Pip underpayment confusion

I was told by the claim manager that his calculations were correct and that I shouldn't question his judgement and he did not need to explain his decision in writing i decided to escalate the situation as I was adamant a mistake had been made and after 10 days of back and forth and speaking to half a dozen or more claim managers I was finally called back by the supervisor of the claim manager who actually went through the entire claim with me, listened to where I believed the mistake had been made and after 2 hours on the phone he admitted a mistake had been made and after apologising he released the full payment, I would urge anyone who feels a mistake has been made to push it all the way and demand a full written explanation of how they calculated your back payment as if I had taken his word for it I would have lost out on almost 4 thousand pounds

Yea I totally understand why people give up, I was close a couple of time, the way I was spoken to made me feel like I was a bad person for pursuing what I believed was rightfully mine, I was even told by the claim manager I shouldn't worry what the underpayment amount was and should just be grateful I was getting something, I'm just glad it's over and done with and I got the outcome I always believed I was entitled to