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 · website and downloads · v1.9.6 — 15 interactive browser labs for foundational AI, Transformer language modeling, agent tool use, and adversarial search. Every lab has a standalone HTML download and a Quick Assign, with English, Simplified Chinese, Vietnamese, and Spanish learner support; some supporting teaching materials have narrower language coverage. v1.9.6 improves classroom draft recovery, keyboard navigation, and instructional accuracy. The broader manual file/lab audit remains unfinished.

  Historical archive: v1.0.1 · v1.0.1 DOI. Its twelve bilingual labs, 45 deterministic algorithm checks, and 63-case browser matrix describe that earlier snapshot, not v1.9.6.

• 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.