Autonomous Cislunar NRHO Astrodynamics, Distributed Swarm iSAM2 Bayes-Tree and Metropolis-Hastings Consensus, Femtosecond IAU/IERS Relativistic Reference Frames, Optical Clock Chronometric Geodesy, and Space-Weather Resilience

Sustained autonomous operations in the Earth-Moon cislunar regime and high-density Low Earth Orbit (LEO) constellations require a unified mathematical architecture that bridges multi-body chaotic astrodynamics, decentralized factor-graph estimation over optical Inter-Satellite Links (ISLs), femtosecond-accurate relativistic reference frame transformations, sub-millimeter geophysical crustal loading models, and extreme geomagnetic storm resilience. While Pillar V ([2], Monograph 10.5281/zenodo.23226184; Companion Software 10.5281/zenodo.23226375) established the high-dynamic atmospheric flight, Mach-18 plasma blackout raytracing, 7-element CRPA STAP anti-jamming, and 4D Kustaanheimo-Stiefel (KS) perilune regularization framework, this sixth flagship monograph (Pillar VI: Definitive Version 10.0, Official DOI: 10.5281/zenodo.23227003) formalizes the deep-space cislunar, distributed multi-agent optical swarm, relativistic chronometric geodesy, and space-weather standards layers implemented in our production verification kernels, completing the Six-Pillar Sovereign Hexalogy: 1. Cislunar CR3BP & Artemis 9:2 L2 NRHO Astrodynamics (THM-CISLUNAR-V10-01, Section 2): We formulate the synodic Circular Restricted Three-Body Problem (μ = 0.0121505856) and ephemeris-coupled N-body propagation (Earth J₂, Moon, Sun, Jupiter, and macro-plate Solar Radiation Pressure) for the Artemis Gateway 9:2 lunar synodic resonant southern L₂ Near-Rectilinear Halo Orbit (r_p = 1532 km, r_a = 70,410 km, T = 6.562 days, C_J = 3.048). Using 6th/8th-order symplectic Gauss-Legendre collocation coupled with 4D KS regularization inside the r_moon < 3500 km perilune sphere, Jacobi integral drift is bounded to |ΔC_J / C_J| < 1.5 × 10⁻¹³ with Floquet stability index |ν_max| = 1.32, paired with JPL DE440/DE441 iterative light-time retardation and solar Shapiro gravitational deflection. 2. Distributed Swarm Optical ISL iSAM2 Bayes Trees, DIF & Covariance Intersection (THM-CISLUNAR-V10-02, Section 3): For GPS-denied cislunar and LEO constellations connected by bidirectional laser links, we derive the Asymmetric Two-Way Ranging (TWR) observable incorporating Sagnac non-reciprocity Δt_Sagnac and platform acceleration kinematics Δt_acc. We synthesize Incremental Smoothing and Mapping (iSAM2) via Givens QR factorization and Bayes-tree fluid relinearization (β_relin = 0.045 m), Metropolis-Hastings Decentralized Information Filtering (Y_i = P_i⁻¹, y_i = Y_i x_i), and closed-form Covariance Intersection (CI) over Bierman UDUᵀ factors, achieving < 2.8 mm relative baseline precision and < 0.015 ns clock synchronization. 3. Femtosecond Split-Time Ephemerides, IERS Crustal Loading & Optical Chronometric Geodesy (THM-CISLUNAR-V10-03, Section 4): Utilizing a two-word Knuth-Dekker compensated split-time representation (mjd_int, frac_day, err_day) with 106-bit effective mantissa precision (< 10⁻¹⁵ s closure across millennia), we unify the 4D relativistic time chain (UTC–TAI–TT–TCG–TDB–TCB), IAU 2006/2000A Celestial Intermediate Origin (CIO) transformations, dynamic solid-Earth Love number harmonics (ΔC̄₂ₘ, ΔS̄₂ₘ), 11-constituent FES2014 ocean tide loading, and ECMWF/MPIOM AOD1B non-tidal barometric crustal deformation. Coupling this frame to ⁸⁷Sr (429.228 THz) and ¹⁷¹Yb (518.295 THz) optical lattice clock links resolves geoid height anomalies at Δf/f₀ = g₀ΔH/c² ≈ 1.091 × 10⁻¹⁸ cm⁻¹ (σ_ΔH ≤ 13.8 mm). 4. NOAA SWPC Geomagnetic Storm Kinematics & 77-Gate Cryptographic Attestation (THM-CISLUNAR-V10-04, Section 5): We formalize the NRLMSISE-00 thermospheric density inflation law under G0–G5 solar-geomagnetic storms (F₁₀.₇ ∈ [68, 350] sfu, K_p ∈ [1, 9], A_p ∈ [4, 500] nT), proving that Carrington/Halloween G5 events induce 17.95×–29.85× drag surges, severe ionospheric amplitude/phase scintillation (S₄, σ_ϕ), and Single-Event Upset (SEU) hazards, while anchoring all 77 Sovereign Hexalogy certification gates into the TMD-Hash v12.0 ([3], 10.5281/zenodo.23218553) post-quantum oracle. Classifications & Subject Identifiers Primary AMS Classifications: 70F07, 70F15, 83C10, 86A30, 93E11, 68W15, 94A60 PACS Codes: 95.10.Ce, 91.10.-v, 04.80.-y, 94.20.Vv, 06.30.Ft, 84.40.Ua Keywords Cislunar Astrodynamics, Near-Rectilinear Halo Orbit (NRHO), Artemis Gateway, Circular Restricted Three-Body Problem (CR3BP), iSAM2 Bayes Tree, Optical Inter-Satellite Links (ISL), Metropolis-Hastings Consensus, Decentralized Information Filtering (DIF), Covariance Intersection, Relativistic Reference Frames, IAU 2006/2000A, IERS Conventions, Chronometric Geodesy, Optical Lattice Clocks, FES2014 Ocean Tide Loading, AOD1B Crustal Loading, Space Weather Resilience, NRLMSISE-00, Geomagnetic Storms, Post-Quantum Cryptography, TMD-Hash v12.0, Sovereign Hexalogy