From Adversarial Debate to Auditable Mathematical Discovery: A Longitudinal Study of the Quantiterate MathLab Research System

Extended AI-assisted mathematical research confronts a decision problem that theorem-solving benchmarks do not capture: when should a claim be promoted, a review objection withdrawn, a proof architecture reopened, or an unproductive search stopped? We present a longitudinal, source-grounded study of Quantiterate MathLab, a human-directed mathematical research program and evolving software ecosystem documented across March–October 2026. We examine an evidence-justified research-state transition: a versioned decision whose mathematical scope, exact supporting record, dependencies, and permitted consequences can be inspected. The history includes an early two-agent War Room with novelty and cost monitors; four-role review persistence; a proposed blind Fibonacci Jury; Crystal Farmer campaign allocation; proof-ledger and Strand Loop designs; an obstruction atlas; corpus-synthesis procedures; and research-observer governance. Two case studies distinguish different failure classes. The September R88–R89 Riemann Hypothesis packets record an Abel-weighted representation that returned to a known signed-cancellation obstruction, motivating a scoped NO GAIN judgment rather than a proof claim. The Navier–Stokes War Room records deterministic appendix-parser repairs and reconstructed reviewer-context deficits while preserving unresolved mathematical objections. Our contribution is a traceable account of how differently typed evidence supports different research decisions, together with explicit obstruction/reopening semantics and a preregistration-ready comparative design. The cases demonstrate mechanisms and documentary chronology; they do not establish a new theorem, independent mathematical verification, or a causal performance improvement.