I agree -- this sort of approach makes a lot more sense, and will scale very well to any amount of input. I'd just make one minor adjustment:

while (<FILE>) {
#  $phi = substr($_, 0, 6);
#  $psi = substr($_, 8, 6);

   ( $phi, $psi ) = split;
   ...
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The OP didn't show us any lines of data with single-digit numbers in one or both columns. Such lines might or might not have fixed-width fields, and if not, substr() would do the wrong thing; split() would always do the right thing.

(For that matter, it's not clear whether the column separator is two spaces or a single tab character -- again, split works in any case, while substr would get tripped up when you guess wrong about that.)