How do we know that strangulation is the fourth type of death penalty? TB Sanhedrin 53

The Mishna lists for methods of execution by the court. “Four types of the death penalty were given over to the court, with which those who committed certain transgressions are executed. They are, in descending order of severity: Stoning, burning, killing by decapitation, and strangulation.” (TB Sanhedrin 49b, Sefaria.org translation) only three methods as punishments are actually mentioned in the Torah, stoning, burning, killing. Where do we learn that strangulation is the fourth method of execution? The Gemara provides two different answers to our question beginning on daf TB Sanhedrin 52 and continuing on daf 53.

Rabbi Yoshiya teaches when an unspecified death penalty is mentioned, strangulation is the mode of execution because it is the least severe out of the four. “‘Shall be put to death’” means death by strangulation. Do you say that his execution is by strangulation, or is it rather by one of all the other types of death penalty stated in the Torah? You must say that it is by strangulation, as everywhere that the death penalty is stated in the Torah without specification you may not take it to be more stringent with regard to it, i.e., to mean that the sinner should be sentenced to a severe type of execution; rather, you must take it to be more lenient with regard to it, i.e., that a lenient type of execution should be applied. Consequently, the sinner is sentenced to be executed by strangulation, which is the least severe type of capital punishment. This is the statement of Rabbi Yoshiya.” (Sefaria.org translation)

Rabbi Yonatan teaches that strangulation is unlike the other three methods of execution. Only strangulation is similar to kareit, death at the hand of Heaven because neither leave an external mark on the condemned person. “The baraita continues: Rabbi Yonatan says: It is not because strangulation is the most lenient type of capital punishment; rather, there is a principle that every death penalty stated in the Torah without specification is nothing other than strangulation, whereas the other types of capital punishment must be stated explicitly in the verse.

“Rabbi Yehuda HaNasi says, in accordance with the opinion of Rabbi Yonatan: Death at the hand of Heaven is stated in the Torah, and death at the hands of a person, i.e., court-imposed capital punishment, is stated in the Torah. Just as the death at the hand of Heaven that is stated in the Torah is a death that leaves no external mark, so too, the death at the hands of a person that is stated in the Torah is a death that leaves no external mark, i.e., strangulation.” (Sefaria.org translation)

Although we don’t have an explicit source for strangulation in Rabbi Yoshiya’s explanation,  Rava said that Rabbi Yoshiya would teach us the answer how we would know in one word, Tradition!“…according to Rabbi Yoshiya, from where is it derived that there is a punishment of execution by strangulation in the world, i.e., in halakha, at all? Since this type of capital punishment is not mentioned in the Torah explicitly, say that decapitation by the sword is the least severe type, as it is mentioned in the Torah.

“Rava said: The four types of the death penalty are learned as a tradition. There is no question as to the types of capital punishment that exist in halakha. Rather, the question is which type of execution is meted out as punishment for which sins.”(Sefaria.org translation)