Early progress is not a persistent indicator
The idea of a persistent system is that in the future things will be as they were up to today. Weather is a good example, since assuming that tomorrow will be as cold (or hot) as today is normally a good prediction. We may fail some days a year but overall is a good estimator.
When we start new projects, we will make some early progress that can be driven by different factors. However, this progress is not persistent in time, and is not necessarily a continuous function. There is always a chance that progress is halted on one very specific moment.
One day, something will not work, and progress will halt. If we define progress as the cumulative number of objectives we've achieved over time, we can observe initial exponential progress. As challenges become harder to overcome, progress will transition to linear and perhaps even flat out. This is the moment when the system stops being persistent.
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