Autonomous Traffic Control System (ATCS v2.0) for Low Earth Orbit Debris Mitigation: 12.5-ms Hardware-in-the-Loop Multi-Objective Optimization, Post-Quantum Cryptographic Governance (ML-KEM-768 / Decoy-State QKD), Q-SAFA Self-Executing Orbital Circular Economy, and Isomorphic Pedagogical Communication

Abstract

The exponential proliferation of mega-constellations in Low Earth Orbit (LEO) has completely surpassed the operational limits of legacy ground-based, Human-in-the-Loop Space Traffic Management (STM). According to the European Space Agency (ESA) Space Environment Report 2026, more than 300 rocket launches injected over 4,000 new payloads in 2025 alone, while intact atmospheric re-entries remained near 1,200 objects per year, driving a tenfold (one order of magnitude) deterioration in orbital collision risk within a single year and elevating the ESA Space Environment Health Index from 4 to 50. Under these extreme boundary conditions, this monograph presents a comprehensive technical verification, mathematical validation, and architectural evaluation of the Autonomous Traffic Control System (ATCS v2.0) Final System Requirements Specification and its accompanying Isomorphic Pedagogical Framework for General and Youth Audiences. ATCS v2.0 integrates orbital edge computing with a 70-quadrillion-yen ($460 trillion USD equivalent classical replacement valuation) Sovereign Compute Grid—comprising Photonic Attractor Networks (Coherent Ising Machines, CIM), Quantum Processing Units (QPUs), and massively parallel CPUs—to execute sub-12.5-millisecond Hardware-in-the-Loop Optimization (HITLO). We formally verify: (1) physical infrastructure baselines across the 340–570 km LEO shell (16,100–16,234 active payloads, 54,000 cataloged debris, and 1,200,000 Lethal Non-Trackable (LNT) 1–10 cm debris triggered at Probability of Collision PoC₀ = 10⁻⁵); (2) four-dimensional Multi-Objective Optimization (MOO) balancing primary collision avoidance (f₁), shared-burden Nash equilibrium propellant expenditure (f₂: nominal Δv = 0.0265 m/s, emergency cap 1.4 m/s), Kinetic Theory of Gases (KTG) Poisson secondary collision probability (f₃ ≤ θ_ethics = 0.05 enforced via infinite step-function penalty Φ_Q-SAFA = ∞), and Active Debris Removal (ADR) capture tube Priority Rights (Φ_PR = ∞); (3) cyber-physical cryptographic governance combining Decoy-State BB84 / Twin-Field QKD (QBER cutoff at 6.91% ± 1.04%) with FIPS 203 ML-KEM-768 implemented on Secure Control FPGAs via 7-stage Incomplete Number Theoretic Transform (NTT) over R_q = Z_3329[x] / ⟨x²⁵⁶ + 1⟩ achieving 0.80 μs per polynomial vector; (4) the Q-SAFA self-executing smart contract and Quantum Audit Record (QAR) mechanism funding the Space Regeneration Fund for In-Space Servicing, Assembly, and Manufacturing (ISAM) via Laser-Wire Directed Energy Deposition (Metal3D) and Tempered Rotary Friction Stir Deposition (TR-AFSD) of recycled AA6061 aluminum debris; and (5) strict mathematical isomorphism in science communication translating NP-hard orbital governance into intuitive pedagogical models without oversimplification.