Разгон из состояния покоя, путь при равноускоренном движении, кинетическая энергия, а также КПД машины против предела Карно между резервуарами 300 и 600 К.

Разгон с ускорением 20 м/с² за 20 с даёт 400 м/с, равноускоренное движение за оговорённое время — путь 525 м, тело массой 4 кг со скоростью 10 м/с несёт 200 Дж. КПД 200 Дж из 500 Дж равен точной дроби 2/5, предел Карно между 300 и 600 К равен 1/2, и 2/5 в него укладывается. Машина с работой 300 Дж из тех же 500 Дж даёт 3/5 — превышение предела выведено отдельным утверждением, а не оставлено читателю.

Это пояснение ассистента, а не результат расчёта. Проверяйте выводы по основаниям и источникам ниже.

Кратко

Выберите результат, чтобы перейти к основаниям

Конечная скорость разгонаПроверка условияУстановленоВыполнение: РассчитаноЛогический вывод: Установлено Путь при равноускоренном движенииПроверка условияУстановленоВыполнение: РассчитаноЛогический вывод: Установлено Кинетическая энергияПроверка условияУстановленоВыполнение: РассчитаноЛогический вывод: Установлено КПД машиныПроверка условияУстановленоВыполнение: РассчитаноЛогический вывод: Установлено Предел КарноПроверка условияУстановленоВыполнение: РассчитаноЛогический вывод: Установлено Превышение предела КарноПроверка условияУстановленоВыполнение: РассчитаноЛогический вывод: Установлено

Подробный разбор

Проверка условия

Конечная скорость разгона

Дата контекста 06.09.2026

Результат расчёта

Установлено

Исходные параметры

Что определяем

v = v₀ + at — конечная скорость при постоянном ускорении

m1400 m_per_s

Исходные факты

расчёт, предъявленный делом: данные величины и вопрос, заданный о них
c: m1
Общий субъект фактов ниже
начальная скорость, данная для расчёта
v0: 0 m_per_s
постоянное ускорение, данное для расчёта
a: 20 m_per_s2
истёкшее время, данное для расчёта
t: 20 s

Пакет: calc-mechanics

Дополнительные сведения

Сохранить доказательство: Да

Исходные данные · JSON

{
  "args": [
    "urn:case:calc:m1",
    "400 m_per_s"
  ],
  "facts": [
    {
      "args": [
        "urn:case:calc:m1",
        "0 m_per_s"
      ],
      "predicate": "given_initial_velocity"
    },
    {
      "args": [
        "urn:case:calc:m1",
        "20 m_per_s2"
      ],
      "predicate": "given_acceleration"
    },
    {
      "args": [
        "urn:case:calc:m1",
        "20 s"
      ],
      "predicate": "given_elapsed_time"
    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "final_velocity",
  "proof": true
}

Почему такой результатПрименённые правила и условия

Путь вывода5 шагов

1
начальная скорость, данная для расчёта
c: urn:case:calc:m1; v0: 0 m_per_s
факт дела
2
постоянное ускорение, данное для расчёта
c: urn:case:calc:m1; a: 20 m_per_s2
факт дела
3
истёкшее время, данное для расчёта
c: urn:case:calc:m1; t: 20 s
факт дела
4
v = v₀ + at
400 m_per_s = (0 m_per_s → m_per_s) + (20 m_per_s2 → m_per_s2) × (20 s → s)
Идентификатор
urn:law:calc:mechanics#FinalVelocity
правило
5
Вычисление запроса
запрос

проверено движком: 2 · факт дела: 3 · Полный граф: 6 узлов

Шаги сохранённого доказательства от фактов дела к ответу. Формулы показаны как записаны в норме, с подставленными значениями; страница ничего не пересчитывает.

Основание этого ответа

Правила из сохранённой цепочки доказательства ответа.

calc-mechanics

v = v₀ + at
Идентификатор
urn:law:calc:mechanics#FinalVelocity

Другие правила расчёта1

Применены в общем расчёте, но не входят в цепочку доказательства этого ответа.

calc-mechanics

x = v₀t + ½at²
Идентификатор
urn:law:calc:mechanics#Displacement

Другие выводы2

расчёт, предъявленный делом: данные величины и вопрос, заданный о них
c: m1
Общий субъект фактов ниже
x = v₀t + ½at² — перемещение при постоянном ускорении
x: 4000
v = v₀ + at — конечная скорость при постоянном ускорении
v: 400

x = v₀t + ½at² — перемещение при постоянном ускорении
c	x
m1	4000

v = v₀ + at — конечная скорость при постоянном ускорении
c	v
m1	400

Скрыто выведенных фактов: 0. В кратком ответе движок оставляет относящиеся к вопросу; полный перечень — в JSON расчёта ниже.

Граф доказательств

Граф доказательства · 3 слой

Узлы доказательств: 6 · assertion 3, rule_application 2, query_evaluation 1

assertion · urn:proof:assert:urn:mcp:case#fact-1

attributes

assertion: fact-1

conclusion

Аргументы

Идентификатор
m1
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m_per_s
value
0

Тип

literal

Знак

positive

Условие

given_initial_velocity

evidence

—

Идентификатор

fact-1

Тип

assertion

Посылки

—

sourceAnchors

—

assertion · urn:proof:assert:urn:mcp:case#fact-2

attributes

assertion: fact-2

conclusion

Аргументы

Идентификатор
m1
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m_per_s2
value
20

Тип

literal

Знак

positive

Условие

given_acceleration

evidence

—

Идентификатор

fact-2

Тип

assertion

Посылки

—

sourceAnchors

—

assertion · urn:proof:assert:urn:mcp:case#fact-3

attributes

assertion: fact-3

conclusion

Аргументы

Идентификатор
m1
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
s
value
20

Тип

literal

Знак

positive

Условие

given_elapsed_time

evidence

—

Идентификатор

fact-3

Тип

assertion

Посылки

—

sourceAnchors

—

rule_application · urn:proof:apply:Displacement:6b680668b2e765991940e268de3e3296675473aeb7fb52d9ae6877c756ebf610

attributes

—

conclusion

Аргументы

Идентификатор
m1
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m
value
4000

Тип

literal

Знак

positive

Условие

displacement

evidence

—

Идентификатор

6b680668b2e765991940e268de3e3296675473aeb7fb52d9ae6877c756ebf610

Тип

rule_application

Посылки

fact-1
fact-2
fact-3

Правило

Displacement

sourceAnchors

—

substitution

Идентификатор: m1
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

m_per_s

value

Тип

value

type

name: Quantity

Единица срока

m_per_s2

value

Тип

value

type

name: Quantity

Единица срока

value

rule_application · urn:proof:apply:FinalVelocity:ef4eae15fda3b695c435cd7964c8bd195d2027f8312de4402a7acb2c4229f186

attributes

—

conclusion

Аргументы

Идентификатор
m1
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m_per_s
value
400

Тип

literal

Знак

positive

Условие

final_velocity

evidence

—

Идентификатор

ef4eae15fda3b695c435cd7964c8bd195d2027f8312de4402a7acb2c4229f186

Тип

rule_application

Посылки

fact-1
fact-2
fact-3

Правило

FinalVelocity

sourceAnchors

—

substitution

Идентификатор: m1
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

m_per_s

value

Тип

value

type

name: Quantity

Единица срока

m_per_s2

value

Тип

value

type

name: Quantity

Единица срока

value

query_evaluation · urn:proof:query:mcp

attributes

—

conclusion

literal

Аргументы

Идентификатор
m1
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m_per_s
value
400

Тип

literal

Знак

positive

Условие

final_velocity

truthStatus

Установлено

evidence

—

Идентификатор

mcp

Тип

query_evaluation

Посылки

ef4eae15fda3b695c435cd7964c8bd195d2027f8312de4402a7acb2c4229f186

sourceAnchors

—

Идентификаторы календаря и доказательства

Ссылка на доказательство: mcp

Исходное обоснование · JSON

{
  "derived": [
    "displacement(urn:case:calc:m1, 4000)",
    "final_velocity(urn:case:calc:m1, 400)"
  ],
  "derivedOmitted": 0,
  "evaluation": {
    "proofGraph": {
      "nodes": [
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-1"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m1",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "m_per_s",
                "value": "0"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_initial_velocity"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-1",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-2"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m1",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "m_per_s2",
                "value": "20"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_acceleration"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-2",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-3"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m1",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "s",
                "value": "20"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_elapsed_time"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-3",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {},
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m1",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "m",
                "value": "4000"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#displacement"
          },
          "evidence": [],
          "id": "urn:proof:apply:Displacement:6b680668b2e765991940e268de3e3296675473aeb7fb52d9ae6877c756ebf610",
          "kind": "rule_application",
          "premises": [
            "urn:proof:assert:urn:mcp:case#fact-1",
            "urn:proof:assert:urn:mcp:case#fact-2",
            "urn:proof:assert:urn:mcp:case#fact-3"
          ],
          "rule": "urn:law:calc:mechanics#Displacement",
          "sourceAnchors": [],
          "substitution": {
            "v0": {
              "id": "urn:case:calc:m1",
              "kind": "entity_ref"
            },
            "v1": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "m_per_s",
              "value": "0"
            },
            "v2": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "m_per_s2",
              "value": "20"
            },
            "v3": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "s",
              "value": "20"
            }
          }
        },
        {
          "attributes": {},
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m1",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "m_per_s",
                "value": "400"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#final_velocity"
          },
          "evidence": [],
          "id": "urn:proof:apply:FinalVelocity:ef4eae15fda3b695c435cd7964c8bd195d2027f8312de4402a7acb2c4229f186",
          "kind": "rule_application",
          "premises": [
            "urn:proof:assert:urn:mcp:case#fact-1",
            "urn:proof:assert:urn:mcp:case#fact-2",
            "urn:proof:assert:urn:mcp:case#fact-3"
          ],
          "rule": "urn:law:calc:mechanics#FinalVelocity",
          "sourceAnchors": [],
          "substitution": {
            "v0": {
              "id": "urn:case:calc:m1",
              "kind": "entity_ref"
            },
            "v1": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "m_per_s",
              "value": "0"
            },
            "v2": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "m_per_s2",
              "value": "20"
            },
            "v3": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "s",
              "value": "20"
            }
          }
        },
        {
          "attributes": {},
          "conclusion": {
            "literal": {
              "args": [
                {
                  "id": "urn:case:calc:m1",
                  "kind": "entity_ref"
                },
                {
                  "kind": "value",
                  "type": {
                    "name": "urn:law:std#Quantity"
                  },
                  "unit": "m_per_s",
                  "value": "400"
                }
              ],
              "kind": "literal",
              "polarity": "positive",
              "predicate": "urn:law:calc:mechanics#final_velocity"
            },
            "truthStatus": "TRUE_ONLY"
          },
          "evidence": [],
          "id": "urn:proof:query:mcp",
          "kind": "query_evaluation",
          "premises": [
            "urn:proof:apply:FinalVelocity:ef4eae15fda3b695c435cd7964c8bd195d2027f8312de4402a7acb2c4229f186"
          ],
          "sourceAnchors": []
        }
      ],
      "proofHash": "sha256:3e1707e1552b25ff9dab1b4c2c0ddc410db4bbcabe9ec7a348164e12949516d1",
      "roots": [
        "urn:proof:query:mcp"
      ]
    },
    "resultHash": "sha256:8cc6af2e66328cffe6b1c7d44d9932ff749cea8e081b33b0d22d3002a8bcbbdd",
    "schemaVersion": "law.core.evaluation/0.1"
  },
  "proofRef": "urn:proof:query:mcp",
  "rulesApplied": [
    "urn:law:calc:mechanics#Displacement",
    "urn:law:calc:mechanics#FinalVelocity"
  ]
}

ИсточникиТексты не сохранены

Тексты источников в этом снимке не сохранены.

Пакеты в снимке

calc-mechanics
units-si

Технические данныеПолный ответ, параметры и контрольные суммы

Статус расчёта: COMPUTED

Полный ответ движка

final_velocity: TRUE_ONLY — установлено Выведено правом: displacement(urn:case:calc:m1, 4000); final_velocity(urn:case:calc:m1, 400) Применены правила: Displacement, FinalVelocity Право (вне юрисдикции государства): calc-mechanics (programHash sha256:0402ab611e2a…) Вместе с актами: units-si proof-граф: 6 узлов — поле evaluation готово для law_explain

Полный машинный результат · JSON

{
  "answer": {
    "evaluationStatus": "COMPUTED",
    "kind": "TRUTH",
    "meaning": "установлено",
    "missingInputs": [],
    "truthStatus": "TRUE_ONLY"
  },
  "closedEditionRules": [],
  "derived": [
    "displacement(urn:case:calc:m1, 4000)",
    "final_velocity(urn:case:calc:m1, 400)"
  ],
  "derivedOmitted": 0,
  "evaluation": {
    "proofGraph": {
      "nodes": [
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-1"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m1",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "m_per_s",
                "value": "0"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_initial_velocity"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-1",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-2"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m1",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "m_per_s2",
                "value": "20"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_acceleration"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-2",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-3"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m1",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "s",
                "value": "20"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_elapsed_time"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-3",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {},
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m1",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "m",
                "value": "4000"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#displacement"
          },
          "evidence": [],
          "id": "urn:proof:apply:Displacement:6b680668b2e765991940e268de3e3296675473aeb7fb52d9ae6877c756ebf610",
          "kind": "rule_application",
          "premises": [
            "urn:proof:assert:urn:mcp:case#fact-1",
            "urn:proof:assert:urn:mcp:case#fact-2",
            "urn:proof:assert:urn:mcp:case#fact-3"
          ],
          "rule": "urn:law:calc:mechanics#Displacement",
          "sourceAnchors": [],
          "substitution": {
            "v0": {
              "id": "urn:case:calc:m1",
              "kind": "entity_ref"
            },
            "v1": {
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Исполнение · JSON

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Метаданные отображения

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        "urn:proof:assert:urn:mcp:case#fact-2",
        "urn:proof:assert:urn:mcp:case#fact-3"
      ],
      "rule": "urn:law:calc:mechanics#FinalVelocity",
      "strength": "strict",
      "substitution": {
        "v0": {
          "id": "urn:case:calc:m1",
          "kind": "entity_ref"
        },
        "v1": {
          "kind": "value",
          "type": {
            "name": "urn:law:std#Quantity"
          },
          "unit": "m_per_s",
          "value": "0"
        },
        "v2": {
          "kind": "value",
          "type": {
            "name": "urn:law:std#Quantity"
          },
          "unit": "m_per_s2",
          "value": "20"
        },
        "v3": {
          "kind": "value",
          "type": {
            "name": "urn:law:std#Quantity"
          },
          "unit": "s",
          "value": "20"
        }
      },
      "trust": "engine",
      "variables": [
        {
          "id": "v0",
          "type": {
            "name": "urn:law:calc:mechanics#Calculation"
          }
        },
        {
          "id": "v1",
          "type": {
            "name": "urn:law:std#Quantity"
          }
        },
        {
          "id": "v2",
          "type": {
            "name": "urn:law:std#Quantity"
          }
        },
        {
          "id": "v3",
          "type": {
            "name": "urn:law:std#Quantity"
          }
        }
      ]
    },
    {
      "conclusion": {
        "literal": {
          "args": [
            {
              "id": "urn:case:calc:m1",
              "kind": "entity_ref"
            },
            {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "m_per_s",
              "value": "400"
            }
          ],
          "kind": "literal",
          "polarity": "positive",
          "predicate": "urn:law:calc:mechanics#final_velocity"
        },
        "truthStatus": "TRUE_ONLY"
      },
      "id": "urn:proof:query:mcp",
      "kind": "query_evaluation",
      "originStatus": "available",
      "premises": [
        "urn:proof:apply:FinalVelocity:ef4eae15fda3b695c435cd7964c8bd195d2027f8312de4402a7acb2c4229f186"
      ],
      "trust": "engine"
    }
  ],
  "symbols": [
    {
      "id": "urn:law:calc:mechanics#Calculation",
      "kind": "type_decl",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "a calculation the case presents: the given quantities and the question asked of them"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "расчёт, предъявленный делом: данные величины и вопрос, заданный о них"
        }
      ],
      "name": "Calculation",
      "package": "urn:law:calc:mechanics"
    },
    {
      "id": "urn:law:calc:mechanics#Displacement",
      "kind": "rule",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "x = v₀t + ½at²"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "x = v₀t + ½at²"
        }
      ],
      "package": "urn:law:calc:mechanics",
      "strength": "strict"
    },
    {
      "id": "urn:law:calc:mechanics#FinalVelocity",
      "kind": "rule",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "v = v₀ + at"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "v = v₀ + at"
        }
      ],
      "package": "urn:law:calc:mechanics",
      "strength": "strict"
    },
    {
      "id": "urn:law:calc:mechanics#displacement",
      "kind": "symbol_decl",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "x = v₀t + ½at² — the displacement under constant acceleration"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "x = v₀t + ½at² — перемещение при постоянном ускорении"
        }
      ],
      "name": "displacement",
      "package": "urn:law:calc:mechanics",
      "parameters": [
        {
          "id": "urn:law:calc:mechanics#displacement/arg/c",
          "labels": [],
          "name": "c",
          "type": {
            "name": "urn:law:calc:mechanics#Calculation"
          }
        },
        {
          "id": "urn:law:calc:mechanics#displacement/arg/x",
          "labels": [],
          "name": "x",
          "type": {
            "name": "urn:law:std#Quantity"
          }
        }
      ],
      "symbolKind": "relation"
    },
    {
      "id": "urn:law:calc:mechanics#final_velocity",
      "kind": "symbol_decl",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "v = v₀ + at — the final velocity under constant acceleration"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "v = v₀ + at — конечная скорость при постоянном ускорении"
        }
      ],
      "name": "final_velocity",
      "package": "urn:law:calc:mechanics",
      "parameters": [
        {
          "id": "urn:law:calc:mechanics#final_velocity/arg/c",
          "labels": [],
          "name": "c",
          "type": {
            "name": "urn:law:calc:mechanics#Calculation"
          }
        },
        {
          "id": "urn:law:calc:mechanics#final_velocity/arg/v",
          "labels": [],
          "name": "v",
          "type": {
            "name": "urn:law:std#Quantity"
          }
        }
      ],
      "symbolKind": "relation"
    },
    {
      "id": "urn:law:calc:mechanics#given_acceleration",
      "kind": "symbol_decl",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "the constant acceleration given for the calculation"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "постоянное ускорение, данное для расчёта"
        }
      ],
      "name": "given_acceleration",
      "package": "urn:law:calc:mechanics",
      "parameters": [
        {
          "id": "urn:law:calc:mechanics#given_acceleration/arg/c",
          "labels": [],
          "name": "c",
          "type": {
            "name": "urn:law:calc:mechanics#Calculation"
          }
        },
        {
          "id": "urn:law:calc:mechanics#given_acceleration/arg/a",
          "labels": [],
          "name": "a",
          "type": {
            "name": "urn:law:std#Quantity"
          }
        }
      ],
      "symbolKind": "relation"
    },
    {
      "id": "urn:law:calc:mechanics#given_elapsed_time",
      "kind": "symbol_decl",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "the elapsed time given for the calculation"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "истёкшее время, данное для расчёта"
        }
      ],
      "name": "given_elapsed_time",
      "package": "urn:law:calc:mechanics",
      "parameters": [
        {
          "id": "urn:law:calc:mechanics#given_elapsed_time/arg/c",
          "labels": [],
          "name": "c",
          "type": {
            "name": "urn:law:calc:mechanics#Calculation"
          }
        },
        {
          "id": "urn:law:calc:mechanics#given_elapsed_time/arg/t",
          "labels": [],
          "name": "t",
          "type": {
            "name": "urn:law:std#Quantity"
          }
        }
      ],
      "symbolKind": "relation"
    },
    {
      "id": "urn:law:calc:mechanics#given_initial_velocity",
      "kind": "symbol_decl",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "the initial velocity given for the calculation"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "начальная скорость, данная для расчёта"
        }
      ],
      "name": "given_initial_velocity",
      "package": "urn:law:calc:mechanics",
      "parameters": [
        {
          "id": "urn:law:calc:mechanics#given_initial_velocity/arg/c",
          "labels": [],
          "name": "c",
          "type": {
            "name": "urn:law:calc:mechanics#Calculation"
          }
        },
        {
          "id": "urn:law:calc:mechanics#given_initial_velocity/arg/v0",
          "labels": [],
          "name": "v0",
          "type": {
            "name": "urn:law:std#Quantity"
          }
        }
      ],
      "symbolKind": "relation"
    }
  ],
  "tables": []
}

JSON · расчёты, источники и точные данные

{
  "acts": [
    {
      "contributed": true,
      "fragmentCount": 0,
      "fragments": [],
      "jurisdiction": "none",
      "namespace": "urn:law:calc:mechanics",
      "package": "calc-mechanics",
      "title": "calc-mechanics"
    },
    {
      "contributed": false,
      "fragmentCount": 0,
      "fragments": [],
      "jurisdiction": null,
      "namespace": "urn:law:units:si",
      "package": "units-si",
      "title": "units-si"
    }
  ],
  "caseHash": "sha256:6b3b8817c480b7ae093cfcc616f9485c8e03a732ad2da4f6b32804b188261517",
  "codeHash": "sha256:9bcca6a33805c1c364ca1bc8e9d39d6a9c51ba44203c0406bafbf397b96be699",
  "jurisdiction": "вне юрисдикции государства",
  "legalTime": "2026-09-06",
  "mode": "audit",
  "programHash": "sha256:0402ab611e2a073ec4ae0b3ab9cc9496e5b9b3fc4dba3c4b8c2081856bb7291a",
  "resultHash": "sha256:8cc6af2e66328cffe6b1c7d44d9932ff749cea8e081b33b0d22d3002a8bcbbdd",
  "rustCodeHash": "sha256:d368cafc7162ed7a6563df5e5c943a57be26fa8aeb3179b530fe3bdd67fe9be4",
  "timezone": "Asia/Qyzylorda"
}

evaluation SHA-256: sha256:5b116e2debd1c65b89c6ea5f138f4975af7bcea41988bdd4bbbf477065fbc701

Исходные данные · JSON

{
  "args": [
    "urn:case:calc:m1",
    "400 m_per_s"
  ],
  "facts": [
    {
      "args": [
        "urn:case:calc:m1",
        "0 m_per_s"
      ],
      "predicate": "given_initial_velocity"
    },
    {
      "args": [
        "urn:case:calc:m1",
        "20 m_per_s2"
      ],
      "predicate": "given_acceleration"
    },
    {
      "args": [
        "urn:case:calc:m1",
        "20 s"
      ],
      "predicate": "given_elapsed_time"
    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "final_velocity",
  "proof": true
}

Начальная скорость нулевая, ускорение 20 м/с², время 20 с — конечная скорость 400 м/с.

Проверка условия

Путь при равноускоренном движении

Дата контекста 06.09.2026

Результат расчёта

Установлено

Исходные параметры

Что определяем

x = v₀t + ½at² — перемещение при постоянном ускорении

m3525 m

Исходные факты

расчёт, предъявленный делом: данные величины и вопрос, заданный о них
c: m3
Общий субъект фактов ниже
начальная скорость, данная для расчёта
v0: 30 m_per_s
постоянное ускорение, данное для расчёта
a: 30 m_per_s2
истёкшее время, данное для расчёта
t: 5 s

Пакет: calc-mechanics

Дополнительные сведения

Сохранить доказательство: Да

Исходные данные · JSON

{
  "args": [
    "urn:case:calc:m3",
    "525 m"
  ],
  "facts": [
    {
      "args": [
        "urn:case:calc:m3",
        "30 m_per_s"
      ],
      "predicate": "given_initial_velocity"
    },
    {
      "args": [
        "urn:case:calc:m3",
        "30 m_per_s2"
      ],
      "predicate": "given_acceleration"
    },
    {
      "args": [
        "urn:case:calc:m3",
        "5 s"
      ],
      "predicate": "given_elapsed_time"
    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "displacement",
  "proof": true
}

Почему такой результатПрименённые правила и условия

Путь вывода5 шагов

1
начальная скорость, данная для расчёта
c: urn:case:calc:m3; v0: 30 m_per_s
факт дела
2
постоянное ускорение, данное для расчёта
c: urn:case:calc:m3; a: 30 m_per_s2
факт дела
3
истёкшее время, данное для расчёта
c: urn:case:calc:m3; t: 5 s
факт дела
4
x = v₀t + ½at²
525 m = (30 m_per_s → m_per_s) × (5 s → s) + 1 / 2 × (30 m_per_s2 → m_per_s2) × (5 s → s) × (5 s → s)
Идентификатор
urn:law:calc:mechanics#Displacement
правило
5
Вычисление запроса
запрос

проверено движком: 2 · факт дела: 3 · Полный граф: 6 узлов

Основание этого ответа

Правила из сохранённой цепочки доказательства ответа.

calc-mechanics

x = v₀t + ½at²
Идентификатор
urn:law:calc:mechanics#Displacement

Другие правила расчёта1

Применены в общем расчёте, но не входят в цепочку доказательства этого ответа.

calc-mechanics

v = v₀ + at
Идентификатор
urn:law:calc:mechanics#FinalVelocity

Другие выводы2

расчёт, предъявленный делом: данные величины и вопрос, заданный о них
c: m3
Общий субъект фактов ниже
x = v₀t + ½at² — перемещение при постоянном ускорении
x: 525
v = v₀ + at — конечная скорость при постоянном ускорении
v: 180

x = v₀t + ½at² — перемещение при постоянном ускорении
c	x
m3	525

v = v₀ + at — конечная скорость при постоянном ускорении
c	v
m3	180

Граф доказательств

Граф доказательства · 3 слой

Узлы доказательств: 6 · assertion 3, rule_application 2, query_evaluation 1

assertion · urn:proof:assert:urn:mcp:case#fact-1

attributes

assertion: fact-1

conclusion

Аргументы

Идентификатор
m3
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m_per_s
value
30

Тип

literal

Знак

positive

Условие

given_initial_velocity

evidence

—

Идентификатор

fact-1

Тип

assertion

Посылки

—

sourceAnchors

—

assertion · urn:proof:assert:urn:mcp:case#fact-2

attributes

assertion: fact-2

conclusion

Аргументы

Идентификатор
m3
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m_per_s2
value
30

Тип

literal

Знак

positive

Условие

given_acceleration

evidence

—

Идентификатор

fact-2

Тип

assertion

Посылки

—

sourceAnchors

—

assertion · urn:proof:assert:urn:mcp:case#fact-3

attributes

assertion: fact-3

conclusion

Аргументы

Идентификатор
m3
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
s
value
5

Тип

literal

Знак

positive

Условие

given_elapsed_time

evidence

—

Идентификатор

fact-3

Тип

assertion

Посылки

—

sourceAnchors

—

rule_application · urn:proof:apply:Displacement:1d71817ddef341c10adec4aa74921823e4d857ee023e46b810c196a21a2838f9

attributes

—

conclusion

Аргументы

Идентификатор
m3
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m
value
525

Тип

literal

Знак

positive

Условие

displacement

evidence

—

Идентификатор

1d71817ddef341c10adec4aa74921823e4d857ee023e46b810c196a21a2838f9

Тип

rule_application

Посылки

fact-1
fact-2
fact-3

Правило

Displacement

sourceAnchors

—

substitution

Идентификатор: m3
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

m_per_s

value

Тип

value

type

name: Quantity

Единица срока

m_per_s2

value

Тип

value

type

name: Quantity

Единица срока

value

rule_application · urn:proof:apply:FinalVelocity:b8f3a9b1e788566a2b55b7e93a2a9ddff40663b300713ca74220feacba477534

attributes

—

conclusion

Аргументы

Идентификатор
m3
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m_per_s
value
180

Тип

literal

Знак

positive

Условие

final_velocity

evidence

—

Идентификатор

b8f3a9b1e788566a2b55b7e93a2a9ddff40663b300713ca74220feacba477534

Тип

rule_application

Посылки

fact-1
fact-2
fact-3

Правило

FinalVelocity

sourceAnchors

—

substitution

Идентификатор: m3
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

m_per_s

value

Тип

value

type

name: Quantity

Единица срока

m_per_s2

value

Тип

value

type

name: Quantity

Единица срока

value

query_evaluation · urn:proof:query:mcp

attributes

—

conclusion

literal

Аргументы

Идентификатор
m3
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
m
value
525

Тип

literal

Знак

positive

Условие

displacement

truthStatus

Установлено

evidence

—

Идентификатор

mcp

Тип

query_evaluation

Посылки

1d71817ddef341c10adec4aa74921823e4d857ee023e46b810c196a21a2838f9

sourceAnchors

—

Идентификаторы календаря и доказательства

Ссылка на доказательство: mcp

Исходное обоснование · JSON

{
  "derived": [
    "displacement(urn:case:calc:m3, 525)",
    "final_velocity(urn:case:calc:m3, 180)"
  ],
  "derivedOmitted": 0,
  "evaluation": {
    "proofGraph": {
      "nodes": [
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-1"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m3",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "m_per_s",
                "value": "30"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_initial_velocity"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-1",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-2"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m3",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "m_per_s2",
                "value": "30"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_acceleration"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-2",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-3"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m3",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "s",
                "value": "5"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_elapsed_time"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-3",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {},
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m3",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
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                "unit": "m",
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ИсточникиТексты не сохранены

Тексты источников в этом снимке не сохранены.

Пакеты в снимке

calc-mechanics
units-si

Технические данныеПолный ответ, параметры и контрольные суммы

Статус расчёта: COMPUTED

Полный ответ движка

displacement: TRUE_ONLY — установлено Выведено правом: displacement(urn:case:calc:m3, 525); final_velocity(urn:case:calc:m3, 180) Применены правила: Displacement, FinalVelocity Право (вне юрисдикции государства): calc-mechanics (programHash sha256:0402ab611e2a…) Вместе с актами: units-si proof-граф: 6 узлов — поле evaluation готово для law_explain

Полный машинный результат · JSON

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Исполнение · JSON

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JSON · расчёты, источники и точные данные

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evaluation SHA-256: sha256:5108772d3cf0df41d5810ad2b91907473c7294f02fd2f6a7a0f3602fdf3d1b56

Исходные данные · JSON

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  "args": [
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  "facts": [
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        "urn:case:calc:m3",
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      ],
      "predicate": "given_elapsed_time"
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  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "displacement",
  "proof": true
}

Путь считается из начальной скорости, ускорения и времени.

Проверка условия

Кинетическая энергия

Дата контекста 06.09.2026

Результат расчёта

Установлено

Исходные параметры

Что определяем

K = ½mv² — кинетическая энергия

m5200 J

Исходные факты

масса и путевая скорость, данные для расчёта
c: m5m: 4 kgv: 10 m_per_s

Пакет: calc-mechanics

Дополнительные сведения

Сохранить доказательство: Да

Исходные данные · JSON

{
  "args": [
    "urn:case:calc:m5",
    "200 J"
  ],
  "facts": [
    {
      "args": [
        "urn:case:calc:m5",
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        "10 m_per_s"
      ],
      "predicate": "given_mass_and_speed"
    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "kinetic_energy",
  "proof": true
}

Почему такой результатПрименённые правила и условия

Путь вывода3 шагов

1
масса и путевая скорость, данные для расчёта
c: urn:case:calc:m5; m: 4 kg; v: 10 m_per_s
факт дела
2
K = ½mv²
200 J = 1 / 2 × (4 kg → kg) × (10 m_per_s → m_per_s) × (10 m_per_s → m_per_s)
Идентификатор
urn:law:calc:mechanics#KineticEnergy
правило
3
Вычисление запроса
запрос

проверено движком: 2 · факт дела: 1 · Полный граф: 4 узлов

Основание этого ответа

Правила из сохранённой цепочки доказательства ответа.

calc-mechanics

K = ½mv²
Идентификатор
urn:law:calc:mechanics#KineticEnergy

Другие правила расчёта1

Применены в общем расчёте, но не входят в цепочку доказательства этого ответа.

calc-mechanics

p = mv
Идентификатор
urn:law:calc:mechanics#Momentum

Другие выводы2

расчёт, предъявленный делом: данные величины и вопрос, заданный о них
c: m5
Общий субъект фактов ниже
K = ½mv² — кинетическая энергия
k: 200
p = mv — импульс
p: 40

K = ½mv² — кинетическая энергия
c	k
m5	200

p = mv — импульс
c	p
m5	40

Граф доказательств

Граф доказательства · 3 слой

Узлы доказательств: 4 · assertion 1, rule_application 2, query_evaluation 1

assertion · urn:proof:assert:urn:mcp:case#fact-1

attributes

assertion: fact-1

conclusion

Аргументы

Идентификатор
m5
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
kg
value
4
Тип
value
type
name
Quantity
Единица срока
m_per_s
value
10

Тип

literal

Знак

positive

Условие

given_mass_and_speed

evidence

—

Идентификатор

fact-1

Тип

assertion

Посылки

—

sourceAnchors

—

rule_application · urn:proof:apply:KineticEnergy:905fbe5923c46dab022f2b33d31a1b4a9719e36b911be7c235d6a589419a02aa

attributes

—

conclusion

Аргументы

Идентификатор
m5
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
J
value
200

Тип

literal

Знак

positive

Условие

kinetic_energy

evidence

—

Идентификатор

905fbe5923c46dab022f2b33d31a1b4a9719e36b911be7c235d6a589419a02aa

Тип

rule_application

Посылки

fact-1

Правило

KineticEnergy

sourceAnchors

—

substitution

Идентификатор: m5
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

value

Тип

value

type

name: Quantity

Единица срока

m_per_s

value

rule_application · urn:proof:apply:Momentum:f5886b2b0f38737106a6cf0dacc2ea064ecc31bbb91e7282402e855f707c7a1e

attributes

—

conclusion

Аргументы

Идентификатор
m5
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
kg_m_per_s
value
40

Тип

literal

Знак

positive

Условие

momentum

evidence

—

Идентификатор

f5886b2b0f38737106a6cf0dacc2ea064ecc31bbb91e7282402e855f707c7a1e

Тип

rule_application

Посылки

fact-1

Правило

Momentum

sourceAnchors

—

substitution

Идентификатор: m5
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

value

Тип

value

type

name: Quantity

Единица срока

m_per_s

value

query_evaluation · urn:proof:query:mcp

attributes

—

conclusion

literal

Аргументы

Идентификатор
m5
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
J
value
200

Тип

literal

Знак

positive

Условие

kinetic_energy

truthStatus

Установлено

evidence

—

Идентификатор

mcp

Тип

query_evaluation

Посылки

905fbe5923c46dab022f2b33d31a1b4a9719e36b911be7c235d6a589419a02aa

sourceAnchors

—

Идентификаторы календаря и доказательства

Ссылка на доказательство: mcp

Исходное обоснование · JSON

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    "momentum(urn:case:calc:m5, 40)"
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  "derivedOmitted": 0,
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                "unit": "kg",
                "value": "4"
              },
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            "polarity": "positive",
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          "evidence": [],
          "id": "urn:proof:apply:Momentum:f5886b2b0f38737106a6cf0dacc2ea064ecc31bbb91e7282402e855f707c7a1e",
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              ],
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              "polarity": "positive",
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            },
            "truthStatus": "TRUE_ONLY"
          },
          "evidence": [],
          "id": "urn:proof:query:mcp",
          "kind": "query_evaluation",
          "premises": [
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          "sourceAnchors": []
        }
      ],
      "proofHash": "sha256:8377250384f804770f23d978641dfae94af35e67e3a5c2cc77e68facbe284084",
      "roots": [
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    },
    "resultHash": "sha256:2adedd9fe02f56b1f4d7560ee55aca1efe59b42070f9bee6e842635905f21288",
    "schemaVersion": "law.core.evaluation/0.1"
  },
  "proofRef": "urn:proof:query:mcp",
  "rulesApplied": [
    "urn:law:calc:mechanics#KineticEnergy",
    "urn:law:calc:mechanics#Momentum"
  ]
}

ИсточникиТексты не сохранены

Тексты источников в этом снимке не сохранены.

Пакеты в снимке

calc-mechanics
units-si

Технические данныеПолный ответ, параметры и контрольные суммы

Статус расчёта: COMPUTED

Полный ответ движка

kinetic_energy: TRUE_ONLY — установлено Выведено правом: kinetic_energy(urn:case:calc:m5, 200); momentum(urn:case:calc:m5, 40) Применены правила: KineticEnergy, Momentum Право (вне юрисдикции государства): calc-mechanics (programHash sha256:0402ab611e2a…) Вместе с актами: units-si proof-граф: 4 узлов — поле evaluation готово для law_explain

Полный машинный результат · JSON

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    "evaluationStatus": "COMPUTED",
    "kind": "TRUTH",
    "meaning": "установлено",
    "missingInputs": [],
    "truthStatus": "TRUE_ONLY"
  },
  "closedEditionRules": [],
  "derived": [
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    "momentum(urn:case:calc:m5, 40)"
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  "derivedOmitted": 0,
  "evaluation": {
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                "type": {
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                },
                "unit": "kg",
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            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#momentum"
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          "evidence": [],
          "id": "urn:proof:apply:Momentum:f5886b2b0f38737106a6cf0dacc2ea064ecc31bbb91e7282402e855f707c7a1e",
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                },
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                  },
                  "unit": "J",
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              "kind": "literal",
              "polarity": "positive",
              "predicate": "urn:law:calc:mechanics#kinetic_energy"
            },
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          "evidence": [],
          "id": "urn:proof:query:mcp",
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  "provenance": {
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        "fragments": [],
        "jurisdiction": "none",
        "namespace": "urn:law:calc:mechanics",
        "package": "calc-mechanics",
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        "contributed": false,
        "fragmentCount": 0,
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    "caseHash": "sha256:cd9e3daa76d7adfb32039df658c4c673d90d471bcc4e71e48c09bce279719bcc",
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    "jurisdiction": "вне юрисдикции государства",
    "legalTime": "2026-09-06",
    "mode": "audit",
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        "labels": [],
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      {
        "labels": [],
        "name": "k",
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    "predicate": "urn:law:calc:mechanics#kinetic_energy",
    "schemaVersion": "law.answers.signature/0.1",
    "types": {
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          },
          {
            "language": "ru",
            "status": "unofficial",
            "text": "расчёт, предъявленный делом: данные величины и вопрос, заданный о них"
          }
        ],
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        "package": "calc.mechanics"
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    "vocab": {}
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  "vulnerableTo": [],
  "whyNot": []
}

Исполнение · JSON

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Метаданные отображения

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JSON · расчёты, источники и точные данные

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evaluation SHA-256: sha256:af3f7ff601fc227e9a87260f892e0c5e12bc1eba7c8661b0b76f2c9925cda2b3

Исходные данные · JSON

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    "urn:case:calc:m5",
    "200 J"
  ],
  "facts": [
    {
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        "urn:case:calc:m5",
        "4 kg",
        "10 m_per_s"
      ],
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    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "kinetic_energy",
  "proof": true
}

Масса 4 кг и скорость 10 м/с дают 200 Дж.

Проверка условия

КПД машины

Дата контекста 06.09.2026

Результат расчёта

Установлено

Исходные параметры

Что определяем

КПД — работа, делённая на поглощённую теплоту; безразмерен

m72/5

Исходные факты

совершённая работа и поглощённая теплота — обе как энергии
c: m7w: 200 Jq: 500 J

Пакет: calc-mechanics

Дополнительные сведения

Сохранить доказательство: Да

Исходные данные · JSON

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  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "efficiency",
  "proof": true
}

Почему такой результатПрименённые правила и условия

Путь вывода3 шагов

1
совершённая работа и поглощённая теплота — обе как энергии
c: urn:case:calc:m7; w: 200 J; q: 500 J
факт дела
2
КПД есть отношение работы к поглощённой теплоте — единицы сокращаются
2/5 = число(200 J / 500 J)
Идентификатор
urn:law:calc:mechanics#Efficiency
правило
3
Вычисление запроса
запрос

проверено движком: 2 · факт дела: 1 · Полный граф: 3 узлов

Основание этого ответа

Правила из сохранённой цепочки доказательства ответа.

calc-mechanics

КПД есть отношение работы к поглощённой теплоте — единицы сокращаются
Идентификатор
urn:law:calc:mechanics#Efficiency

Другие выводы1

КПД — работа, делённая на поглощённую теплоту; безразмерен
c: m7value: 2/5

КПД — работа, делённая на поглощённую теплоту; безразмерен
c	value
m7	²⁄₅

Граф доказательств

Граф доказательства · 3 слой

Узлы доказательств: 3 · assertion 1, rule_application 1, query_evaluation 1

assertion · urn:proof:assert:urn:mcp:case#fact-1

attributes

assertion: fact-1

conclusion

Аргументы

Идентификатор
m7
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
J
value
200
Тип
value
type
name
Quantity
Единица срока
J
value
500

Тип

literal

Знак

positive

Условие

given_work_and_heat

evidence

—

Идентификатор

fact-1

Тип

assertion

Посылки

—

sourceAnchors

—

rule_application · urn:proof:apply:Efficiency:88ad2c0fe350590e8372e56023b2458b4b18b3b033914a4c7baf68fcd5fecd33

attributes

—

conclusion

Аргументы

Идентификатор
m7
Тип
entity_ref
Тип
value
type
name
Rational
value
2/5

Тип

literal

Знак

positive

Условие

efficiency

evidence

—

Идентификатор

88ad2c0fe350590e8372e56023b2458b4b18b3b033914a4c7baf68fcd5fecd33

Тип

rule_application

Посылки

fact-1

Правило

Efficiency

sourceAnchors

—

substitution

Идентификатор: m7
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

value

200

Тип

value

type

name: Quantity

Единица срока

value

500

query_evaluation · urn:proof:query:mcp

attributes

—

conclusion

literal

Аргументы

Идентификатор
m7
Тип
entity_ref
Тип
value
type
name
Rational
value
2/5

Тип

literal

Знак

positive

Условие

efficiency

truthStatus

Установлено

evidence

—

Идентификатор

mcp

Тип

query_evaluation

Посылки

88ad2c0fe350590e8372e56023b2458b4b18b3b033914a4c7baf68fcd5fecd33

sourceAnchors

—

Идентификаторы календаря и доказательства

Ссылка на доказательство: mcp

Исходное обоснование · JSON

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    "efficiency(urn:case:calc:m7, 2/5)"
  ],
  "derivedOmitted": 0,
  "evaluation": {
    "proofGraph": {
      "nodes": [
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-1"
          },
          "conclusion": {
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                "id": "urn:case:calc:m7",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "J",
                "value": "200"
              },
              {
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                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "J",
                "value": "500"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_work_and_heat"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-1",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {},
          "conclusion": {
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              {
                "id": "urn:case:calc:m7",
                "kind": "entity_ref"
              },
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                "type": {
                  "name": "urn:law:std#Rational"
                },
                "value": "2/5"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#efficiency"
          },
          "evidence": [],
          "id": "urn:proof:apply:Efficiency:88ad2c0fe350590e8372e56023b2458b4b18b3b033914a4c7baf68fcd5fecd33",
          "kind": "rule_application",
          "premises": [
            "urn:proof:assert:urn:mcp:case#fact-1"
          ],
          "rule": "urn:law:calc:mechanics#Efficiency",
          "sourceAnchors": [],
          "substitution": {
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              "kind": "entity_ref"
            },
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              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "J",
              "value": "200"
            },
            "v2": {
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              },
              "unit": "J",
              "value": "500"
            }
          }
        },
        {
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          "conclusion": {
            "literal": {
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                {
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                  "kind": "entity_ref"
                },
                {
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                  },
                  "value": "2/5"
                }
              ],
              "kind": "literal",
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            },
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          },
          "evidence": [],
          "id": "urn:proof:query:mcp",
          "kind": "query_evaluation",
          "premises": [
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          ],
          "sourceAnchors": []
        }
      ],
      "proofHash": "sha256:abdbcea6862cb4a82b06d0d8a12a6b3829c37ac3ee9a68d6692f657b4f1b1c56",
      "roots": [
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      ]
    },
    "resultHash": "sha256:82bec7d215a190c7e8eaab7c56a4ceb4db6c0607b8676ff450fdf6dc6445a4c2",
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  },
  "proofRef": "urn:proof:query:mcp",
  "rulesApplied": [
    "urn:law:calc:mechanics#Efficiency"
  ]
}

ИсточникиТексты не сохранены

Тексты источников в этом снимке не сохранены.

Пакеты в снимке

calc-mechanics
units-si

Технические данныеПолный ответ, параметры и контрольные суммы

Статус расчёта: COMPUTED

Полный ответ движка

efficiency: TRUE_ONLY — установлено Выведено правом: efficiency(urn:case:calc:m7, 2/5) Применены правила: Efficiency Право (вне юрисдикции государства): calc-mechanics (programHash sha256:0402ab611e2a…) Вместе с актами: units-si proof-граф: 3 узлов — поле evaluation готово для law_explain

Полный машинный результат · JSON

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    "kind": "TRUTH",
    "meaning": "установлено",
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    "truthStatus": "TRUE_ONLY"
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  "derived": [
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  ],
  "derivedOmitted": 0,
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          "id": "urn:proof:apply:Efficiency:88ad2c0fe350590e8372e56023b2458b4b18b3b033914a4c7baf68fcd5fecd33",
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          "sourceAnchors": [],
          "substitution": {
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              },
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        },
        {
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                  },
                  "value": "2/5"
                }
              ],
              "kind": "literal",
              "polarity": "positive",
              "predicate": "urn:law:calc:mechanics#efficiency"
            },
            "truthStatus": "TRUE_ONLY"
          },
          "evidence": [],
          "id": "urn:proof:query:mcp",
          "kind": "query_evaluation",
          "premises": [
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        }
      ],
      "proofHash": "sha256:abdbcea6862cb4a82b06d0d8a12a6b3829c37ac3ee9a68d6692f657b4f1b1c56",
      "roots": [
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      ]
    },
    "resultHash": "sha256:82bec7d215a190c7e8eaab7c56a4ceb4db6c0607b8676ff450fdf6dc6445a4c2",
    "schemaVersion": "law.core.evaluation/0.1"
  },
  "evaluationStatus": "COMPUTED",
  "issues": [],
  "judgmentRequests": [],
  "proofRef": "urn:proof:query:mcp",
  "provenance": {
    "acts": [
      {
        "contributed": true,
        "fragmentCount": 0,
        "fragments": [],
        "jurisdiction": "none",
        "namespace": "urn:law:calc:mechanics",
        "package": "calc-mechanics",
        "title": "calc-mechanics"
      },
      {
        "contributed": false,
        "fragmentCount": 0,
        "fragments": [],
        "jurisdiction": null,
        "namespace": "urn:law:units:si",
        "package": "units-si",
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    ],
    "caseHash": "sha256:589584b05a4799f6cf41e6faa34b9c71e8245a80e688162fb691fb2f7e2d149c",
    "codeHash": "sha256:9bcca6a33805c1c364ca1bc8e9d39d6a9c51ba44203c0406bafbf397b96be699",
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  "signature": {
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    "vocab": {}
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  "vulnerableTo": [],
  "whyNot": []
}

Исполнение · JSON

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Метаданные отображения

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        },
        {
          "language": "ru",
          "status": "unofficial",
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        }
      ],
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          "text": "совершённая работа и поглощённая теплота — обе как энергии"
        }
      ],
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      "package": "urn:law:calc:mechanics",
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JSON · расчёты, источники и точные данные

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evaluation SHA-256: sha256:986bee4a1acd4a18b86bc12340f2ed9c9d8dc2e9620ab69a4afdb156d22883a4

Исходные данные · JSON

{
  "args": [
    "urn:case:calc:m7",
    {
      "kind": "value",
      "type": {
        "name": "urn:law:std#Rational"
      },
      "value": "2/5"
    }
  ],
  "facts": [
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        "200 J",
        "500 J"
      ],
      "predicate": "given_work_and_heat"
    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "efficiency",
  "proof": true
}

Работа 200 Дж из теплоты 500 Дж — КПД 2/5, безразмерная точная дробь.

Проверка условия

Предел Карно

Дата контекста 06.09.2026

Результат расчёта

Установлено

Исходные параметры

Что определяем

предел Карно 1 − T_c/T_h — наибольший возможный КПД между этими резервуарами

m71/2

Исходные факты

температуры холодного и горячего резервуаров
c: m7cold: 300 Khot: 600 K

Пакет: calc-mechanics

Дополнительные сведения

Сохранить доказательство: Да

Исходные данные · JSON

{
  "args": [
    "urn:case:calc:m7",
    {
      "kind": "value",
      "type": {
        "name": "urn:law:std#Rational"
      },
      "value": "1/2"
    }
  ],
  "facts": [
    {
      "args": [
        "urn:case:calc:m7",
        "300 K",
        "600 K"
      ],
      "predicate": "given_reservoir_temperatures"
    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "carnot_limit",
  "proof": true
}

Почему такой результатПрименённые правила и условия

Путь вывода3 шагов

1
температуры холодного и горячего резервуаров
c: urn:case:calc:m7; cold: 300 K; hot: 600 K
факт дела
2
предел Карно есть единица минус отношение температуры холодного резервуара к горячему
1/2 = 1 / 1 − число(300 K / 600 K)
Идентификатор
urn:law:calc:mechanics#CarnotLimit
правило
3
Вычисление запроса
запрос

проверено движком: 2 · факт дела: 1 · Полный граф: 3 узлов

Основание этого ответа

Правила из сохранённой цепочки доказательства ответа.

calc-mechanics

предел Карно есть единица минус отношение температуры холодного резервуара к горячему
Идентификатор
urn:law:calc:mechanics#CarnotLimit

Другие выводы1

предел Карно 1 − T_c/T_h — наибольший возможный КПД между этими резервуарами
c: m7value: 1/2

предел Карно 1 − T_c/T_h — наибольший возможный КПД между этими резервуарами
c	value
m7	¹⁄₂

Граф доказательств

Граф доказательства · 3 слой

Узлы доказательств: 3 · assertion 1, rule_application 1, query_evaluation 1

assertion · urn:proof:assert:urn:mcp:case#fact-1

attributes

assertion: fact-1

conclusion

Аргументы

Идентификатор
m7
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
K
value
300
Тип
value
type
name
Quantity
Единица срока
K
value
600

Тип

literal

Знак

positive

Условие

given_reservoir_temperatures

evidence

—

Идентификатор

fact-1

Тип

assertion

Посылки

—

sourceAnchors

—

rule_application · urn:proof:apply:CarnotLimit:3bc89ee3182ca538c4d850b15a774159ad520d6baa330c8bc643b30d0d5ca3b6

attributes

—

conclusion

Аргументы

Идентификатор
m7
Тип
entity_ref
Тип
value
type
name
Rational
value
1/2

Тип

literal

Знак

positive

Условие

carnot_limit

evidence

—

Идентификатор

3bc89ee3182ca538c4d850b15a774159ad520d6baa330c8bc643b30d0d5ca3b6

Тип

rule_application

Посылки

fact-1

Правило

CarnotLimit

sourceAnchors

—

substitution

Идентификатор: m7
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

value

300

Тип

value

type

name: Quantity

Единица срока

value

600

query_evaluation · urn:proof:query:mcp

attributes

—

conclusion

literal

Аргументы

Идентификатор
m7
Тип
entity_ref
Тип
value
type
name
Rational
value
1/2

Тип

literal

Знак

positive

Условие

carnot_limit

truthStatus

Установлено

evidence

—

Идентификатор

mcp

Тип

query_evaluation

Посылки

3bc89ee3182ca538c4d850b15a774159ad520d6baa330c8bc643b30d0d5ca3b6

sourceAnchors

—

Идентификаторы календаря и доказательства

Ссылка на доказательство: mcp

Исходное обоснование · JSON

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              }
            ],
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            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#carnot_limit"
          },
          "evidence": [],
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  ]
}

ИсточникиТексты не сохранены

Тексты источников в этом снимке не сохранены.

Пакеты в снимке

calc-mechanics
units-si

Технические данныеПолный ответ, параметры и контрольные суммы

Статус расчёта: COMPUTED

Полный ответ движка

carnot_limit: TRUE_ONLY — установлено Выведено правом: carnot_limit(urn:case:calc:m7, 1/2) Применены правила: CarnotLimit Право (вне юрисдикции государства): calc-mechanics (programHash sha256:0402ab611e2a…) Вместе с актами: units-si proof-граф: 3 узлов — поле evaluation готово для law_explain

Полный машинный результат · JSON

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Исполнение · JSON

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Метаданные отображения

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        {
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          "status": "unofficial",
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      ],
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        },
        {
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          "status": "unofficial",
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JSON · расчёты, источники и точные данные

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evaluation SHA-256: sha256:a742a9c88f7eaf85ba3453c1f28b669af70cd73fbdf462a8888298754d5c87df

Исходные данные · JSON

{
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    "urn:case:calc:m7",
    {
      "kind": "value",
      "type": {
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      },
      "value": "1/2"
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  ],
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        "300 K",
        "600 K"
      ],
      "predicate": "given_reservoir_temperatures"
    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "carnot_limit",
  "proof": true
}

Резервуары 300 и 600 К задают предел 1/2.

Проверка условия

Превышение предела Карно

Дата контекста 06.09.2026

Результат расчёта

Установлено

Исходные параметры

Что определяем

данный КПД превосходит предел Карно — такая машина невозможна

m10

Исходные факты

расчёт, предъявленный делом: данные величины и вопрос, заданный о них
c: m10
Общий субъект фактов ниже
совершённая работа и поглощённая теплота — обе как энергии
w: 300 Jq: 500 J
температуры холодного и горячего резервуаров
cold: 300 Khot: 600 K

Пакет: calc-mechanics

Дополнительные сведения

Сохранить доказательство: Да

Исходные данные · JSON

{
  "args": [
    "urn:case:calc:m10"
  ],
  "facts": [
    {
      "args": [
        "urn:case:calc:m10",
        "300 J",
        "500 J"
      ],
      "predicate": "given_work_and_heat"
    },
    {
      "args": [
        "urn:case:calc:m10",
        "300 K",
        "600 K"
      ],
      "predicate": "given_reservoir_temperatures"
    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "efficiency_exceeds_carnot_limit",
  "proof": true
}

Почему такой результатПрименённые правила и условия

Путь вывода6 шагов

1
совершённая работа и поглощённая теплота — обе как энергии
c: urn:case:calc:m10; w: 300 J; q: 500 J
факт дела
2
КПД есть отношение работы к поглощённой теплоте — единицы сокращаются
3/5 = число(300 J / 500 J)
Идентификатор
urn:law:calc:mechanics#Efficiency
правило
3
температуры холодного и горячего резервуаров
c: urn:case:calc:m10; cold: 300 K; hot: 600 K
факт дела
4
предел Карно есть единица минус отношение температуры холодного резервуара к горячему
1/2 = 1 / 1 − число(300 K / 600 K)
Идентификатор
urn:law:calc:mechanics#CarnotLimit
правило
5
КПД, больший предела Карно, невозможен
данный КПД превосходит предел Карно — такая машина невозможна: c: urn:case:calc:m10
Идентификатор
urn:law:calc:mechanics#EfficiencyAboveLimit
правило
6
Вычисление запроса
запрос

проверено движком: 4 · факт дела: 2 · Полный граф: 6 узлов

Основание этого ответа

Правила из сохранённой цепочки доказательства ответа.

calc-mechanics

предел Карно есть единица минус отношение температуры холодного резервуара к горячему
Идентификатор
urn:law:calc:mechanics#CarnotLimit
КПД есть отношение работы к поглощённой теплоте — единицы сокращаются
Идентификатор
urn:law:calc:mechanics#Efficiency
КПД, больший предела Карно, невозможен
Идентификатор
urn:law:calc:mechanics#EfficiencyAboveLimit

Вывод по запросу

данный КПД превосходит предел Карно — такая машина невозможна
c: m10

Другие выводы2

расчёт, предъявленный делом: данные величины и вопрос, заданный о них
c: m10
Общий субъект фактов ниже
КПД — работа, делённая на поглощённую теплоту; безразмерен
value: 3/5
предел Карно 1 − T_c/T_h — наибольший возможный КПД между этими резервуарами
value: 1/2

КПД — работа, делённая на поглощённую теплоту; безразмерен
c	value
m10	³⁄₅

предел Карно 1 − T_c/T_h — наибольший возможный КПД между этими резервуарами
c	value
m10	¹⁄₂

данный КПД превосходит предел Карно — такая машина невозможна
c
m10

Что способно поразить вывод1 правил

1
КПД, не превосходящий предела Карно, его не превосходит
Чего не хватает
- v1 ≤ v2DEPENDSименно этого не хватает
- КПД — работа, делённая на поглощённую теплоту; безразмеренm10, v1DEPENDSименно этого не хватает
- предел Карно 1 − T_c/T_h — наибольший возможный КПД между этими резервуарамиm10, v2DEPENDSименно этого не хватает
Идентификатор
urn:law:calc:mechanics#EfficiencyWithinLimit
правило

Перечислены правила, чья голова отвечает вопросу, и их невыполненные посылки. Отсутствие факта не означает его опровержения.

Граф доказательств

Граф доказательства · 4 слой

Узлы доказательств: 6 · assertion 2, rule_application 3, query_evaluation 1

assertion · urn:proof:assert:urn:mcp:case#fact-1

attributes

assertion: fact-1

conclusion

Аргументы

Идентификатор
m10
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
J
value
300
Тип
value
type
name
Quantity
Единица срока
J
value
500

Тип

literal

Знак

positive

Условие

given_work_and_heat

evidence

—

Идентификатор

fact-1

Тип

assertion

Посылки

—

sourceAnchors

—

rule_application · urn:proof:apply:Efficiency:9d66f82f0e837e8ac0bb3a1a17ca74e9af9f765b90376b95313eefd90ca2c05d

attributes

—

conclusion

Аргументы

Идентификатор
m10
Тип
entity_ref
Тип
value
type
name
Rational
value
3/5

Тип

literal

Знак

positive

Условие

efficiency

evidence

—

Идентификатор

9d66f82f0e837e8ac0bb3a1a17ca74e9af9f765b90376b95313eefd90ca2c05d

Тип

rule_application

Посылки

fact-1

Правило

Efficiency

sourceAnchors

—

substitution

Идентификатор: m10
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

value

300

Тип

value

type

name: Quantity

Единица срока

value

500

assertion · urn:proof:assert:urn:mcp:case#fact-2

attributes

assertion: fact-2

conclusion

Аргументы

Идентификатор
m10
Тип
entity_ref
Тип
value
type
name
Quantity
Единица срока
K
value
300
Тип
value
type
name
Quantity
Единица срока
K
value
600

Тип

literal

Знак

positive

Условие

given_reservoir_temperatures

evidence

—

Идентификатор

fact-2

Тип

assertion

Посылки

—

sourceAnchors

—

rule_application · urn:proof:apply:CarnotLimit:d3b1cff4829346e098f6d89d50d2388c6b4ac827c80e57f4460cec9730b4f72f

attributes

—

conclusion

Аргументы

Идентификатор
m10
Тип
entity_ref
Тип
value
type
name
Rational
value
1/2

Тип

literal

Знак

positive

Условие

carnot_limit

evidence

—

Идентификатор

d3b1cff4829346e098f6d89d50d2388c6b4ac827c80e57f4460cec9730b4f72f

Тип

rule_application

Посылки

fact-2

Правило

CarnotLimit

sourceAnchors

—

substitution

Идентификатор: m10
Тип: entity_ref

Тип

value

type

name: Quantity

Единица срока

value

300

Тип

value

type

name: Quantity

Единица срока

value

600

rule_application · urn:proof:apply:EfficiencyAboveLimit:8c11bc0b559d4de888cd4bf7e065d04540a4195a875344b1e8a83e52802ae4f5

attributes

—

conclusion

Аргументы

Идентификатор
m10
Тип
entity_ref

Тип

literal

Знак

positive

Условие

efficiency_exceeds_carnot_limit

evidence

—

Идентификатор

8c11bc0b559d4de888cd4bf7e065d04540a4195a875344b1e8a83e52802ae4f5

Тип

rule_application

Посылки

d3b1cff4829346e098f6d89d50d2388c6b4ac827c80e57f4460cec9730b4f72f
9d66f82f0e837e8ac0bb3a1a17ca74e9af9f765b90376b95313eefd90ca2c05d

Правило

EfficiencyAboveLimit

sourceAnchors

—

substitution

Идентификатор: m10
Тип: entity_ref

Тип

value

type

name: Rational

value

3/5

Тип

value

type

name: Rational

value

1/2

query_evaluation · urn:proof:query:mcp

attributes

—

conclusion

literal

Аргументы

Идентификатор
m10
Тип
entity_ref

Тип

literal

Знак

positive

Условие

efficiency_exceeds_carnot_limit

truthStatus

Установлено

evidence

—

Идентификатор

mcp

Тип

query_evaluation

Посылки

8c11bc0b559d4de888cd4bf7e065d04540a4195a875344b1e8a83e52802ae4f5

sourceAnchors

—

Идентификаторы календаря и доказательства

Ссылка на доказательство: mcp

Исходное обоснование · JSON

{
  "derived": [
    "efficiency(urn:case:calc:m10, 3/5)",
    "carnot_limit(urn:case:calc:m10, 1/2)",
    "efficiency_exceeds_carnot_limit(urn:case:calc:m10)"
  ],
  "derivedOmitted": 0,
  "evaluation": {
    "proofGraph": {
      "nodes": [
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-1"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m10",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "J",
                "value": "300"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "J",
                "value": "500"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_work_and_heat"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-1",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {},
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m10",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Rational"
                },
                "value": "3/5"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#efficiency"
          },
          "evidence": [],
          "id": "urn:proof:apply:Efficiency:9d66f82f0e837e8ac0bb3a1a17ca74e9af9f765b90376b95313eefd90ca2c05d",
          "kind": "rule_application",
          "premises": [
            "urn:proof:assert:urn:mcp:case#fact-1"
          ],
          "rule": "urn:law:calc:mechanics#Efficiency",
          "sourceAnchors": [],
          "substitution": {
            "v0": {
              "id": "urn:case:calc:m10",
              "kind": "entity_ref"
            },
            "v1": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "J",
              "value": "300"
            },
            "v2": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "J",
              "value": "500"
            }
          }
        },
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-2"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m10",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "K",
                "value": "300"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "K",
                "value": "600"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_reservoir_temperatures"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-2",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {},
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m10",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Rational"
                },
                "value": "1/2"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#carnot_limit"
          },
          "evidence": [],
          "id": "urn:proof:apply:CarnotLimit:d3b1cff4829346e098f6d89d50d2388c6b4ac827c80e57f4460cec9730b4f72f",
          "kind": "rule_application",
          "premises": [
            "urn:proof:assert:urn:mcp:case#fact-2"
          ],
          "rule": "urn:law:calc:mechanics#CarnotLimit",
          "sourceAnchors": [],
          "substitution": {
            "v0": {
              "id": "urn:case:calc:m10",
              "kind": "entity_ref"
            },
            "v1": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "K",
              "value": "300"
            },
            "v2": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "K",
              "value": "600"
            }
          }
        },
        {
          "attributes": {},
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m10",
                "kind": "entity_ref"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#efficiency_exceeds_carnot_limit"
          },
          "evidence": [],
          "id": "urn:proof:apply:EfficiencyAboveLimit:8c11bc0b559d4de888cd4bf7e065d04540a4195a875344b1e8a83e52802ae4f5",
          "kind": "rule_application",
          "premises": [
            "urn:proof:apply:CarnotLimit:d3b1cff4829346e098f6d89d50d2388c6b4ac827c80e57f4460cec9730b4f72f",
            "urn:proof:apply:Efficiency:9d66f82f0e837e8ac0bb3a1a17ca74e9af9f765b90376b95313eefd90ca2c05d"
          ],
          "rule": "urn:law:calc:mechanics#EfficiencyAboveLimit",
          "sourceAnchors": [],
          "substitution": {
            "v0": {
              "id": "urn:case:calc:m10",
              "kind": "entity_ref"
            },
            "v1": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Rational"
              },
              "value": "3/5"
            },
            "v2": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Rational"
              },
              "value": "1/2"
            }
          }
        },
        {
          "attributes": {},
          "conclusion": {
            "literal": {
              "args": [
                {
                  "id": "urn:case:calc:m10",
                  "kind": "entity_ref"
                }
              ],
              "kind": "literal",
              "polarity": "positive",
              "predicate": "urn:law:calc:mechanics#efficiency_exceeds_carnot_limit"
            },
            "truthStatus": "TRUE_ONLY"
          },
          "evidence": [],
          "id": "urn:proof:query:mcp",
          "kind": "query_evaluation",
          "premises": [
            "urn:proof:apply:EfficiencyAboveLimit:8c11bc0b559d4de888cd4bf7e065d04540a4195a875344b1e8a83e52802ae4f5"
          ],
          "sourceAnchors": []
        }
      ],
      "proofHash": "sha256:f1c5c0dfd5bbc5d6dea9735d31feb9402bb91c679b811ca5ecd23e9a32edc09c",
      "roots": [
        "urn:proof:query:mcp"
      ]
    },
    "resultHash": "sha256:2e0944ffe3e827a7cb1680300b1cd6fb4d5fee1e6b93265e804bcfc2191702ae",
    "schemaVersion": "law.core.evaluation/0.1"
  },
  "proofRef": "urn:proof:query:mcp",
  "rulesApplied": [
    "urn:law:calc:mechanics#CarnotLimit",
    "urn:law:calc:mechanics#Efficiency",
    "urn:law:calc:mechanics#EfficiencyAboveLimit"
  ],
  "vulnerableTo": [
    {
      "anchors": [],
      "label": "an efficiency not exceeding the Carnot limit does not exceed it",
      "missing": [
        "v1 ≤ v2",
        "efficiency(urn:case:calc:m10, v1)",
        "carnot_limit(urn:case:calc:m10, v2)"
      ],
      "premises": [
        {
          "note": "терм-гард: операнды не связаны фактами",
          "premise": "v1 ≤ v2",
          "status": "DEPENDS"
        },
        {
          "note": "зависит от несвязанной переменной",
          "premise": "efficiency(urn:case:calc:m10, v1)",
          "status": "DEPENDS"
        },
        {
          "note": "зависит от несвязанной переменной",
          "premise": "carnot_limit(urn:case:calc:m10, v2)",
          "status": "DEPENDS"
        }
      ],
      "rule": "EfficiencyWithinLimit"
    }
  ]
}

ИсточникиТексты не сохранены

Тексты источников в этом снимке не сохранены.

Пакеты в снимке

calc-mechanics
units-si

Технические данныеПолный ответ, параметры и контрольные суммы

Статус расчёта: COMPUTED

Полный ответ движка

efficiency_exceeds_carnot_limit: TRUE_ONLY — установлено Выведено правом: efficiency(urn:case:calc:m10, 3/5); carnot_limit(urn:case:calc:m10, 1/2); efficiency_exceeds_carnot_limit(urn:case:calc:m10) Применены правила: CarnotLimit, Efficiency, EfficiencyAboveLimit Ответ поражаем правилом «an efficiency not exceeding the Carnot limit does not exceed it» — оно отменило бы вывод, будь установлено: v1 ≤ v2; efficiency(urn:case:calc:m10, v1); carnot_limit(urn:case:calc:m10, v2) (поражающее правило не сработало из-за неустановленных фактов — подайте их в facts, если они есть в деле) Право (вне юрисдикции государства): calc-mechanics (programHash sha256:0402ab611e2a…) Вместе с актами: units-si proof-граф: 6 узлов — поле evaluation готово для law_explain

Полный машинный результат · JSON

{
  "answer": {
    "evaluationStatus": "COMPUTED",
    "kind": "TRUTH",
    "meaning": "установлено",
    "missingInputs": [],
    "truthStatus": "TRUE_ONLY"
  },
  "closedEditionRules": [],
  "derived": [
    "efficiency(urn:case:calc:m10, 3/5)",
    "carnot_limit(urn:case:calc:m10, 1/2)",
    "efficiency_exceeds_carnot_limit(urn:case:calc:m10)"
  ],
  "derivedOmitted": 0,
  "evaluation": {
    "proofGraph": {
      "nodes": [
        {
          "attributes": {
            "assertion": "urn:mcp:case#fact-1"
          },
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m10",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "J",
                "value": "300"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Quantity"
                },
                "unit": "J",
                "value": "500"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#given_work_and_heat"
          },
          "evidence": [],
          "id": "urn:proof:assert:urn:mcp:case#fact-1",
          "kind": "assertion",
          "premises": [],
          "sourceAnchors": []
        },
        {
          "attributes": {},
          "conclusion": {
            "args": [
              {
                "id": "urn:case:calc:m10",
                "kind": "entity_ref"
              },
              {
                "kind": "value",
                "type": {
                  "name": "urn:law:std#Rational"
                },
                "value": "3/5"
              }
            ],
            "kind": "literal",
            "polarity": "positive",
            "predicate": "urn:law:calc:mechanics#efficiency"
          },
          "evidence": [],
          "id": "urn:proof:apply:Efficiency:9d66f82f0e837e8ac0bb3a1a17ca74e9af9f765b90376b95313eefd90ca2c05d",
          "kind": "rule_application",
          "premises": [
            "urn:proof:assert:urn:mcp:case#fact-1"
          ],
          "rule": "urn:law:calc:mechanics#Efficiency",
          "sourceAnchors": [],
          "substitution": {
            "v0": {
              "id": "urn:case:calc:m10",
              "kind": "entity_ref"
            },
            "v1": {
              "kind": "value",
              "type": {
                "name": "urn:law:std#Quantity"
              },
              "unit": "J",
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Исполнение · JSON

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Метаданные отображения

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          "value": "1/2"
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          "status": "official",
          "text": "a calculation the case presents: the given quantities and the question asked of them"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "расчёт, предъявленный делом: данные величины и вопрос, заданный о них"
        }
      ],
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      "package": "urn:law:calc:mechanics"
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      "id": "urn:law:calc:mechanics#CarnotLimit",
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      "labels": [
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          "status": "official",
          "text": "the Carnot limit is one minus the ratio of the cold to the hot reservoir temperature"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "предел Карно есть единица минус отношение температуры холодного резервуара к горячему"
        }
      ],
      "package": "urn:law:calc:mechanics",
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      "kind": "rule",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "efficiency is the ratio of work to absorbed heat — the units cancel"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "КПД есть отношение работы к поглощённой теплоте — единицы сокращаются"
        }
      ],
      "package": "urn:law:calc:mechanics",
      "strength": "strict"
    },
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      "id": "urn:law:calc:mechanics#EfficiencyAboveLimit",
      "kind": "rule",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "an efficiency greater than the Carnot limit is impossible"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "КПД, больший предела Карно, невозможен"
        }
      ],
      "package": "urn:law:calc:mechanics",
      "strength": "strict"
    },
    {
      "id": "urn:law:calc:mechanics#EfficiencyWithinLimit",
      "kind": "rule",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "an efficiency not exceeding the Carnot limit does not exceed it"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "КПД, не превосходящий предела Карно, его не превосходит"
        }
      ],
      "package": "urn:law:calc:mechanics",
      "strength": "strict"
    },
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      "kind": "symbol_decl",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "the Carnot limit 1 − T_c/T_h — the greatest efficiency possible between these reservoirs"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "предел Карно 1 − T_c/T_h — наибольший возможный КПД между этими резервуарами"
        }
      ],
      "name": "carnot_limit",
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          "status": "official",
          "text": "the efficiency — work divided by absorbed heat; dimensionless"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "КПД — работа, делённая на поглощённую теплоту; безразмерен"
        }
      ],
      "name": "efficiency",
      "package": "urn:law:calc:mechanics",
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      "kind": "symbol_decl",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "the given efficiency exceeds the Carnot limit — no such engine is possible"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "данный КПД превосходит предел Карно — такая машина невозможна"
        }
      ],
      "name": "efficiency_exceeds_carnot_limit",
      "package": "urn:law:calc:mechanics",
      "parameters": [
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        },
        {
          "language": "ru",
          "status": "unofficial",
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        }
      ],
      "name": "given_reservoir_temperatures",
      "package": "urn:law:calc:mechanics",
      "parameters": [
        {
          "id": "urn:law:calc:mechanics#given_reservoir_temperatures/arg/c",
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        },
        {
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        },
        {
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          "labels": [],
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          "type": {
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        }
      ],
      "symbolKind": "relation"
    },
    {
      "id": "urn:law:calc:mechanics#given_work_and_heat",
      "kind": "symbol_decl",
      "labels": [
        {
          "language": "en",
          "status": "official",
          "text": "the work performed and the heat absorbed, both as energies"
        },
        {
          "language": "ru",
          "status": "unofficial",
          "text": "совершённая работа и поглощённая теплота — обе как энергии"
        }
      ],
      "name": "given_work_and_heat",
      "package": "urn:law:calc:mechanics",
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        },
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        }
      ],
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  ],
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}

JSON · расчёты, источники и точные данные

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  "jurisdiction": "вне юрисдикции государства",
  "legalTime": "2026-09-06",
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evaluation SHA-256: sha256:930311748e3329d590e03f2bcd332861d0f42bfd8fe25d032721b4ad2b4277ce

Исходные данные · JSON

{
  "args": [
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  "facts": [
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      "args": [
        "urn:case:calc:m10",
        "300 J",
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      "predicate": "given_work_and_heat"
    },
    {
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        "300 K",
        "600 K"
      ],
      "predicate": "given_reservoir_temperatures"
    }
  ],
  "kind": "truth",
  "legalTime": "2026-09-06",
  "package": "calc-mechanics",
  "predicate": "efficiency_exceeds_carnot_limit",
  "proof": true
}

Машина с КПД 3/5 против предела 1/2: превышение выведено правилом.

Как сослаться

Снимок неизменяем: его закрепляет SHA-256 скачиваемого JSON, поэтому дата обращения не нужна.

Текст ссылки

«Разгон из состояния покоя, путь при равноускоренном движении, кинетическая энергия, а также КПД машины против предела Карно между резервуарами 300 и 600 К.». Arxo Lens, по состоянию на 06.09.2026. https://lens.arxo.io/a/a_WbZhjMMXHpN8Lp3mjy7yL1YN. SHA-256 снимка: 214038b4c735606b53cb179661054b050f2e7d27d648aa177e4b4bc6b81c581e.

BibTeX

@misc{arxo-lens-a_WbZhjMMXHpN8,
  title = {Разгон из состояния покоя, путь при равноускоренном движении, кинетическая энергия, а также КПД машины против предела Карно между резервуарами 300 и 600 К.},
  howpublished = {Arxo Lens},
  url = {https://lens.arxo.io/a/a_WbZhjMMXHpN8Lp3mjy7yL1YN},
  note = {по состоянию на 06.09.2026; SHA-256 214038b4c735606b53cb179661054b050f2e7d27d648aa177e4b4bc6b81c581e}
}

Код для вставки

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<iframe src="https://lens.arxo.io/embed/a_WbZhjMMXHpN8Lp3mjy7yL1YN?lang=ru" width="100%" height="390" loading="lazy" title="Механика и предел Карно — Arxo Lens" style="border:0"></iframe>

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