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    $\begingroup$ is identically zero for when −ϵ√<r<ϵ√ By just plotting your CCJ12, you can see this is not true. It seems CCJ12 is zero between 0 and Sqrt[\[Epsilon]]. i.sstatic.net/f591N3a6.png try Reduce see if it works. $\endgroup$ Commented Jul 5, 2025 at 9:20
  • $\begingroup$ I think I accidentally copied the wrong expression initially, now it should be correct, at least I get a plot between numbers of the 10^{-14} order. @Nasser $\endgroup$ Commented Jul 5, 2025 at 9:24
  • $\begingroup$ I did try Reduce overnight, after 9 hours of letting Mathematica run I gave up. $\endgroup$ Commented Jul 5, 2025 at 9:37
  • $\begingroup$ You asked for zero between ~-0.328 and ~0.328. I try a larger range s[r_]:=FullSimplify[CCJ12]; Table[If[r==0,{0,"dividebyzero"},{r,s[r]}],{r,-57/100,57/100,1/100}] and it returns exactly zero for every one of those. If I include r==0 it fails with divide by zero. If I try s[1/Pi] or s[1/E] or s[1/Sqrt[13]] then it runs for so long that I bail out. There must be a reason it is EXACTLY zero for 114 different rationals and a different reason why it runs for a very long time or never finishes for irrationals. Try Plot[s[r],{r,-57/100,57/100},WorkingPrecision->1000,PlotRange->{-10^-32,10^-32}] $\endgroup$ Commented Jul 6, 2025 at 16:17