Independent research · mathematics · machine learning
I study structural questions in nonlinear systems and machine learning. Analytic arguments carry the general results; exact or certified computation enters where a finite witness or quantitative bound bears proof weight.
Recent papers ask when local or finite structure determines global behavior: exactness for signed supports, global inversion and counterexamples for ridge networks, and kernels of geometric representations.
Characterizes when an interior signed support is SONC-exact through nonseparability. The universal theorem is analytic; exact elimination, interval arithmetic, and certificate replay support the explicit three-negative witness and quantitative benchmark.
Develops a global inversion theorem for planar saturating ridge networks and resolves the certified separation witness as an injective global diffeomorphism onto an explicit nonconvex octagon. Exact and validated parameter certificates show that the mechanism persists on an explicit open neighborhood.
Gives an exact rational counterexample at planar width four: the Jacobian determinant is positive everywhere, an exact rational target has winding number two, and two distinct preimages are certified independently. Together with the positive results at the two lower widths, the construction yields the sharp hidden-width threshold.
Identifies the Ptolemy identity behind complex orthogonality, proves essential rigidity of the sign rule, and determines the rational kernel on the inner pure braid groups at n = 3 and n = 4 along certified Delaunay flip sequences.
Interactive teaching tools and compact engineering studies make the same ideas inspectable at a different scale.
Fifteen multilingual, offline-ready AI labs span 13 Foundations/course-track mechanisms and two Modern AI extensions. The current v1.9.6 release improves classroom draft recovery, keyboard navigation, and instructional accuracy. Every lab has a Quick Assign and a standalone HTML download, with English, Simplified Chinese, Vietnamese, and Spanish learner support.
15 learner labs · 15 Quick Assigns · EN/ZH/VI/ES learner support · offline-ready
Evaluator migrations can change individual benchmark verdicts even when aggregate scores look stable. EvalCanary holds the output corpus fixed, replays before-and-after verifiers, classifies verdict transitions, estimates paired uncertainty, checks subgroup effects, preserves source and execution provenance, and enforces explicit CI policy gates.
GitHub Action · evaluator migration diffs · paired uncertainty · provenance · policy gates
A CPU-scale reproduction of a qualitative DeepSeekMath ranking, paired with a compact operator zoo for comparing regularized policy-improvement updates under one notation and one training interface.
I am an independent researcher and computer-science educator with a background spanning computer science, mathematics, physics, and secondary STEM education.
I am interested in problems where a structural argument can replace brute force, or where computation can be made exact enough to carry a proof obligation. Current work crosses nonlinear optimization, neural networks, algebraic computation, ML evaluation, and AI post-training.
I teach computer science and AI. That work shapes the research presentation: definitions arrive before machinery, claims remain scoped to their evidence, and an implementation should reveal the idea rather than conceal it.
For research collaboration, technical review, or roles in mathematical AI, machine learning, and research engineering.