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We will pick a parent by default:

1. if there are no previous branching sections, pick the previous section as parent
2. if there are, pick the same parent as the previous

We will also allow clicking on \ from "Foo Bar" to change the parent.

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The big question is what to do with the existing branch sections button:

1. Keep it as is
2. Making it so it uses the heuristic above and people can use the \ from "Foo Bar" link to change it

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Finally, we will add an explicit x Clear at the top of the branching section menu (instead of having folks click the currently checked one to disable).

There is also a "bug" when mixing zen mode with branching sections. Zen mode merges all code cells together, making it impossible to know which code belongs to a branching section and which does not.

I think we should provide very thin horizontal lines as session separators, potentially with an icon identifying the section. The goal is to keep it as unobtrusive as possible.