The Arsonist-Firefighter Paradox of Probabilistic AI: Deterministic QFS-zkVM Interlocks, SEC Rule 15c3-5 Market Access Prohibitions, and Caremark Fiduciary Liability Against Catastrophic-Risk AI IPOs (邦題:確率的AIの「放火魔・消防士パラドックス」:破滅的リスクを伴うAI企業のIPOに対する決定論

Empirical evidence from October 2026 exposes a terminal structural pathology in the contemporary artificial intelligence ecosystem, herein formalized as the Arsonist-Firefighter Paradox. On one front, autonomous probabilistic AI offensive frameworks (such as the ARTEX penetration suite and AI-synthesized ransomware deployed by groups like Qilin) have compressed terminal-intrusion-to-exfiltration latency to an average of 29 minutes and a minimum of 27 seconds, compromising tens of millions of corporate records (including 53.23 million at Sagawa Express, 11.77 million at Capcom, and 11.18 million at Burger King Japan) and physically sabotaging critical civil infrastructure—ranging from forced defrost thermal runaway ($50^\circ\text{C}$) across hundreds of French retail refrigeration networks to the paralysis of United States municipal water purification systems. Concurrently, frontier AI developers such as Anthropic have filed Form S-1 registration statements with the U.S. Securities and Exchange Commission (SEC) seeking over $100 billion (approx. 16 trillion JPY) at a $1.5 to $2.0 trillion valuation while operating at an operating loss of nearly $700 million against $16.2 billion in H1 2026 revenue, explicitly warning in their statutory risk disclosures that autonomous frontier AI poses "catastrophic or existential risks to humanity." This monograph proves mathematically, thermodynamically, and legally that permitting capital-market securitization of unverified probabilistic AI models constitutes an uninsurable systemic externality and a per se breach of corporate and securities law. First, we model the macroeconomic and cyber-physical instability of the probabilistic AI arms race, demonstrating that defensive AI subscriptions sold to mitigate offensive AI exploits generate adivergent positive-feedback rent-seeking loop with strictly negative net social utility. Second, we establish that underwriting and distributing securities for an enterprise that self-certifies existential risk while externalizing cyber-physical damages violates SEC Rule 15c3-5 (Market Access Rule) and triggers non-exculpable director liability under Delaware Caremark (In re Caremark International Inc. Derivative Litigation) mission-critical oversight standards. Third, we specify a deterministic hardware and cryptographic replacement architecture anchored in RTO P2.0, the QFS-zkVM operating over the 64-bit Goldilocks prime field ($\mathbb{F}_p, p = 2^{64} - 2^{32} + 1$), Q-SAFA (Quantum-Safe Autonomous Field Attestation), and PHOENIX_BRIDGE / PHOENIX_ROUTER under strict Human-in-Command (HIC) governance. Every state transition in critical infrastructure and financial clearing is gated by zero-knowledge polynomial commitments with zero probabilistic hallucination tolerance. License & Integrity Covenant: Creative Commons Attribution 4.0 International (CC BY 4.0) with Strict No-Learn Covenant (NLL-v1.0-2026). Unauthorized AI training, web scraping, weight ingestion, or uncompensated commercial exploitation is strictly prohibited.