Peirushim ha'Mekubalim - Received Explanations from Moshe
This category of laws are, like Halakhot l'Moshe m'Sinai, received explanations from Moshe. However, unlike Halakhot l'Moshe m'Sinai they can be supported through exegetic analysis, i.e. they have a remez – a hint – to them in the written Torah. Examples in the Talmud are found in Bava Metzia 22a, Sanhedrin 75a, Avoda Zara 76b and Shavuot 19a.This is unlike a Halakha l'Moshe m'Sinai which can only have a "asmachta b'alma" - an associated verse with the law but from which one is unable to theoretically derive the law. See Rambam, Hakdama l’Peirush ha’Mishnayot.
The Rambam in Sefer ha'Mitzvot, Shoresh Shayni, writes that discovering scriptural hints for already known laws “shows the wisdom of the written Torah” in that it demonstrates how the Oral Torah is planted within the written Torah. Also see the Hakdama l’Mishna, pgs. 11-12 (M’hochmat ha’Torah…). R. Zvi Lampel extends this idea and points out that the Sages looked for scriptural support for well-known facts such as natural phenomena For example, the Sages bring scriptural support for the ability of rain to cause plant growth (Ketubot 10b; also see Bava Batra 25b, Gitten 6a and Taanit 9b). He explains that since the Torah is the blueprint of existence it should include everything within it in some hinted way. However, this understanding of "Received Explanations" does seems to contradict the Talmudic rule "s'vara hi, lama li kra - it is logical, why is a verse required." In a later post we will discuss the role of logic in the halakhic system.
Sometimes these received explanations can contradict the plain meaning of the text. See, for example, Mechilta on Mishpatim, Makkot 22a, Sotah 16a, and Mishneh la’Melech on Chametz u’Matza 1:7).
Lastly, there can also be hints to these laws from Nakh (for example, Berachot 8a or 48b). In this case the laws have the status of Biblical law (see Torat ha’Nevi’im of Maharatz Chayes).