Heterogeneous collective criticality in cryptocurrency volatility: Scaling collapse, tail synchronization, and cascade amplification

This paper tests whether the volatility of Bitcoin (BTC), Ethereum (ETH), and Solana (SOL) is better characterized as a heterogeneous collective-critical regime than as asset-by-asset turbulence. Using daily and hourly data, with the daily S&P 500 cash index and the near-continuously-traded EUR/USD reference rate as contrast benchmarks, we extend the Bergmann–Oliveira critical-boundary framework from single-series classification to coupled volatility dynamics. Four results support the claim. First, Ethereum is robustly supercritical and Solana is supercritical under finite-sample validation, whereas Bitcoin is boundary-adjacent, with a point estimate below the boundary but a circular-block interval crossing CR = 1. Second, boundary distance and tail-clustering depth are distinct system-level coordinates: Solana has the largest boundary distance, while Bitcoin exhibits the slowest tail-dependence decay. Third, crypto clustering functions exhibit scaling collapse near a common exponent, β ≈ 0.31, and pairwise and triadic co-exceedances remain above circular-shift, block-shuffle, and factor-residual null envelopes. Fourth, short-horizon volatility-of-volatility preserves cascade amplification, while long smoothing absorbs it; intraday boundary estimates are scale- and estimator-sensitive rather than fixed activation constants. The boundary configuration is not a conditional-heteroskedasticity artifact: heavy tails persist after GARCH/EGARCH/FIGARCH filtering, FIGARCH confirms genuine fractional integration, and a Gaussian-innovation GARCH cannot reproduce the observed supercriticality. The regime is further corroborated by marginal-matched surrogates that isolate the collective component. Conceptually, it recasts a single-series phase boundary as a diagnostic of synchronized collective instability. Practically, crypto tail risk should be monitored through boundary proximity, tail synchronization, and cascade propagation rather than marginal volatility alone.