Correcting the error in getnetworkhashrateps

The exploration into the behavior of Poisson processes in the context of blockchain and mining reveals intriguing findings regarding the correction needed for accurately estimating work based on a specified number of blocks found within a given timeframe. Initially, an assumption was made that a correction factor of (N-1)/N might be necessary to adjust for the variability in hashes per fixed time period when calculating hashrate or adjusting difficulty levels. However, experimental data suggest a different approach might be more accurate.

Through experimentation involving 100,000 runs with a setup of five blocks to be found, it became evident that a correction factor of (b+1)/b is required, contrary to the initial hypothesis. This correction suggests that for any given number of blocks b observed, the mean work calculated needs to be adjusted upward slightly to account for the randomness in hash outcomes within a uniform distribution. The experiment's formula and results underscore the importance of this adjustment: without it, the calculated work deviates from what would be expected under a Poisson distribution.

The experiment conducted provided detailed data points: with a difficulty target set to 0.01% of the maximum target, out of 100,000 runs, 6,156 resulted in exactly five blocks being found. The mean work when exactly five blocks were discovered was 600, aligning perfectly with the corrected Poisson work after applying the (b+1)/b multiplier. This finding is significant as it illustrates the necessity of adjusting our understanding of how work correlates with block discovery in a uniformly random hash environment.

Furthermore, the standard deviation of the work divided by the mean work when b blocks were seen highlights the variability inherent in such processes, which coincides closely with the theoretical standard deviation derived from the Poisson distribution formula. This close match between experimental results and theoretical predictions reinforces the validity of the corrective approach suggested by the experiment.

In conclusion, the insights gained from this analysis challenge previous assumptions about the need for correction factors in estimating work based on block discovery over time. It presents a refined method that accounts for the uniform randomness of hashes and provides a more accurate framework for understanding the dynamics of blockchain mining and difficulty adjustments. This research contributes valuable knowledge to the field, offering a more nuanced perspective on the mathematical models that underpin blockchain technology.