Post
Topic
Board Speculation
Re: Gold collapsing. Bitcoin UP.
by
TPTB_need_war
on 05/07/2015, 03:03:28 UTC
Let τ be the time it takes to verify a typical block and let T be the average block time (10 min).  The fraction of time the miner does not know whether the most recent block was valid is clearly τ / T; the fraction of the time the miner does know is 1 - τ / T = (T - τ) / T.  We will assume that every miner applies the same policy of producing empty SPV blocks before they've verified, and blocks of size S' after they've verified.  

Under these conditions, the expectation value of the blocksize is equal to the expectation value of the blocksize during the time a miner doesn't know, plus the expectation value of the blocksize during the time he does know:

    Seffective = ~0 [(τ / T)]   +  S' [(T - τ) / T]          
                 = S' [(T - τ) / T]                          (Eq. 1)

The time, τ, it takes to process a block is not constant, but rather depends linearly** on the size of the block.  Approximating the size of the previous block as S', we get:

    τ = k S'

....

QED. We've shown that there exists a limit on the maximum value of the average blocksize, due to the time it takes to verify a block, irrespective of any protocol enforced limits.

Your egregious mathematical error (myopia) of course is that you assume k is the same for all miners. And this is why you totally miss the centralization caused by your nonproof.