Yup ... fight it.  If the police didn't even bother to look and see if you had a cell phone, well ... that was stupid of them.

Generally (not positive about your state, but generally), if you plead not guilty, the police also have to show up at the hearing and testify as to what they observed that made them write the ticket.  If all that they observed was that you had one hand up near your ear ... then that's all they are going to have to support their case.  More than likely ... since that's all they have, they might not even show up, in which case the whole thing will be dismissed.

Brilliant idea to take your cell phone records, which would show that no calls were made or received during the time around the issuance of the ticket.  That's all that is really key .... not how many calls you make, but given the time of the ticket, were you on the phone at that time or just before? If not, then you have a defense if the cops decide to lie on the stand.

As someone mentioned, if they decide to argue that you could have more than one cell phone provider, it is up to them not only to prove that you do, but also that you were on the phone through that provider at the time of the ticket.  All you have to do is testify that this is your only provider and that you were NOT on the phone at the time or before the time that the ticket is dated and timed.

If they don't prove their case, then you win.  If you don't fight it ... you lose automatically.  Your case would be very difficult to prove, and my thought is that the cops are not going to bother to show up .... as noted, that should lead to an automatic dismissal.  But ... again, on the off chance that they show up ... have your evidence in hand.  They won't expect that and it will bolster the fact of our innocence.

Oh, and yes .... I have noticed for a LONG time that your font is teeeeeny tiny.  I always end up with my nose right up to the screen so that I can read it.  But, your posts are always worth reading. 

Could be worse, could be raining.