Independent researcher and computer science educator working across mathematical AI, nonlinear systems, machine-learning evaluation, and reproducible computation.

Research site · ORCID · LinkedIn

• Nonseparability characterizes SONC exactness for interior signed supports

  An analytic characterization of SONC exactness, with exact and interval-certified computation for the explicit witness and quantitative benchmark.

• Asymptotic-polygon global inversion for planar saturating ridge networks and an injective neural-Jacobian separation witness

  A global inversion theorem resolving the certified separation witness as an injective global diffeomorphism onto an explicit nonconvex octagon, with exact and validated parameter certificates.

• A positive-Jacobian noninjective sigmoid ridge map and the sharp hidden-width threshold

  An exact rational counterexample at planar width four with an everywhere-positive Jacobian determinant, winding number two at an explicit rational target, and two independently certified preimages; together with the lower-width positive results, it gives the sharp hidden-width threshold.

• Ptolemy structure, sign rigidity, and pure-braid kernels in colored braid groupoid representations

  Exact structural identities, exhaustive sign-rule analysis, and rational inner pure-braid kernel computations along certified flip sequences.

Each research repository distinguishes analytic arguments from computational verification and links its principal claims to reproducible artifacts.

• AI Playgrounds — live site · source · v1.0.1 · DOI — twelve bilingual browser-based visualizations for search, logic, probability, machine learning, neural networks, vision, and reinforcement learning; the archived release carries 45 deterministic algorithm checks and a 63-case browser matrix.
• EvalCanary — evaluator-migration tooling that holds model outputs fixed, replays before-and-after verifiers, classifies verdict transitions, estimates paired uncertainty, checks subgroup effects, preserves execution provenance, and enforces explicit CI policy gates.
• RLVR and GRPO studies — compact studies of regularized policy-improvement operators and a CPU-scale GRPO reproduction.
• Engineering portfolio — projects across evaluation, retrieval, agents, machine learning, Rust systems, infrastructure, and security.

I prefer analytic structure where it is available, then exact algebra, interval arithmetic, certified computation, and independent reconstruction where finite computation carries claim weight.

Primary tools: Python, Rust, NumPy, SciPy, SymPy, TensorFlow/Keras, Hugging Face, and Terraform.

Open to research collaboration, technical review, and roles in mathematical AI, machine learning, and research engineering.