Research
Papers & Preprints
Original research in dynamical systems, stochastic analysis, fractal geometry, and their applications to finance and AI.
2026
Liminal Motion — An Upgrade to Brownian Motion
A deterministic process from backward iteration on Julia sets whose partial sums couple to Brownian motion via the ASIP. Includes the Lévy area formula E12 = Im(c)/2, seven algebraic constructions producing exact Brownian motion (Brownian completeness), and seven reverse constructions. All proofs included.
2026
Degree-6 Julia Set Watermarking for EU AI Act Article 50 Compliance
A watermarking system for LLM outputs built on backward iteration on degree-6 Julia sets. The half-plane decomposition yields a detectable watermark channel (1 bit/step) and an invisible cover channel (1.58 bits/step). Two-key architecture mapping onto the EU Code of Practice.