AryaArunachalaAnanda Ghulam-e-Shah-e-Unmani

ActOne Studio: A Sovereign Neurosymbolic Engine for Deterministic Screenplay Synthesis, Zero-Width Steganographic Provenance, and Algebraic Permutation Attestation over F_{2^64-59}

We present ActOne Studio, an enterprise-grade sovereign neurosymbolic synthesis engine and cryptographic provenance infrastructure engineered for deterministic multimedia screenplays, zero-allocation reactive Abstract Syntax Tree (AST) parsing, and tamper-evident artifact lineage...

Nath Darsana: Aerospace-Grade VSOP87 Astrodynamical Computation Engine, Deterministic WASM Ephemerides, and Multi-Varga Agentic RAG Synthesis

We present the architectural and mathematical framework of Nath Darsana, a distributed, edge-computed astrodynamical engine engineered for sub-arcsecond aerospace ephemeris generation, continuous-to-discrete phase-space quantization (Varga / Dasha boundary evaluation), and multi-...

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 Li...

Phase-Synchronized Trajectory Optimization on Curved Manifolds with High-Order Non-Separable Symplectic Thermostats, Adaptive Manifold Restraints, and 3D Braid-Group Spacetime Knot

Abstract We formulate and prove Version 4.0 of the unified geometric, thermodynamic, and topological framework governing relativistic N-body systems evolving on pseudo-Riemannian spacetimes. This work rigorously resolves fundamental challenges across relativistic astrophysics, ge...

Finite-Dimensional Modular Theory, Non-Commutative Relative-Entropy Geometry, and Resilient Quantum Mirror Descent for Holographic State Reconstruction (Version 3)

Abstract We establish an exact mathematical framework connecting finite-dimensional Tomita–Takesaki modular theory, Kubo–Mori–Bogoliubov (KMB) Riemannian geometry, and entropic optimization for quantum states. First, we prove that the second directional derivative (Hessian) of th...