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Prompt

https://arxiv.org/html/2609.11319v2 read this paper fully then MAGENTA in Rust: Build Plan Plan for implementing Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification (arXiv:2609.11319v2) as a Rust system. 9 October 2026. 1. Goal and scope Build a training-free pipeline that takes a natural-language math problem and returns a final answer, a Lean 4 statement and a Lean-checked proof, or UNCERTIFIED if the budgets run out. Scope is Algorithms 1 to 4 of the paper. No model training and no custom provers. MVP target: an end-to-end run on 10 to 20 AIME-style problems, with a full JSONL trace of every attempt. 2. System at a glance Five LLM-backed roles and one deterministic checker: • Reasoner (R): problem plus optional feedback in, reasoning chain and boxed answer out. • Formaliser (F): problem plus answer in, Lean 4 theorem statement out. • Statement judge (Js): accepts a statement only if it faithfully encodes the problem and the proposed answer. • Prover (P): problem, chain, accepted statement and last Lean diagnostic in, Lean proof out. • Error judge (Je): labels a failed proof MATH (re-derive the mathematics) or SYNTAX (repair the Lean proof). • Lean verifier (V): Vs checks that the statement elaborates; Vp checks that the proof is complete, the statement is unchanged and no forbidden constructs are used. Control flow is three nested, bounded loops: reasoner attempts (T), statement samples per answer (M) and proof attempts per statement (K). Three rules must hold: • Statement resampling never calls the reasoner. • The accepted statement stays fixed during proof search. • Only a MATH label sends control back to the reasoner. The routing step is the heart of the system: match lean.check_proof(&s, &pi).await? { Ok(()) => return Certified(c, a, s, pi), Err(e) => match error_judge.label(&q, &c, &a, &s, &pi, &e).await? { Label::Math => { feedback = Some((c, a, s, pi, e)); break; } // back to reasoner Label::Syntax => eps = Some(e), // repair proof only }, } 3. Rust project layout One crate, magenta: • types.rs: Problem, Statement, Proof, Diagnostic, Label, Outcome. • llm.rs: one client for any OpenAI-compatible chat endpoint, with timeouts and retries. • prompts.rs: templates copied from Appendix B.1 of the paper. • lean.rs: check_statement and check_proof. • roles.rs: each role is a model config, a prompt and an output parser. • pipeline.rs: Algorithms 2 to 4. • eval.rs: batch runner, concurrency and metrics. • main.rs: clap CLI that reads problems.jsonl and writes results.jsonl. Endpoints and budgets live in config.toml. Crates: tokio, reqwest, serde, serde_json, toml, clap, anyhow, tempfile, regex, futures, tracing. 4. Build phases Effort is relative: S is small, M is medium. Phases 0 to 5 are the MVP. Phase 0: Environment (S) • Install Rust with rustup, Lean with elan, and a Lake project that depends on Mathlib. Run lake exe cache get so Mathlib is downloaded prebuilt instead of compiled. • Pick LLM endpoints and API keys. • Done when lake env lean test.lean compiles a theorem that imports Mathlib. Phase 1: Lean runner (M) • check_statement: write import Mathlib, the statement and := by sorry to a temp file, run lake env lean, and pass if there are no error lines. The sorry warning is expected. • check_proof: reject if the file does not start with the accepted statement (whitespace-normalised) or contains sorry, admit, axiom, unsafe or native_decide. Otherwise compile, append #print axioms for the theorem, and accept only propext, Classical.choice and Quot.sound. This is a cheap stand-in for SafeVerify, which you can adopt later. • Use tokio::time::timeout with kill_on_drop(true), and a Semaphore to cap parallel Lean processes, because each Mathlib import can use several GB of RAM. • Return Lean's output verbatim as the diagnostic. • Done when 4 unit tests pass: a good proof is accepted, and a proof with sorry, a changed statement or native_decide is rejected. Phase 2: LLM client and reasoner (S) • Generic chat client, the reasoner prompt, and answer extraction from the boxed block with regex. • Done when one sample problem returns a reasoning chain and a parsed answer. Phase 3: Statement search, Algorithm 3 (M) • Formaliser, then check_statement, then the statement judge returning strict JSON (right or wrong, with rationale and mismatch details). • The judge must not solve the problem, and must judge against the proposed answer even if that answer is wrong. • Done when a solved problem yields an accepted statement, or REJECTED after M samples, with the judge rationale logged. Phase 4: Proof search and error attribution, Algorithm 4 (M) • The prover receives the last diagnostic; check_proof; the error judge returns strict JSON (math_error or code_error). Ambiguous cases default to code_error (SYNTAX), as in the paper. • Done when a deliberately broken proof is repaired through the SYNTAX path and a deliberately wrong answer triggers the MATH path. Phase 5: Controller and logging, Algorithm 2 (S) • Outer loop with the self-correction prompt (previous solution, immutable Lean target, latest proof, exact diagnostic). • Log every attempt (prompts, outputs, diagnostics, labels, budget counters) as JSONL. • Done when 10 problems run end to end and each ends CERTIFIED or UNCERTIFIED. Phase 6: Scale and measure (M) • Run problems concurrently with buffer_unordered(n), and sample formaliser candidates in small batches. • Metrics: Ver, VerCor and the false certification rate FCR = 1 - VerCor/Ver. Reference answers are used only for evaluation and never shown to the pipeline. • Done when a 30-problem run is reproducible (fixed temperature, seed and config saved with the results). Phase 7: Ablations (S) • Flag to disable the statement judge (accept the first statement that elaborates). • Flag to replace diagnostic-conditioned repair with independent resampling. • Optional: paraphrase robustness test. • Done when Ver, VerCor and FCR are compared with and without each mechanism. 5. Budgets The paper uses T = 32, M = 512 and K = 4096, with prover trajectories of up to 4M output tokens, which is far beyond a first build. Worst-case calls per problem are T reasoner calls, T times M formaliser and judge calls, and T times K prover, verifier and error-judge calls. Suggested starting values (mine, not the paper's): T = 4, M = 8, K = 8. Log which budget is exhausted for each UNCERTIFIED problem, and raise only that one. 6. Model choices You do not need the paper's exact models. Start with one strong model behind an OpenAI-compatible API for every role, then specialise per role through config.toml. The paper uses a separate reasoner, formaliser and prover, and one model prompted two ways for both judges. Expect lower scores than the paper's 100%, which relies on strong components and large budgets. 7. Risks and mitigations • Unfaithful statements. Lean only certifies the statement, so the output is a soft certificate. Keep the statement judge: in the paper's ablation, removing it made 45.5% of certificates false on AIME 2026 with the Goedel formaliser. Spot-check certified outputs by hand. • Lean cost and memory. Use the prebuilt Mathlib cache, a process cap and timeouts. • Formaliser long tail. Weaker formalisers need many samples (the paper reports about 120 calls to cover AIME 2026 for Goedel against about 6 for Codex). Batch samples and raise M first. • Judge output that is not valid JSON. Retry once; default to reject for the statement judge and SYNTAX for the error judge. • Runaway cost. Hard caps T, M and K, plus a per-problem token counter. • Weaker results than the paper. Compare against a single-model, no-Lean baseline so you can see what the loop adds. 8. Next actions 1. cargo new magenta and add the crates above. 2. Set up Lean and Mathlib; compile a test theorem. 3. Write lean.rs with its four unit tests. 4. Add llm.rs and the reasoner; run one problem. 5. Wire Algorithms 2 to 4 with tiny budgets and run 10 problems. l ike i want to develop this as a systrm code i have no idea how u needed to plan this as fast as possibr in rust if wanted help me to build this paper plan effieciently give in this token liimit is that plan ok if upgrades needed give me as a updated plan abd full plan dot miss any full architecture and all