RESEARCH / MANUSCRIPTS & TECHNICAL NOTES
Three independent papers. Each now has a dedicated technical walkthrough, source PDF, important assumptions, and a clear boundary between mathematics and measured performance.
ROBOTICS / CONTROL THEORY
An analytical synthesis of SE(2) kinematics, exact actuator-feasible twist geometry, a squared-wheel-speed Riemannian metric, and a locally stable stationary-pose regulator for an idealized four-wheel X-drive.
TOPOLOGICAL DATA ANALYSIS / STOCHASTIC SYSTEMS
A finite correlation-metric construction feeds a persistent-homology feature into a well-posed stochastic process, with deterministic and stochastic sensitivity estimates, an exact four-asset example, and a falsifiable evaluation plan.
MATHEMATICAL PHYSICS / ELECTROMAGNETISM
A geometry-first synthesis of differential forms, toroidal manifolds, magnetic helicity, plasma descriptions and topological reasoning for possible future confinement research.
These pages explain the papers in depth while keeping the evidence status readable. For more hands-on examples, visit the interactive lab; for collaboration and critique, get in touch.