Shared Trends and the Bitcoin Power Law: Forecasting and Network Evidence

I assess the Bitcoin price power law as a forecast and as the product of adoption and valuation exponents. On eleven annual origins (2014 to 2024), an expanding power law has log10 root mean squared error (RMSE) of 0.376 and 0.356 at 12 and 24 months, against 0.515 and 0.687 for the last price. Significance depends on the test. The Frisch–Waugh–Lovell theorem gives an exact least-squares identity for the exponent product. On 182 month-ends, the primary product (5.42) is within 1.8% of the time slope (5.52). Across the original four balance-bin proxies and three price series, the shared-trend term equals 99.3 to 99.8% of the product, a signed ratio of fitted coefficients. It has no variance-share interpretation. On the same dates, an added Coin Metrics nonzero-balance stock has a composition gap of 2.1%, versus 13.7% for daily address activity; their signed ratios are 99.48% and 98.58%. The primary partial address coefficient is imprecise. The expanding exponent stays between 5.5 and 6 since 2018. In a post hoc six-proxy, four-penalty grid, all 24 address corrections per price source raise 12-month error and eight lower 24-month error relative to the expanding power law. All evidence is retrospective and leaves the mechanism unidentified. Replication materials: https://doi.org/10.5281/zenodo.23961735