In plain English
Think of bitcoin’s long-run path as a highway with painted edges. The middle line is the fitted trend. The lower dashed line is a typical floor; the upper dashed line is a typical stretch ceiling.
Two extra lines from the blockchain: realized is roughly what the average coin last sold for (the crowd’s cost basis). Terminal is a historically extreme “too hot” line that has sat near past blow-off tops. Pi Cycle arrows mark one overheating timer, not a bottom timer.
Math and metrics
Overlay of the site OLS power law plus Coin Metrics realized/terminal and Pi Cycle top dates. Genesis t0 = 2009-01-03. Fit sample from 2010-07-18.
trend(t) = 10^(a + b·log10(days)). floor = trend·10^(−1.15σ). ceiling = trend·10^(+2σ).
headline vsTrend = spot/trend − 1. σ = population stdev of log10 residuals.
Realized ≈ realized cap / supply. Terminal = 21 × cumulative (price·CDD) / (supply · days). Pi tops: SMA_111 crosses up through 2×SMA_350. This plate does not invent a new model.