Zackary Loevseth
Independent research · Human–AI workflows · Verification design
zloevseth@gmail.com · github.com/ZackaryLoevseth
Research focus
I direct AI-assisted work in mathematics and research reliability: defining questions, specifying checks, tracking evidence, correcting claims, and deciding what is ready to release. I'm seeking AI evaluation or research-workflow work.
My role
I lead problem selection, task framing, verification requirements, corrections, preservation, and release scope. AI systems substantially assist with source discovery, proof and code development, computation, checking, and writing. This is not a claim of independent authorship of every proof or implementation.
Selected public research · 2026
Counterexample families for five Graffiti³ inequalities
Public preprint with exact infinite-family arguments and database-scoped finite corroboration. Covers five specified conjectures, not the full collection.
Planar projection bounds for semiorder ideals
Public preprint using a largest-index zonotope decomposition in the represented-semiorder setting. Exact finite checks support, but do not replace, the proof. Unrestricted parametric closure remains open.
Excess-degree bounds for minimal counterexamples
Public preprint constraining hypothetical lexicographically minimal counterexamples to the Erdős–Gyárfás conjecture. The global conjecture remains open.
Erdős #409: a certified pointwise trajectory
Released certificate for F(400000287233629) = 104, with multiple evaluator paths, mutation tests, and integrity manifests. No maximum, priority, unboundedness, or global-solution claim.
Working research program
Epistemic Transition Integrity. A proposed approach to preserving targets, evidence, dependencies, and correction state across long-running human–AI work. A comparative study is preregistered; no comparative efficacy result is claimed.
Methods used in the work
Problem framing; evidence and claim tracking; verification requirements; proof reconstruction workflows; exact-computation and mutation-test workflows; versioned releases; correction and handoff records.
Status boundary: The three preprints remain internally checked, with external specialist review pending in the recorded release state. They are not represented here as peer-reviewed publications. Technical tools used in AI-assisted projects are not presented as a blanket claim of independent proficiency.
Research-only edition · 4 September 2026 · zackaryloevseth.github.io/research-portfolio/