About Zachary Roth
I’m Zachary Roth, a product leader, software builder, independent researcher in computational mathematics, and musician in the Bay Area. I work across financial products, AI systems, discrete mathematics, and music theory.
Work
At Solflare, I managed product roadmaps and led user research for wallet and trading products. At Aptos Labs, I worked as a product engineer supporting developers and partners through integration readiness, workshops, and launch feedback.
Raintree Technology
I run Raintree Technology, an independent software company that operates BetterOff and publishes open-source developer tools.
Research
My computational research uses exhaustive search, exact arithmetic, and separate verification systems.
Erdős Problem #84: graph cycle sets
I classified the cycle-length sets of all 1,018,997,864 non-isomorphic graphs on 11 vertices enumerated by nauty geng 2.9.3. Two independent implementations agreed on 247 sets. A separate definition-level verifier checked a graph6 witness for every set. The evidence supports the candidate f(11) = 247, assuming geng produced the complete corpus. I submitted “The number of cycle sets of graphs on 11 vertices” on September 4, 2026. Expert review remains pending.
Erdős Problem #382: consecutive products
For Erdős Problem #382, I computed a new candidate fixed-width value for a product of ten consecutive integers. Two structurally different exhaustive algorithms ruled out every earlier start. They agreed on the same first qualifying interval, largest-prime-factor witness, and square anchor. Specialist review and a final current-source novelty check remain pending. This fixed-width result does not solve the unrestricted problem.
Erdős Problem #488: density of multiples
I developed draft partial results for Erdős Problem #488, supported by exact-integer verification and a separate bounded checker. Specialist review and a publication-grade novelty search remain pending. The unrestricted problem remains open.
AI systems
I wrote PolicyStrata, a 13-page paper and open-source test suite for cross-layer policy drift in LLM data agents. The project includes a PyPI command-line interface, scanner, npm recorder and runtime, and customer-hosted Agent Trust Gateway. Its deterministic benchmark detected all 1,720 represented faults and emitted no witness for 80 clean controls. This result measures the published fault model, not recall on unknown production failures.
Music
My music-theory work includes Ordered Reflection Systems in Cyclic Scales, published by Raintree Press in 2026. The project classifies exact interval-word reversal across the seven canonical Messiaen modes with independent Python and Lean implementations. It publishes all 2,048 positive interval words summing to 12, their 351 rotation classes, and an interactive cyclic-scale generator. I am also developing Finite Patterns, a book about structure in finite musical systems.
I earned a B.M. in Classical Music from DePaul University.
How I work
I work across graph enumeration, combinatorics, elementary number theory, exact search, dynamic programming, independent verification, and reproducible command-line workflows. My primary programming tools are Python, C, C++, Rust, TypeScript, Lean, shell, and Git.
Erdős Engine records claims, certificates, environments, hashes, and exact commands. It separates search from verification and rejects altered evidence and overclaimed finite results.