-small#zero_below/arg/k","labels":[],"name":"k","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#zero_below/arg/col","labels":[],"name":"col","type":{"name":"urn:law:std#Integer"}},{"id":"urn:law:calc:matrix-small#zero_below/arg/r","labels":[],"name":"r","type":{"name":"urn:law:std#Integer"}}],"symbolKind":"relation"}],"tables":[]},"provenance":{"acts":[{"contributed":true,"fragmentCount":0,"fragments":[],"jurisdiction":"none","namespace":"urn:law:calc:matrix-small","package":"calc-matrix-small","title":"calc.matrix_small — ОБЩИЙ ВЫЧИСЛИТЕЛЬ, НЕ АКТ: пошаговое исключение Гаусса для квадратной системы A·x = b размера 1..6 с точными рациональными коэффициентами (DECISION-0123). Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. Проверен сценариями §267, байтовый differential lawc/lawref."}],"caseHash":"sha256:99c4a6ce02773120535097d5e699d7625b6d8796527f2e2807d4c9376de44cdc","codeHash":"sha256:9bcca6a33805c1c364ca1bc8e9d39d6a9c51ba44203c0406bafbf397b96be699","jurisdiction":"вне юрисдикции государства","legalTime":"2026-09-06","mode":"audit","programHash":"sha256:a6548d14de8d5440db779f685fb65fcd8be651dff6da586720f1ba5a46b19e93","resultHash":"sha256:df59e1649c115e3cebb67ffca1cde710c47480492d286f72025c0cc73e694be5","rustCodeHash":"sha256:d368cafc7162ed7a6563df5e5c943a57be26fa8aeb3179b530fe3bdd67fe9be4","timezone":"Asia/Qyzylorda"},"request":{"args":["urn:calc:matrix:dense",{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"facts":[{"args":["urn:calc:matrix:dense",3,10],"predicate":"system"},{"args":["urn:calc:matrix:dense",1,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-3/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",2,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"1/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",3,3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"2/1"}],"predicate":"coefficient"},{"args":["urn:calc:matrix:dense",1,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"8/1"}],"predicate":"constant"},{"args":["urn:calc:matrix:dense",2,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-11/1"}],"predicate":"constant"},{"args":["urn:calc:matrix:dense",3,{"kind":"value","type":{"name":"urn:law:std#Rational"},"value":"-3/1"}],"predicate":"constant"}],"kind":"truth","legalTime":"2026-09-06","package":"calc-matrix-small","predicate":"determinant","proof":true},"sources":[],"text":"determinant: **TRUE_ONLY** — установлено\nВыведено правом: admissible(urn:calc:matrix:dense, 3, 10); cell(urn:calc:matrix:dense, 0, 2, 2, -1/1); cell(urn:calc:matrix:dense, 0, 2, 1, -3/1); cell(urn:calc:matrix:dense, 0, 3, 2, 1/1); cell(urn:calc:matrix:dense, 0, 1, 1, 2/1); cell(urn:calc:matrix:dense, 0, 1, 2, 1/1); cell(urn:calc:matrix:dense, 0, 3, 1, -2/1); cell(urn:calc:matrix:dense, 0, 3, 3, 2/1); cell(urn:calc:matrix:dense, 0, 1, 3, -1/1); cell(urn:calc:matrix:dense, 0, 2, 3, 2/1); cell(urn:calc:matrix:dense, 0, 3, 4, -3/1); cell(urn:calc:matrix:dense, 0, 1, 4, 8/1); cell(urn:calc:matrix:dense, 0, 2, 4, -11/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 4, -11/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 1, -3/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 2, -1/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 1, -2/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 4, -3/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 2, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 0, 3, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 0, 1, 2, 1/1); state_complete(urn:calc:matrix:dense, 0); phase(urn:calc:matrix:dense, 0, 1, 1, 1); zero_below(urn:calc:matrix:dense, 0, 1, 0); pivot(urn:calc:matrix:dense, 0, 1, 1, 2/1); pivot_column(urn:calc:matrix:dense, 1); elim(urn:calc:matrix:dense, 0, 1, 1, 2, 1); row_op(urn:calc:matrix:dense, 0, 1, 1, 2, -3/2); cell(urn:calc:matrix:dense, 1, 3, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 2, 1/1); cell(urn:calc:matrix:dense, 1, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 3, -1/1); cell(urn:calc:matrix:dense, 1, 3, 3, 2/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 3, 2/1); cell(urn:calc:matrix:dense, 1, 3, 4, -3/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 4, -3/1); cell(urn:calc:matrix:dense, 1, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 4, 8/1); cell(urn:calc:matrix:dense, 1, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 2, 1/1); cell(urn:calc:matrix:dense, 1, 3, 1, -2/1); nonzero_cell(urn:calc:matrix:dense, 1, 3, 1, -2/1); cell(urn:calc:matrix:dense, 1, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 1, 1, 1, 2/1); cell(urn:calc:matrix:dense, 1, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 1, 2, 2, 1/2); cell(urn:calc:matrix:dense, 1, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 1, 2, 3, 1/2); cell(urn:calc:matrix:dense, 1, 2, 1, 0/1); cell(urn:calc:matrix:dense, 1, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 1, 2, 4, 1/1); state_complete(urn:calc:matrix:dense, 1); elim(urn:calc:matrix:dense, 1, 1, 1, 3, 1); row_op(urn:calc:matrix:dense, 1, 1, 1, 3, -1/1); cell(urn:calc:matrix:dense, 2, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 2, 1/1); cell(urn:calc:matrix:dense, 2, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 1, 2/1); cell(urn:calc:matrix:dense, 2, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 4, 8/1); cell(urn:calc:matrix:dense, 2, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 2, 4, 1/1); cell(urn:calc:matrix:dense, 2, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 2, 1, 3, -1/1); cell(urn:calc:matrix:dense, 2, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 2, 2, 2, 1/2); cell(urn:calc:matrix:dense, 2, 2, 1, 0/1); cell(urn:calc:matrix:dense, 2, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 2, 2, 3, 1/2); cell(urn:calc:matrix:dense, 2, 3, 1, 0/1); cell(urn:calc:matrix:dense, 2, 3, 2, 2/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 2, 2/1); cell(urn:calc:matrix:dense, 2, 3, 3, 1/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 3, 1/1); cell(urn:calc:matrix:dense, 2, 3, 4, 5/1); nonzero_cell(urn:calc:matrix:dense, 2, 3, 4, 5/1); state_complete(urn:calc:matrix:dense, 2); elim(urn:calc:matrix:dense, 2, 1, 1, 4, 1); phase(urn:calc:matrix:dense, 2, 2, 2, 1); zero_below(urn:calc:matrix:dense, 2, 2, 1); pivot(urn:calc:matrix:dense, 2, 2, 2, 1/2); pivot_column(urn:calc:matrix:dense, 2); elim(urn:calc:matrix:dense, 2, 2, 2, 3, 1); row_op(urn:calc:matrix:dense, 2, 2, 2, 3, 4/1); cell(urn:calc:matrix:dense, 3, 1, 2, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 2, 1/1); cell(urn:calc:matrix:dense, 3, 1, 4, 8/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 4, 8/1); cell(urn:calc:matrix:dense, 3, 1, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 3, -1/1); cell(urn:calc:matrix:dense, 3, 2, 2, 1/2); nonzero_cell(urn:calc:matrix:dense, 3, 2, 2, 1/2); cell(urn:calc:matrix:dense, 3, 2, 3, 1/2); nonzero_cell(urn:calc:matrix:dense, 3, 2, 3, 1/2); cell(urn:calc:matrix:dense, 3, 1, 1, 2/1); nonzero_cell(urn:calc:matrix:dense, 3, 1, 1, 2/1); cell(urn:calc:matrix:dense, 3, 2, 1, 0/1); cell(urn:calc:matrix:dense, 3, 2, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 2, 4, 1/1); cell(urn:calc:matrix:dense, 3, 3, 1, 0/1); cell(urn:calc:matrix:dense, 3, 3, 3, -1/1); nonzero_cell(urn:calc:matrix:dense, 3, 3, 3, -1/1); cell(urn:calc:matrix:dense, 3, 3, 4, 1/1); nonzero_cell(urn:calc:matrix:dense, 3, 3, 4, 1/1); cell(urn:calc:matrix:dense, 3, 3, 2, 0/1); state_complete(urn:calc:matrix:dense, 3); elim(urn:calc:matrix:dense, 3, 2, 2, 4, 1); phase(urn:calc:matrix:dense, 3, 3, 3, 1); zero_below(urn:calc:matrix:dense, 3, 3, 2); pivot(urn:calc:matrix:dense, 3, 3, 3, -1/1); pivot_column(urn:calc:matrix:dense, 3); elim(urn:calc:matrix:dense, 3, 3, 3, 4, 1); phase(urn:calc:matrix:dense, 3, 4, 4, 1); forward_done(urn:calc:matrix:dense, 3, 3, 1); diagonal_product(urn:calc:matrix:dense, 0, 1/1); final_cell(urn:calc:matrix:dense, 3, 1, 0/1); final_cell(urn:calc:matrix:dense, 2, 2, 1/2); final_cell(urn:calc:matrix:dense, 1, 4, 8/1); final_cell(urn:calc:matrix:dense, 1, 2, 1/1); final_cell(urn:calc:matrix:dense, 2, 4, 1/1); final_cell(urn:calc:matrix:dense, 1, 1, 2/1); diagonal_product(urn:calc:matrix:dense, 1, 2/1); diagonal_product(urn:calc:matrix:dense, 2, 1/1); final_cell(urn:calc:matrix:dense, 3, 4, 1/1); final_cell(urn:calc:matrix:dense, 3, 3, -1/1); diagonal_product(urn:calc:matrix:dense, 3, -1/1); determinant(urn:calc:matrix:dense, -1/1); final_cell(urn:calc:matrix:dense, 3, 2, 0/1); final_cell(urn:calc:matrix:dense, 2, 3, 1/2); final_cell(urn:calc:matrix:dense, 1, 3, -1/1); final_cell(urn:calc:matrix:dense, 2, 1, 0/1); rank(urn:calc:matrix:dense, 3); consistent(urn:calc:matrix:dense); augmented_rank(urn:calc:matrix:dense, 3); outcome(urn:calc:matrix:dense, UNIQUE); back_partial(urn:calc:matrix:dense, 2, 3, 1/1); back_partial(urn:calc:matrix:dense, 3, 3, 1/1); back_partial(urn:calc:matrix:dense, 1, 3, 8/1); check_partial(urn:calc:matrix:dense, 1, 0, 0/1); check_partial(urn:calc:matrix:dense, 2, 0, 0/1); check_partial(urn:calc:matrix:dense, 3, 0, 0/1); solution(urn:calc:matrix:dense, 3, -1/1); back_partial(urn:calc:matrix:dense, 1, 2, 7/1); back_partial(urn:calc:matrix:dense, 2, 2, 3/2); solution(urn:calc:matrix:dense, 2, 3/1); back_partial(urn:calc:matrix:dense, 1, 1, 4/1); solution(urn:calc:matrix:dense, 1, 2/1); check_partial(urn:calc:matrix:dense, 2, 1, -6/1); check_partial(urn:calc:matrix:dense, 1, 1, 4/1); check_partial(urn:calc:matrix:dense, 3, 1, -4/1); check_partial(urn:calc:matrix:dense, 2, 2, -9/1); check_partial(urn:calc:matrix:dense, 2, 3, -11/1); check_partial(urn:calc:matrix:dense, 3, 2, -1/1); check_partial(urn:calc:matrix:dense, 3, 3, -3/1); check_partial(urn:calc:matrix:dense, 1, 2, 7/1); check_partial(urn:calc:matrix:dense, 1, 3, 8/1); row_verified(urn:calc:matrix:dense, 2); row_verified(urn:calc:matrix:dense, 1); row_verified(urn:calc:matrix:dense, 3); solution_verified(urn:calc:matrix:dense); report(urn:calc:matrix:dense)\nПрименены правила: AdmissibleInput, AfterRowOp, BackStart, BackStep, CheckStart, CheckStep, ChoosePivot, ColumnDone, Consistent, ConsistentRank, DeterminantFullRank, DiagonalStart, DiagonalStep, EliminateRow, FinalCell, ForwardDone, InitialCoefficient, InitialConstant, NonzeroNegative, NonzeroPositive, PivotColumn, RankOfA, RowOpCopy, RowOpTransform, RowVerified, SolutionVerified, Solve, Start, StartElimination, StateComplete, UniqueClass, UniqueReport, ZeroBelowStart\nОтвет поражаем правилом «недопустимый вход явно препятствует отчёту» — оно отменило бы вывод, будь установлено: input_error(urn:calc:matrix:dense, v1)\n(поражающее правило не сработало из-за неустановленных фактов — подайте их в facts, если они есть в деле)\nПраво (вне юрисдикции государства): calc.matrix_small — ОБЩИЙ ВЫЧИСЛИТЕЛЬ, НЕ АКТ: пошаговое исключение Гаусса для квадратной системы A·x = b размера 1..6 с точными рациональными коэффициентами (DECISION-0123). Ни юрисдикции, ни нормативного источника у него нет. Ему передают заголовок system(c, n, budget), коэффициенты coefficient(c, i, j, p/q) и свободные члены constant(c, i, p/q); он строит снимки расширенной матрицы, выбирает ведущий элемент (первая строка с ненулевым коэффициентом), переставляет строки, вычисляет множители и преобразует строки, отвечает рангами A и [A|b], определителем, классификацией UNIQUE/INCONSISTENT/INFINITE, решением с проверкой подстановкой либо опорными и свободными неизвестными; бюджет считает элементарные преобразования, его исчерпание — явный незавершённый расчёт. Проверен сценариями §267, байтовый differential lawc/lawref. (programHash sha256:a6548d14de8d…)\nproof-граф: 187 узлов — поле evaluation готово для law_explain"}],"language":"ru","question":{"origin":"user","text":"Система 2x + y − z = 8, −3x − y + 2z = −11, −2x + y + 2z = −3. Как метод Гаусса приводит её к треугольному виду и чему равны решение и определитель?"},"schemaVersion":"law.answers.document/0.1"}