@DannyuNDos But a binary tree can have 2 entries in it. In a binary tree, there is normally an entry in each leaf and each branch node.

The test cases do not include any nodes with one child, like: [L,] or [[L,],[L,L]] Note that this could break some parsers based on the existing test cases.

I really like the 12,12,10,10,... sequence; and part of me wants to enumerate all valid sorted sequences.

@CursorCoercer Strangely, my original 145 byte answer deals with all your new test cases, but not the one I added. Also, you should probably add a variant of Dominic's with the missing 7 added. (even if it doesn't meet the assumptions.)

@CursorCoercer, I was putting in an edit saying it failed as you added cases. Well, I think my tests are necessary but not sufficient.

Two necessary conditions that are sufficient to eliminate the Falsy examples: the sum of the sequence must be 78. For every n>=6 there must be at least 13-n entries in the sequence >= n. I don't know if we are just missing another Falsy sequence, or if this is enough.

@Neil As I understand it, "ye" is actually a pronoun form. The use of it as "the" is a french misreading of the word spelled Þe. Þ (thorn) is one of the lost English letters, pronounced as soft "th.