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I get from Wolfram Alpha 1.93277 Calculation 1 I get with else original values 4.23555 Calculation 2

That is in accordance with the result by OP, who obtained ##KE=E-M=M##, which implies ##E=2M##. This demonstrates that my removal of the...

Interesting! How much the last term ##i=N## contributes to the full sum? What happens if you take ##v=1## but compute the sum only up to...

Also note that the constraint of constant density per a local, comoving observer, means adding particles to outer rings as they are sped...

But the uniform COM frame density follows necessarily from any simple (i.e. not including stress energy of holding the disc together)...