Description Without Prediction: A Methodological Critique of Bitcoin Price Power Law Models

This paper identifies nine methodological concerns across two prominent Bitcoin price power law analyses: a widely circulated retail Monte Carlo simulation and Santostasi and Perrenod (2026), “A Mechanistic Derivation of the Bitcoin Price Power Law.” Both analyses demonstrate that Bitcoin’s price history from 2010 to 2026 is well described by a power law with exponent approximately 5.69. Neither establishes that this relationship constitutes a forward-binding structural constraint. The retail variant fails on five grounds: residual stationarity demonstrates historical consistency but not causal necessity; the Monte Carlo boundary condition is circular; the volatility decay narrative is a log-scale coordinate artefact; the halving-cycle regime segmentation is entirely in-sample; and no generative mechanism is provided for the relationship’s expected persistence. The academic variant fails on four additional grounds: the composition identity β = β₁ × β₂ is algebraic necessity, not independent evidence; the epidemic spreading derivation is post-hoc rationalisation fitted to the measured exponent rather than an independent prediction; the Bayesian stability analysis applies a conjugate update to autocorrelated rolling estimates as though they were independent draws, artificially compressing posterior uncertainty by a factor of approximately 5.6; and the paper omits a Granger causality test between price and address count, leaving the direction of causation unestablished. The paper concludes with a five-stage pattern analysis and a diagnostic checklist for identifying when quantitative models have crossed from empirical description into unfalsifiable advocacy.