{
  "abstract": "We present Pillar X (Zenodo Official DOI: 10.5281/zenodo.23529386), the definitive collaborative capstone monograph uniting three sovereign computational workstations: DILATON STUDIO (theoretical field and stochastic pullback foundations), TRIBODY WORKSTATION (celestial mechanics and non-smooth contact terramechanics), and the RELATIVISTIC PNT ENGINE (operational aerospace navigation, high-dynamic state estimation, and zero-allocation WebAssembly kernels). We establish rigorous mathematical proofs, regularized contact mechanics, and client-side production software across three primary archival trajectories:\n\nTrajectory 1 (Planetary Mobility & Terramechanics): Generalization of the 14-dimensional Burdet-Ferrandiz projective focal manifold M_BF^14 to non-smooth Bekker-Wong plastic regolith dynamics under cryogenic lunar south pole conditions (Shackleton Crater Permanently Shadowed Regions, T &asymp; 40 K, c = 1.84 kPa, k_c = 41.2 kPa/m^n, k_&phi; = 2450.0 kPa/m^(n+1)). We derive the exact closed-form inversion for equilibrium wheel sinkage z_0 = [3W / (b(k_c/b + k_&phi;)(3-n)&radic;(2r_w))]^(2/(2n+1)) and introduce a non-singular Sundman-regularized slip boundary condition s_reg(s) = s / &radic;(s^2 + &epsilon;_s^2) (&epsilon;_s = 1.84 × 10^-4) that purges wheel sinkage velocity singularities (ż &rarr; &infin;) during zero-velocity transitions, coupling rover odometry to 16-body Barycentric Celestial Reference System (BCRS) ephemerides.\n\nTrajectory 2 (Topological Cislunar Swarms): Application of pure Artin braid group invariants PB_N &sub; B_N and cyclotomic Gelfand spectral radius bounds &rho;(M_β(e^(iπ/3))) = 1.000000 to multi-satellite constellations operating along Artemis 9:2 Near Rectilinear Halo Orbits (NRHO). We prove that identical vanishing of pairwise Gauss linking numbers Lk(γ_i, γ_j) &equiv; 0 strictly certifies zero collision events over continuous 180-day horizons, verified via a zero-heap WebAssembly v128 SIMD kernel operating at < 9.4 ns per strand.\n\nTrajectory 3 (Universal Aeroelastic Limit Cycles): Unification of low-altitude ground-effect underfloor diffuser boundary-layer porpoising with Mach 18 hypersonic shock-wave/boundary-layer interactions (SWBLI). We prove via Kunita-It&ocirc;-Wentzell stochastic pullback flows that supercritical Hopf bifurcations are strict contractions (contraction factor κ = 0.995488 < 1). Coupled to an augmented 25 × 25 Square-Root Information Filter (SRIF) integrating an 8-pole Sz.-Nagy unitary dilation, the filter suppresses attitude divergence (||δ&theta;|| ≤ 0.08 mrad) under 40G kerb shock vibrations.",
  "abstract_shown": true,
  "affiliations": [
    "BhutaDamaraSena R&D Labs"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "AryaArunachalaAnanda Ghulam-e-Shah-e-Unmani",
      "orcid": "0009-0004-5288-3949"
    },
    {
      "affs": [
        0
      ],
      "name": "Aghora Abraham Global LLC"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48y66e690cqa7.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23529386",
  "fulltext_url": null,
  "id": "48y66e690cqa7",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23529386",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23529386/files/Pillar_X_V1.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48y66e690cqa7.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:13Z",
      "native_id": "23529386",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23529386"
    }
  ],
  "subjects": [],
  "title": "Pillar X: Sovereign Tri-Applet Capstone on Non-Smooth Planetary Terramechanics, Topological Cislunar Swarm Astrodynamics, and Stochastic Aeroelastic Limit Cycles",
  "title_text": "Pillar X: Sovereign Tri-Applet Capstone on Non-Smooth Planetary Terramechanics, Topological Cislunar Swarm Astrodynamics, and Stochastic Aeroelastic Limit Cycles",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:13Z",
  "url": "https://research.draconitic.com/paper/48y66e690cqa7",
  "venue": "Zenodo",
  "versions": []
}