What is the legal basis allowing all the conditional eruv scenarios in Siman 413?

When making an eruv techumin for many people from one's own food, how much food must be provided?

5 opinions

When the eruv-maker did not inform a potential beneficiary before Shabbat, can that person rely on the eruv after nightfall?

3 opinions

If a person was informed of the eruv before Shabbat but did not consciously decide to rely on it until after nightfall, is the eruv valid for them?

4 opinions

If one placed an eruv for all Shabbatot of the year with the condition 'whichever one I choose I will rely on,' but did not decide until Shabbat morning, is the eruv valid?

4 opinions

Is notification required for an eruv techumin made for others, and why?

2 opinions

Is an eruv valid when placed for a conditional contingency (e.g., 'if the scholar comes from the east, my eruv is eastward') even if the scholar was outside the 4,000-amah range at twilight?

2 opinions

Must the eruv-maker transfer ownership (zikui) to beneficiaries through a third party when making an eruv for many from his own food?

3 opinions

Is a food quantity less than two meals for every single person of the town valid if only some people will rely on the eruv?

2 opinions