Bitcoin Power Law: The End of Exponential Growth | Matthew Mezinskis

— Bitcoin grows on a power curve (proportional, sustainable growth) rather than exponential growth like traditional finance; this means its annual growth rate declines over time as the network scales.

— Power curves exhibit straight-line relationships on log-log charts, whereas exponential systems (TradFi, bonds, stocks, credit-based instruments) show straight lines on log-linear charts—a fundamental structural difference.

— Bitcoin's doubling time increases proportionally with network age; early Bitcoin doubled every ~7 days, now approximately every ~700 days (two years)—contrasting sharply with exponential systems that double at fixed intervals.

— The jury remains open on whether Bitcoin will be pulled into TradFi's exponential model or eventually pull TradFi toward Bitcoin's power law; credit-based lending cannot work sustainably on power curves because interest requires constant compounding.

— Bitcoin priced in gold ounces is near historical lows (~25.39 oz vs. trend of 63 oz), suggesting potential rotation from gold back to Bitcoin despite recent gold strength.

— AI and top tech stocks are currently growing at 41% CAGR—matching gold's recent pace—but face mean reversion pressure; market caps would need to reach ~$35 trillion to exceed prior records, suggesting a potential boom-bust cycle ahead.

— Bitcoin currently trading just over $101,000, positioned at approximately the 55th percentile (slightly below trend) on the power curve; between 50th and 60th percentile on the OLS regression line.

— Bitcoin has not breached trend line since 2022; compared to prior cycles, 2024–2025 cycle has stayed much closer to trend with lower volatility extremes, though Matthew remains uncommitted on whether traditional four-year cycles have ended.

— Bitcoin denominated in gold ounces trading at ~0.4x the 50-year trend (under 20th percentile), suggesting deep relative undervaluation versus precious metals despite 16 years of power curve growth.

— US monetary base doubled from $22 trillion (2015) to $40 trillion (2025); Bitcoin market cap grew from $4 billion to $2.13 trillion over same period, now approaching scale of U.S. cash in circulation.

— Use the power curve as a relative risk assessment tool rather than a timing mechanism; current position ~55th percentile indicates fair value in dollar terms, but deep discount in gold terms suggests potential rotation opportunity.

— Monitor whether Bitcoin's proportional growth rate sustainably exceeds the fixed interest rates embedded in TradFi debt instruments; if credit cannot adapt to power growth, structural conflict emerges favoring scarce assets like Bitcoin over debt-based systems.

— Recognize that gold and AI tech valuations appear stretched on multi-year trends; if they revert toward historical norms, capital may rotate into Bitcoin, particularly given Bitcoin's immunity to supply-demand mean reversion through fixed protocol supply.