Your logic in this argument does not make sense to me. For instance I believe that you do agree that s is calculated only by performing the chi squared fitting in maple or manually. Ie in this formula I(t) = Imax * ( fR((t-tmax)/w) + b all the variables are known from the template and tables and z is supplied as the redshift value for each SN. So s is the unknown that is calculated by the chi fitting. In other words you cant find out s until you have done the chi squared fit. Yet you contradict yourself and say that you dont have to do the fit to find out what s is when z is either .49 or 0. Dont you see how that does not make sense? For instance here I will set you a test. You claim that you can calculate s just by looking at the formula . So I will set you a test to derive s for a SN where z=0.49 I know what s is because I have taken it from another paper where someone else has already calculated it so I can check if your answer is correct.
Now according to your logic the formula `tells` you what s will be. So please what does the formula tell you what s is for that SN where z=0.49? And then, what is s where z=0 for that SN? Do you still `hear` the formula telling you the answer or will you now admit that you have to do the chi squared fit to derive s where z=.49 and z=0 And if you admit that you have to do the fit then that is a direct contradiction of your earlier statement that you can `hear `the answer because the formula is `telling` you the answer.