Continual Graph Memory and Community Infrastructure for AI-Assisted Mathematical Discovery

Abstract

Mathematical discovery requires preserving partial ideas and the evidence supporting their reuse. We present Ansatz, a research harness whose continual graph memory separates model-accepted claims and dependencies from curated exploration, and Ansatze, a community platform for inspecting, guiding and checking this work. On First Proof, Ansatz recorded nine local verifier closures in each of two ten-problem batches; a partial result in the Second Batch also counted as a pass under the study's criterion. These model-assessed outcomes include continued searches and differ from expert validation. Component studies and re-review expose disagreements and their dependency reach. Open-problem investigations produced candidate results, with five Lean formalizations reported. The platform connects problem discovery, research records, manuscript analysis and formal checking while preserving distinct evidence states. Together, these systems support cumulative human-AI research through persistent investigation and inspectable contributions.