Bo, I don't have the time to get into it now, but this seems very similar to the problem:
\[
\text{The half iterate of}\,\,-z + \lambda z^2\,\,\text{has no power series at 0 for all}\,\,\lambda \neq 0\\
\]
Which is absolutely provable. And for higher powers of \(z\), it's reducible to this.
It can quite literally just become a question of \(y = z^n\) and there are \(n\) branches--in no world is \(y\) holomorphic at \(0\).
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I love how you reduce everything into taylor coefficients. I reduce everything into integrals or something like that. I love the taylor coefficient approach
\[
\text{The half iterate of}\,\,-z + \lambda z^2\,\,\text{has no power series at 0 for all}\,\,\lambda \neq 0\\
\]
Which is absolutely provable. And for higher powers of \(z\), it's reducible to this.
It can quite literally just become a question of \(y = z^n\) and there are \(n\) branches--in no world is \(y\) holomorphic at \(0\).
-----------------------------------------
I love how you reduce everything into taylor coefficients. I reduce everything into integrals or something like that. I love the taylor coefficient approach