What do you do with a tayku? TB Sukkah 4

I think that arguing is part of the DNA of the Jewish people. I remember driving with my wife once and she complained, “You always disagree with me.” I promptly answered, “No I don’t.” On daf TB Sukkah 4 we learn about a disagreement about what the disagreement is about.

“The Sages taught: If one inserted four posts [kundeisin] into the floor and placed roofing over them but no walls, Rabbi Ya’akov deems it a fit sukka and the Rabbis deem it unfit.

“Rav Huna said: The dispute between the Rabbis and Rabbi Ya’akov is in a case where the four posts are aligned on the edge of the roof, directly above the exterior walls of a house, as Rabbi Ya’akov holds that we say the principle: Extend and raise the partitions (גּוּד אַסֵּיק). Since the exterior walls of the house are full-fledged partitions, they are considered as extending upward indefinitely, constituting the walls of the sukka. And the Rabbis hold that we do not say the principle: Extend and raise the partitions. However, if the posts are placed in the center of the roof, then the walls of the house are irrelevant and everyone agrees that it is an unfit sukka. And Rav Naḥman said: The dispute is in the case of a sukka in the center of the roof, as according to Rabbi Ya’akov, if the posts themselves are one handbreadth wide, they serve as the partitions, while the Rabbis hold that it is not a fit sukka until it has two complete walls and a partial third wall.

“A dilemma was raised before the Sages: Is Rav Naḥman saying that only if the sukka is in the center of the roof there is a dispute between Rabbi Ya’akov and the Rabbis, but if it is at the edge of the roof everyone agrees that it is fit? Or perhaps he is saying that there is a dispute both in this case and in that case? No resolution was found, so the dilemma shall stand unresolved. (תֵּיקוּ-tayku)” (Sefaria.org translation)

How do you decide Jewish law if the discussion ends with a tayku? According to most rishonim when the matter under discussion is a Torah law (דאורייתא) we accept the more stringent view. When the matter under discussion is a rabbinic law (דרבנן), we accept the more lenient view. Concerning the sukkah consisting of only four polls and a roof whether the polls are placed on the corners of the roof or in the middle of the roof, we take the more stringent view of the sages. (Shulkhan Arukh, Orekh Hayim, 630:6)