An Introduction to Matrix Concentration Inequalities
Paper • 1501.01571 • Published
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Research Lean Formalization Rollouts
Agent trajectories from two Lean 4 formalization systems. All exports were gated by a strict SFT validator: every rollout must contain reasoning, tool calls must match the declared schemas exactly, no degenerate repetition, and no leaked control markers.
Each record is {conversation, …, token_count, token_count_answer, token_count_think}; in conversation, assistant turns carry content, think and tool_calls. source records the rollout's origin (run, agent_id, segment, part, agent_type, status, path, host); repoprover-undergrad.jsonl additionally records project (book id) and model.
Files
arxivlean.jsonl — 1,838 records, 161.8M tokens
Prover trajectories from arxivlean: Kimi K3 running inside MathArena, one attempt per Lean theorem formalized from arXiv math.* papers (64 problems per array task). Tools: verify_lean (compile a snippet against Mathlib), loogle (Mathlib lemma search by pattern) and leanfinder (semantic search over the LeanExplore index). A run counts as correct only if the final proof compiles with the exact accepted statement. Mean 88k tokens, median 69.5k. Judge-correct but gate-rejected trajectories (~40%) and incorrect attempts are not included.
repoprover-matrix-concentration.jsonl — 14,332 records, 492.7M tokens
One record per finished rollout from RepoProver (Meta; "Automatic Textbook Formalization", Gloeckle et al., 2026) formalizing Joel Tropp, An Introduction to Matrix Concentration Inequalities (arXiv:1501.01571) into a Lean 4 + Mathlib repository — 791 of 791 theorems proven with 0 sorrys over ~19k commits. Record ids are <run>/<agent_id>#<segment>.<part> (a segment is one start-to-finish cycle such as a revision; a part is the stretch between context compactions). The role signal is source.agent_type: sketch, prove, maintain, scan, triage, progress, math_reviewer, engineering_reviewer. Only status-done rollouts that pass the gate are included; system prompts are rebuilt from the agent class because the recordings do not store them. The generating model is not recorded in the run files. (Renamed from repoprover.jsonl on 2026-10-20; content unchanged.)
| Role | Rollouts | Tokens |
|---|---|---|
| engineering_reviewer | 3,975 | 109.4M |
| math_reviewer | 3,950 | 122.5M |
| progress | 2,809 | 117.4M |
| maintain | 2,498 | 82.2M |
| triage | 699 | 39.4M |
| prove | 231 | 11.3M |
| scan | 137 | 8.5M |
| sketch | 33 | 2.0M |
repoprover-undergrad.jsonl — 98,450 records, 6,460.0M tokens
One record per finished rollout from RepoProver formalizing 11 open-LaTeX undergraduate textbooks — selected to cover the topics mathlib's docs/undergrad.yaml marks as missing — into Lean 4 + Mathlib repositories (one job per book; the runs were still in progress when this export was taken, 2026-11-06, and the file grows with re-exports). Two models generated these rollouts, both served by the comet SGLang gateway at max reasoning effort and recorded per record in source.model: kimi-k3 through 2026-10-28 (40,128 records, 1,845.6M tokens) and deepseek-v4.1-flash from 2026-10-28 on (58,322 records, 4,614.4M tokens). The recordings do not store the model, so the label comes from the run directory's start time — the launcher fixes one model per job. Filter on it if you need a single generator. Every assistant turn's reasoning is preserved in think. Record ids and the segment/part scheme are as above: a segment is one start..done cycle such as a revision, a part is the stretch between context compactions — only a segment's final part ends on an assistant turn, so earlier parts are not exported. source.project names the book. System prompts are the recorded ones (not rebuilt). Only status-done rollouts that pass the gate are included.
| Role | Rollouts | Tokens |
|---|---|---|
| engineering_reviewer | 24,664 | 1,533.2M |
| math_reviewer | 22,950 | 1,637.3M |
| prove | 22,899 | 1,286.9M |
| maintain | 13,933 | 924.4M |
| triage | 5,292 | 378.6M |
| sketch | 934 | 61.4M |
| scan | 3,760 | 303.0M |
| progress | 4,018 | 335.1M |
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