Is “Acting as prime minister, he executed Shao Zhengmao” true?

The Records of the Grand Historian, in the 'Hereditary House of Confucius', clearly records that at the age of fifty-six, Confucius, while serving as Grand Minister of Justice, acted as prime minister, and subsequently executed the Lu nobleman Shao Zhengmao on charges of causing political chaos, thereby bringing great order to the state of Lu. The novel also depicts Confucius acting as prime minister and executing Shao Zhengmao, and in terms of the cause, process, and positive impact on Lu's political atmosphere, it remains highly consistent with historical records, without any fictional alterations.