At the fourth comparison we have a mismatch.
At the suggestion of the referee, we consider some simple cases.
The match occurs at position 7 in $T$.
Now $R$ is the localization of $Q$ at a maximal ideal.
Next, $F$ preserves angles at each point of $U$.
We may assume that this is the first point at which these two curves have met.
at the end of Section 2
Now $F$ is defined to make $G$ and $H$ match up at the left end of $I$.
The zeros appear at intervals of $2m$.
We can make $g$ Lipschitz at the price of weakening condition (i).
The two lines intersect at an angle of ninety degrees.
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