The Willow Quantum-Photonic Regime Shift and the CMOS Semiconductor CapEx Cliff: Structural Fragility of the Nikkei 225 at the 70,000-Yen Ceiling — Sub-Threshold AlphaQubit Scaling, Price-Weighted Index Concentration Contagion, and Deterministic QFS-

In mid-October 2026, Japanese equity market commentary focused intensely on whether the Nikkei 225 Stock Average—having briefly touched an intraday high of 70,798 yen on October 6 before retreating to 69,030 yen on October 9 alongside a bearish Heikin-Ashi candlestick reversal—could sustain the 70,000-yen threshold on the back of upcoming U.S. and global semiconductor earnings (including ASML Holding, TSMC, and U.S. AI accelerator vendors). This prevailing market consensus rests on the fragile assumption that brute-force Complementary Metal-Oxide-Semiconductor (CMOS) GPU capital expenditure will expand indefinitely. However, simultaneous empirical signals—including reports that OpenAI's September 2026 revenue missed market expectations and the 8-year electrical grid bottleneck confronting Anthropic and NTT Data's proposed 500 MW Osaka AI data center—reveal that brute-force CMOS scaling has hit both a monetization wall and a thermodynamic grid ceiling. This monograph establishes a formal econometric, quantum-thermodynamic, and index-microstructure proof of the impending CMOS Semiconductor CapEx Cliff and its non-linear contagion into the Nikkei 225: (1) We formulate the Willow–RTO P2.0 Substitution Theorem, demonstrating that the ascent of Google's sub-threshold surface-code quantum processor (Willow with AlphaQubit neural decoding) and our Real-Time Optimization (RTO P2.0 — Subtractive Compute) architecture compresses required AI/optimization silicon and power footprints by > 42.3x, triggering a reverse Samuelson-Clark investment accelerator (\Delta I_SPE << 0) across legacy lithography and wafer-fab equipment orders; (2) We analyze the Price-Weighted Divisor Vulnerability of the Nikkei 225, proving that because high-priced Japanese Semiconductor Production Equipment (SPE) and AI-holding stocks command an artificial index weight up to 3.8x their true market-capitalization weight while exhibiting a cross-border beta \beta_{SPE,SOX} in [1.45, 2.10] to U.S. semiconductor multiples, a Willow-induced U.S. semiconductor re-rating mathematically forces a sharp Nikkei 225 correction below 70,000 yen; and (3) Extending our Quantum-Secure Financial Settlement System (QFS-zkVM) over the 64-bit Goldilocks prime field (F_p, p = 2^64 - 2^32 + 1), we construct a deterministic sovereign portfolio rebalancing and pre-crash liquidity protection protocol. License: Creative Commons Attribution 4.0 International (CC BY 4.0) with Strict No-Learn Covenant (NLL-v1.0-2026).