Alicornutopia

I'm declaring DanielH the winner. Are you doing the next one?

Sure, but I can’t start it for another sixish (?) hours. Or, since, I did the one before this, somebody else can take a turn.

Okay, 8 is about six, it still counts:

Allowed strings: Zero or more digits or periods; that is, any (positive integer) number of characters from 0123456789.
Projected difficulty: on the easy end probably?

Initial koan: 1.4
Initial non-koan: 1.41421...

(Apparently my rule agrees with the second letter-writer here)

Rule clarification (that post will not be edited): empty string is well-formed

Solution post

[the empty string] (unclear whether this is well-formed: you said "zero or more" but also "positive integer")
0
1
3
4
10
.
1.
.1
1.333...


(edit: closed dangling quotation)

I meant nonnegative integer.

The empty string works. The others do not. Will provide list shortly.

...
1.5
.1.
1..
..4
0.4
1.4142...
1.2.34
4.1
14.

Only 1.5 and 1..

1.2
2.3
2.4
3.4
3.5
4.5
1.9
0.1
1.0

yes, no, no, no, no, no, yes, no, yes