The Collapse of Investment Time Horizons in Supercritical Liquidity Panics: Empirical Analysis of the October 15, 2026 Nikkei 225 Intraday Plunge (-3,651.55 JPY), Algorithmic Support-Line Vaporization, Correlation-One Index Contagion, and Optimal Cash-Sovereignty Interlocks via Sobolev-HOCBF and QFS-zkVM

Classical financial economics partitions market participants into two distinct temporal regimes: short-term technical traders (relying on moving averages, historical support lines, and intraday mean reversion) and long-term fundamental investors (relying on multi-year earnings compounding and diversification). Yet during acute algorithmic liquidity panics—exemplified by the October 15, 2026 intraday plunge of the Nikkei 225 Stock Average (INDEXNIKKEI: NI225), which collapsed from a previous close of 67,744.29 JPY to an intraday low of 64,092.74 JPY (-3,651.55 JPY, or -5.39% intraday; -3,247.56 JPY [-4.79%] at 64,496.73 JPY by 14:44 JST)—the distinction between "short-term" and "long-term" completely evaporates. Building upon our 200th Grand Master Monograph (Record 23383049), our proofs of 100x sovereign bond basis-trade unwinding (Record 23382621), multi-agent AI swarm cascades (Record 23382746), and 15%+ GPU private-credit contagion (Record 23384072), this 204th monograph establishes the mathematical theory of Time-Horizon Collapse in Supercritical Liquidity Panics. We prove four core theorems: (1) The "Falling Boulder" Theorem of Short-Term Technical Vaporization: When autonomous CTA, Risk-Parity, and AI execution swarms trigger synchronized risk-off liquidation, limit-order-book bid depth L_bid(P, t) -> 0 across all historical moving-average and chart support levels, driving Kyle price impact Lambda(t) -> infinity and annihilating short-term mean-reversion strategies; (2) Correlation-One Index Contagion (rho_ij -> 1) & The Prospect-Theory Capitulation Boundary for Long-Term Holders: Passive index futures and ETF basket liquidation forces the pairwise correlation matrix R(t) -> 1*1^T, decoupling stock prices from corporate earnings while Kahneman-Tversky loss aversion (lambda_loss ~ 2.25) drives long-term investors into bottom-tick capitulation; (3) The Cash-Sovereignty Dominance Theorem via Sobolev-HOCBF: Proves that shifting portfolio weight to cash (w_cash^*(t) -> 1) is the unique Hamilton-Jacobi-Bellman optimal control when G_panic(t) >= 1; and (4) Sub-7.0 ns PHOENIX_ROUTER x QFS-zkVM 100 ms Batch Clearing. License & Integrity Covenant: Creative Commons Attribution 4.0 International (CC BY 4.0) with Strict No-Learn Covenant (NLL-v1.0-2026).