Resolving Illiquidity Liveness Deadlocks and Spectral Indefiniteness in Asynchronous Cross-Market Quantitative Systems: Timeout-Bounded Subordinated Volume Clocks, Higham-Projected Hayashi-Yoshida Covariance, and Discrete Exchange Lot Quantization

Deploying econometric time-deformation and cross-asset covariance estimators into continuous 24/7 autonomous trading systems exposes three severe operational failure modes that remain unobserved in offline historical backtests: (1) Subordinated Volume-Clock Liveness Deadlock, wherein replacing chronological wall-clock bars with pure volume-threshold sampling (Clark, 1973; Lopez de Prado, 2018) causes the bar generator to stall indefinitely during intraday liquidity vacuums, blinding downstream risk and stop-loss engines to accumulating macroeconomic shocks; (2) Spectral Indefiniteness in Asynchronous Cross-Market Covariance, where applying the Hayashi-Yoshida (2005) overlap estimator across non-synchronously traded global assets (US equities, Tokyo Stock Exchange equities, spot FX, and precious metals futures) eliminates the Epps (1979) downward correlation bias but frequently yields symmetric matrices with strictly negative eigenvalues, causing Cholesky decomposition failures and imaginary portfolio variance in Kelly allocation; and (3) Discrete Exchange Microstructure Quantization Violation, where continuous-share Half-Kelly optimization violates tiered tick-size tables and mandatory 100-share board-lot constraints on the Tokyo Stock Exchange (TSE). Completing the mathematical trilogy established in Hashimoto (2026a, 2026b), we formulate a unified temporal and cross-asset econometric architecture implemented in the open-source lumina-quant library: a Timeout-Bounded Subordinated Volume Clock (1,800s heartbeat) reducing return excess kurtosis by 98.0% with zero liveness deadlocks, a Higham-Projected Hayashi-Yoshida Lead-Lag Operator guaranteeing strictly positive portfolio variance, and a Discrete Exchange Tick-and-Lot Conformance Operator paired with a 3.63 ns Rust Structure-of-Arrays (SoA) execution sentinel.