Rank competing hypotheses or proof skeletons from the complete comparison ledger using a joint batch MAP Bradley-Terry fit and approximate posterior intervals. Use whenever 3 or more candidates compete for the next experiment, or when the user asks which branch currently leads. Do not present the intervals as calibrated confidence bounds.
Diagnose errors, failed tests, crashes, hangs, regressions, suspicious outputs, and unexpected experimental results through reproducible hypothesis-driven debugging. Use whenever a script or system behaves incorrectly, even if the user only says it is broken or pastes an error. Respect diagnosis-only requests; implement a fix only when authorized.
Lock a confirmatory falsification target and its fixed multiple-comparison family before observing the confirmatory result. Use before promoting an exploratory finding to a main claim or whenever several related hypotheses need Bonferroni control. Records metric, threshold, family id/size, correction, and seed budget.
Build and audit a statistical or mathematical proof from proposition capture through skeleton selection, diagnosis, correction, optional empirical checking, and optional Lean reinsurance. Use when the user asks to prove or rigorously derive a proposition, a graph proposition lacks a verified proof, or a reviewer requires a theorem-side gate.
Audit a past pruning or approval decision by creating a counterfactual branch from a saved snapshot without mutating the live graph. Use when the user asks what would have happened under another decision, disputes a paused branch, or wants to inspect an earlier checkpoint.
Run an end-to-end, auditable research workflow from question framing through literature, competing hypotheses, experiment selection, implementation, verification, and claim handoff. Use whenever the user asks to investigate, compare, test, validate, or establish an empirical research claim, including when they do not explicitly call it research. Do not use for a simple factual lookup or a narrowly scoped code change with no research claim.
Produce or revise research reports, result-bearing Markdown, paper sections, and manuscripts without overstating evidence. Use whenever writing text that reports experimental metrics, statistical conclusions, hypothesis rankings, theorem claims, or research findings. Do not trigger for ordinary README edits, changelogs, or prose with no research-result claim.