The problem is that your want data set is not truly using cumulative amounts, because when it is the first day of the sequence, the value you want is 0, when if it was truly cumulative, the first cumulative amount would be the amount. So the first row cumulative would be 3600 and the second row cumulative would be 456.
This is easy to compute, but isn't exactly what you asked for.
data want;
set have;
prev_dt=lag(dt);
if (dt-prev_dt)^=1 then cumulative=0;
cumulative+amount;
drop prev_dt;
run;
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