Complete Transplantation of Orbital Autonomous Traffic Control System (ATCS) Architecture to Residential Smart Kitchens: System Requirements, Control Barrier Functions, and Sub-12.5ms Hardware Interlocks (宇宙デブリ自律交通管理システム(ATCS)アーキテクチャの家庭用スマートキッチンへの完全移

This monograph presents the formal system requirements and mathematical framework for transplanting the Multi-Objective Optimization (MOO) and Quantum-Safe Autonomous Governance (Q-SAFA) architecture—originally engineered for extreme orbital Space Debris Autonomous Traffic Control Systems (ATCS)—into a residential smart kitchen Autonomous AI Fire Prevention and Shutdown System. Because probabilistic AI inference (LLMs and deep reinforcement learning agents) inherently carries the risk of hallucination and non-deterministic failure, software logic alone cannot guarantee safety. To provide provable, deterministic safety, this architecture binds AI decision-making across three independent dimensions: mathematical, physical, and economic. First, at the mathematical and physical control layer, we implement a Control Barrier Function (CBF) safety filter (evaluate_constraints_kitchen(x)). Orbital collision risk ($f_3$) is mapped to residential thermal runaway and secondary incomplete combustion risk ($f_{3\_fire}$), governed by an ethical boundary condition ($\theta_{ethics} = 0.05$) and a strict physical upper bound of $250^\circ\text{C}$ in compliance with Japanese Fire Service Act Si-sensor standards. Utilizing a log-barrier penalty function $\Phi(x)$, any approach to $h(x) \le 0$ triggers an instantaneous step-function penalty ($\Phi = \infty$), bypassing AI software inference to actuate a SIL3-compliant hardware interlock. Second, to prevent post-incident log tampering by the AI, the Quantum Audit Record (QAR) is transplanted as an "Immutable Anti-Liar Diary" anchored by a physically isolated Hardware Root of Trust (HRoT / TPM 2.0 with PUF-derived keys) and FPGA-accelerated post-quantum cryptography (ML-DSA / SHA-256), locking environmental sensor telemetry (temperature $T$, smoke $S$, gas $G$, combustible proximity $D$) into a WORM Merkle hash chain within a strict $< 12.5\text{ ms}$ latency budget. Third, an economic governance layer links the appliance to a Decentralized Physical Infrastructure Network (DePIN) and smart-contract parametric insurance using zero-knowledge proofs (zk-STARKs), enforcing dynamic premium scaling $P(t) = P_0 \exp(\gamma \cdot R_{score})$, automated collateral slashing, and HEMS smart-grid power/gas cutoff upon human safety overrides.