This page lists all written work associated with this project. Most papers are released as preprints and revised iteratively. Earlier papers introduce core structures, while later papers build on and refine those ideas. Version history reflects feedback, testing, and clarification over time.
Recursive Division Tree: A Log–Log Algorithm for Integer Depth DOI: (https://doi.org/10.5281/zenodo.17487651)
Introduces the Recursive Division Tree (RDT), a deterministic recursive decomposition on the integers. Defines recursive depth, ancestry, and saturation behavior, and establishes the tree structure as a partially ordered set.
Recursive-Adic Number Field: Construction, Analysis, and Recursive Depth Transforms DOI: (https://doi.org/10.5281/zenodo.17555644)
Develops a recursion-based analogue of p-adic valuation systems. Defines a valuation derived from recursive depth rather than prime divisibility and establishes non-Archimedean-style behavior generated by algorithmic hierarchy.
Recursive Entropy Calculus: Bounds and Resonance in Hierarchically Partitioned Systems DOI: (https://doi.org/10.5281/zenodo.17862831)
Introduces a depth-dependent entropy framework for recursively partitioned systems. Establishes bounds on entropy growth and examines resonance-like effects arising from finite-depth structure.
Recursive Depth Integration: A Depth-Weighted Measure on the Integers DOI: (https://doi.org/10.5281/zenodo.17753502)
Defines depth-weighted integrals and measures derived from recursive structure. Provides a foundation for treating recursive depth as a measurable quantity rather than a purely combinatorial one.
Recursive Geometric Entropy: A Unified Framework for Information-Theoretic Shape Analysis DOI: (https://doi.org/10.5281/zenodo.17882310)
Applies recursive entropy concepts to geometric subdivision. Studies how entropy evolves under recursive refinement of shapes and establishes connections between hierarchy, geometry, and information measures.
RDT-Based Zeta and Laplace Transforms DOI: (https://doi.org/10.5281/zenodo.17766570)
Develops discrete transforms defined directly on recursive tree structures. Introduces zeta-like and Laplace-like operators compatible with recursive depth and hierarchical organization.
RGE-256: An ARX-Based Pseudorandom Number Generator with Structured Entropy and Empirical Validation DOI: (https://doi.org/10.5281/zenodo.17982804)
Introduces a family of ARX-based PRNGs informed by recursive depth and structured entropy control. Includes empirical validation using established statistical test suites and documents iterative redesign following external testing.
Topological Adam DOI: (https://doi.org/10.5281/zenodo.17489664)
Introduces an experimental optimizer inspired by recursive structure and energy balance concepts. Explores stabilization behavior in gradient-based optimization and includes empirical benchmarks against standard Adam.
A Unified Closure Framework for Euler Potentials in Resistive Magnetohydrodynamics DOI: [(https://doi.org/10.5281/zenodo.17989242)]
An applied analysis of closure constraints in MHD. While distinct from the core recursive-integer work, this paper informed later thinking on structure, constraints, and stability in recursive systems.
Readers are encouraged to treat this as a connected research trajectory rather than a set of isolated results.