Research themes
Work is organized around a small number of long-horizon themes, pursued with depth and supported by analytical, computational, and structural tools.
Theory
- Mathematical physics and analytical frameworks
- Operator-theoretic and spectral perspectives
- Structural invariants and asymptotic analysis
Computation & systems
- Algorithmic modeling and numerical exploration
- Model-to-implementation workflows
- Applied systems integration and prototyping
Current activities
Current work emphasizes building durable scaffolding for research programs: precise definitions, intermediate results, and exploratory artifacts (notes, preprints, computational prototypes).
Exploration
- Feasibility studies and early-stage modeling
- Prototype implementations for hypothesis testing
- Iterative refinement under internal review
Outputs
- Technical notes and preprints
- Algorithms and computational experiments
- Reusable analytical and software components
Selected outputs
A curated selection of recent work. Additional manuscripts and technical notes are available upon request.
Computational & Imaging Systems
- Implicit Cursor-Based Intent Detection for Adaptive Visualization in Diagnostic Radiology — Passive, cursor-driven visualization adjustments designed to support interpretive efficiency without automated image analysis or diagnostic output. Link
Mathematics
- The Aruna Recursive Kernel (ARK) — A nonlinear recursive operator on integer-indexed fields, producing emergent geometric structure from divisor-based dynamics without reliance on primality or factorization. Link
- A Deferral-Based Time-Symmetric Propagator on a Discrete Manifold — Time-symmetric propagator framework on discrete structures, supporting analytical and computational investigation. Link
- The Hatti Monotone Rigidity Lemma — Abstract uniqueness lemma for iterative systems driven by a strictly decreasing inconsistency functional. Link
Physics
- A Constrained Dynamical Framework for Cosmic Evolution from a Unified Initial State — Singularity is replaced by a unified maximal-symmetry initial state and cosmological contexts. Link
- A Unified Constraint Synthesis for a Distant Solar System Perturber — Probabilistic synthesis of the principal observational and dynamical constraints on a distant solar system perturber. Link
For collaborations or grant-related inquiries:
research@aptexcorp.com
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