Unified Relativistic 16-Body Astrodynamics, Vienna Mapping Function 3 (VMF3) Sub-Millimeter Chronometric Geodesy, Chameleon Dilaton Screening, Soft-Min QCRB Petz Holographic Recovery, Kubo-Mori-Bogoliubov Thermal-Time QES Islands, and Distributed Swa

Over the course of seven specialized flagship monographs, one analytical ephemeris and symbolic oracle companion monograph (Nath Darsana V2.0), and their companion software archives (Pillars I-VII & Companion: 10.5281/zenodo.23280282, 10.5281/zenodo.23283888, 10.5281/zenodo.23256017, 10.5281/zenodo.23279863, 10.5281/zenodo.23237005, 10.5281/zenodo.23255435, 10.5281/zenodo.23226375, 10.5281/zenodo.23218553, 10.5281/zenodo.23226184, 10.5281/zenodo.23284416, 10.5281/zenodo.23297029, 10.5281/zenodo.23234784, 10.5281/zenodo.23235638, 10.5281/zenodo.23312522, 10.5281/zenodo.23313881, together with parent releases 10.5281/zenodo.23231816, 10.5281/zenodo.23238341, 10.5281/zenodo.23227003, 10.5281/zenodo.23216274, 10.5281/zenodo.23228645, 10.5281/zenodo.23211885, 10.5281/zenodo.23229575, 10.5281/zenodo.23210362, and 10.5281/zenodo.23204914), and deployed live in production at https://bhutadamarasena.com/#apps , we established eighty-six hardware-certified mathematical gates spanning stochastic partial differential equations on dynamic Riemannian frame bundles, post-Newtonian gravitational-wave braid automata, finite-dimensional modular holography, post-quantum Solinas F_p4 (F_{2^{64}-59} base) Nova IVC cryptography, hypersonic Mach-18 plasma flight, cislunar 9:2 NRHO 106-bit Burdet-Ferrandiz optical swarms, 16-body BCRS DE440 ephemerides, Vienna Mapping Function 3 (VMF3) tropospheric raytracing, multi-GNSS RINEX 3.05/4.00 PPP-AR, RTCM 3.3 HIL casting, and zero-allocation Rust/WASM/WebGPU flight silicon. This eighth and final capstone monograph (Pillar VIII: Definitive Version 12.0 The Sovereign Nonagon Grand Operational Capstone, Official Preprint DOI: 10.5281/zenodo.23314226) preserves our four foundational cross-pillar architectural theorems (Sections 2-5) and establishes nine major cross-disciplinary discoveries (Gates 82-90, Sections 6-8) synthesized jointly across the TriBody Relativistic Workstation, Dilaton Studio, Nath Darsana V2.0, and the Relativistic PNT Engine: [V12-1] Discovery A (Gate 82 / THM-NONAGON-V12-01, Section 6.1): Integrating the Artemis 9:2 southern L2 NRHO under the full 16-body BCRS 1PN EIH ephemeris (10.5281/zenodo.23234784) and lunar J2/C22 mascons reveals a 180.42-day Kozai-Lidov planetary beat mode causing perilune osculations r_p in [1,842.18, 4,688.35] km (h_{p,min} = 104.78 km, |Delta C_{KL}| = 2.14 x 10^-7 <= 10^-6, 1PN periapsis advance +30.57"); coupling 4D KS / 14D Burdet-Ferrandiz regularization with the SPDE v6.0 Master Contraction (Lambda_{V10} = 4.5218 s^-1, 10.5281/zenodo.23280282) suppresses station-keeping cost from 4.55 m/s/yr back to Delta V_{SK} = 1.84 m/s per 180 days (<= 2.50 m/s). [V12-2] Discovery B (Gate 83 / THM-NONAGON-V12-02, Section 6.2): Coupling Pillar VII's VMF3 3-term Marini-Boehm continued fraction and Chen-Herring azimuthal gradients (sigma_{trop}(5 degrees) = 0.39 mm <= 0.50 mm) with AOD1B/FES2014 crustal de-aliasing (sigma_{crust} = 0.18 mm) and 87Sr optical lattice clocks (sigma_y(10^4 s) = 3.6 x 10^-19 single-epoch, tau^{(N=100)} = (c^2 / g_0) * (sigma_y / sqrt(100)) = 0.330 mm across N_{ep} = 100 campaign epochs; single-link RSS = 0.542 mm) fused across M_{link} = 2 bidirectional Earth-Gateway links (1 / sqrt(2) information gain) unlocks true sub-millimeter chronometric geoid leveling (delta_{geoid} = 0.542 / sqrt(2) = 0.38 mm <= 0.42 mm). [V12-3] Discovery C (Gate 84 / THM-NONAGON-V12-03, Section 6.3): Executing the 1000 Hz Asymmetric Double-Sided Two-Way Ranging (ADS-TWR) and SE_2(3) InEKF covariance update inside the 1 MB Rust/WASM v128 SIMD linear arena achieves 1.28 x 10^7 ops/s (78.1 ns/vector, 0 Bytes GC), bounding single-pulse hardware timing jitter to sigma_{jitter} = 41.8 ps <= 48.6 ps and 100-epoch carrier-smoothed range error to delta r = 0.14 mm <= 0.20 mm[cite: 2, 3]. [V12-4] Discovery D (Gate 85 / THM-NONAGON-V12-04, Section 6.4): Coupling the RTCM 10403.3 MSM7 binary caster (0x1864CFB CRC-24Q, P_{err} = 2^-24 = 5.96 x 10^-8) with Cislunar V11.0 Metropolis-Hastings swarm consensus over a 26.5 GHz Ka-band relay from NRHO apolune (71,200 km, FSPL = 217.96 dB) to Lunar South Pole rovers (phi = 89.9 degrees S) achieves C/N_0 = 91.01 dB-Hz, E_b/N_0 = 21.01 dB at 10 Mbps, and a +18.41 dB net link margin without Earth ground stations[cite: 3]. [V12-5] Dilaton Discovery I (Gate 86 / THM-CAPSTONE-V12-01, Section 7.1): As a rigorous BCRS model-completeness and falsifiability bound, Chameleon / Damour-Polyakov thin-shell screening (Delta R_Earth / R_Earth = 3.742 x 10^-7, Delta R_Moon / R_Moon = 8.305 x 10^-6, beta_phi = 1.45 x 10^-2, 16-body solar/planetary screening factor S_{16B} = 0.5074) bounds any putative fifth-force Earth-Moon Eötvös Equivalence Principle violation to eta_{EEP}^{16-body} = 2 * beta_phi^2 * |Delta R_Earth / R_Earth - Delta R_Moon / R_Moon|^2 * S_{16B} = 2.6448 x 10^-14 * 0.5074 = 1.342 x 10^-14 <= 1.800 x 10^-14[cite: 19, 20] and the Cassini conjunction PPN residual to |gamma - 1| = 1.84 x 10^-6 <= 2.3 x 10^-5[cite: 18][cite: 3]. [V12-6] Dilaton Discovery II (Gate 87 / THM-CAPSTONE-V12-02, Section 7.2): Across VMF3 turbulent 1550 nm deep-space optical ISLs (eta_{ISL} = 0.3659, N_{ph} = 10^8, M = 1000 Hz), the Soft-Min Quantum Cramér-Rao Bound (QCRB) establishes the fundamental Helstrom quantum shot-noise floor below the 41.8 ps hardware photodetector bound of Gate 84: sigma_{tau}^{QCRB}(10 GHz) = 2.614 x 10^-16 s (0.261 fs) for a single 10 GHz channel and CRB (10 THz comb) = 2.614 x 10^-19 s (0.261 as) for a 1000-line coherent optical comb (Delta omega = 10^13 rad/s), while the Petz recovery map achieves quantum state fidelity F_{Petz} = 0.999974 >= 0.999900[cite: 3]. [V12-7] Dilaton Discovery III (Gate 88 / THM-CAPSTONE-V12-03, Section 7.3): Under the Kubo-Mori-Bogoliubov (KMB) quantum Fisher metric on the cislunar swarm clock density manifold, the graph-theoretic min-cut capacity bottleneck (the network information-theoretic analog of a Quantum Extremal Surface QES) is periodically re-anchored at the 180.42-day Kozai-Lidov orbital period, bounding KMB geodesic projected mutual clock drift to |delta tau_{ij}^{KMB}(t)| <= 2.452 x 10^-18 s <= 5.000 x 10^-18 s[cite: 3, 4]. [V12-8] Dilaton Discovery IV (Gate 89 / THM-CAPSTONE-V12-04, Section 7.4): A 5.0PN hereditary Christodoulou-BMS supertranslation memory shift (delta nu / nu){BMS} = 1.340 x 10^-20 compensated by Dilaton Studio's soft-hair tensor across co-located 87Sr/171Yb optical lattice clocks (|Delta K{Sr,Yb}| = 0.08075) bounds any unmodeled gravitational-wave memory frequency-ratio shift to Delta(nu_Sr / nu_Yb) / (nu_Sr / nu_Yb) = 1.082 x 10^-21 <= 5.000 x 10^-21[cite: 4]. [V12-9] Dilaton Discovery V (Gate 90 / THM-CAPSTONE-V12-05, Section 7.5): Preserving the strict Tikhonov two-timescale separation of Theorem 2.1, the composite 9-domain Sovereign Nonagon operator is a block-triangular Banach contraction mapping with fast observer/attitude/PLL contraction constant kappa_{Nonagon}^{fast} = exp(-Lambda_{V10} Delta t) = 0.995488 < 1.000000 at Delta t = 1.0 ms and slow apolune orbital Poincaré contraction kappa_{Nonagon}^{slow} = exp(-lambda_{syn}) = 0.88887 < 1.00000 per NRHO revolution[cite: 4].