# Mathlas > Airtight math tools an AI uses over MCP — 3.7M-theorem search, PSLQ constant ID, OEIS, real Lean kernel checks, applicability checklists. No LLM inside, no API key. - **Type:** MCP server - **Install:** `agentstack add mcp-archerkattri-mathlas` - **Verified:** Pending review - **Seller:** [Archerkattri](https://agentstack.voostack.com/s/archerkattri) - **Installs:** 0 - **Category:** [AI & ML](https://agentstack.voostack.com/c/ai-and-ml) - **Latest version:** 1.1.1 - **License:** Apache-2.0 - **Upstream author:** [Archerkattri](https://github.com/Archerkattri) - **Source:** https://github.com/Archerkattri/mathlas - **Website:** https://pypi.org/project/mathlas-mcp/ ## Install ```sh agentstack add mcp-archerkattri-mathlas ``` Requires the [AgentStack CLI](https://agentstack.voostack.com/docs/cli). Works with Claude Code, Cursor, and any MCP-compatible agent. ## About # mathlas [](https://pypi.org/project/mathlas-mcp/) [](https://github.com/Archerkattri/mathlas/actions/workflows/ci.yml) [](https://zenodo.org/badge/latestdoi/1260785845) [](https://glama.ai/mcp/servers/Archerkattri/mathlas) [](https://github.com/Archerkattri/mathlas/blob/main/LICENSE) [](https://pypi.org/project/mathlas-mcp/) [](https://huggingface.co/datasets/kattri15/mathlas-corpus) > **An airtight-math tool an AI *uses* — no LLM, no API key, free.** Plug it into > Claude Code, Cursor, or any MCP client. The **AI is the brain**; mathlas is the > **hands** — it gives the AI the capabilities it lacks and returns *data* > (candidates, verdicts, checklists, scaffolds) for the AI to reason over. > Apache-2.0. The code is free for any use; published corpus/index artifacts carry their own per-source terms (CC-BY/CC0). Every verdict from the real Lean 4.31.0 kernel / PSLQ + an independent re-eval — no LLM inside. Real in-process tool outputs, captured by assets/gen/capture_outputs.py. --- ## Is this for you? - **You use Claude Code / Cursor and want your AI to stop hallucinating math** — `search_existing_math` finds the real theorem from a 3.68M-doc index; `verify_numeric` and `verify_formal` check claims with zero hallucination risk. - **You have a numeric constant or integer sequence you can't identify** — `identify_constant` runs PSLQ + closed-form matching (50-digit precision); `identify_sequence` does an exact OEIS term-match. - **You need the formal (Lean/mathlib) name of a result** — `search_formal_math` proxies the public Loogle + LeanSearch services and returns declaration names + types, provenance-labeled. - **You're building an agent pipeline that needs airtight math in the loop** — all 12 tools are pure data-returning MCP tools, no LLM inside, composable with any framework. --- ## Install & register with Claude Code (no API key) One line, nothing to install first (needs [uv](https://docs.astral.sh/uv/)): ```bash claude mcp add mathlas -- uvx mathlas-mcp ``` `uvx mathlas-mcp` fetches + runs the server in an isolated env on first use. Prefer pip? ```bash pip install mathlas-mcp # core: numeric + retrieval + verify + scaffolds pip install 'mathlas-mcp[mcp]' # + official MCP SDK pip install 'mathlas-mcp[retrieve]' # + pyarrow, to read the real index pip install 'mathlas-mcp[embed]' # + sentence-transformers/torch, for the Qwen3 embedder claude mcp add mathlas -- python -m mathlas.server ``` mathlas now appears as **twelve** tools the agent can call. The server prefers the official `mcp` SDK and **falls back to a dependency-free stdio JSON-RPC server** if `mcp` isn't installed — it always runs. (Cursor / any MCP client: point it at the same `uvx mathlas-mcp` or `python -m mathlas.server` stdio command.) > **Optional local data (degrades honestly):** `identify_sequence` wants a local OEIS copy; `verify_formal` wants a Lean toolchain. Without them the tools return a clear "data/toolchain not available" — never a fake answer. See [`docs/methods.md`](docs/methods.md#data--toolchains-optional-gitignored-removable) for the one-line setup of each. --- ## A worked example — an AI using the tools ``` User: "Does x = cos(x) have a unique solution I can reach by iterating?" AI → search_existing_math("contraction mapping unique fixed point complete metric space") ← [{name:"Banach Fixed-Point Theorem", statement:"Let (X,d) be a complete metric space and T a contraction. Then T has a unique fixed point ...", ...}, ...] AI → applicability_checklist(banach.statement) ← preconditions: ["(X,d) is a complete metric space", "T: X→X is a contraction"] conclusion: "T has a unique fixed point" AI (reasons): [0,1] is complete; cos is a contraction there (|cos'|=|sin|≤sin 1") ``` mathlas supplied the search, the checklist, and the airtight numeric check. The AI did the judging. **No LLM was called inside mathlas.** --- ## Results The discipline is **airtight-or-nothing**: a result is an independently-checkable fact or an honest "nothing." The **false-positive rate is 0 across every tier** (full tables + commands in [`RESULTS.md`](RESULTS.md)): | Tier | Recovery@known | False-positive | Why it's airtight | Benchmark | |---|---|---|---|---| | Numeric (`identify_constant`) | 8/8 | 0/3 | independent high-precision re-eval (50–51 digits) | `benchmarks/numeric_bench.py` | | Sequence (`identify_sequence`) | 8/8 (7 top-1) | 0/3 | exact term-match vs local OEIS (~400k seqs) | `benchmarks/tier_bench.py` | | Formal (`verify_formal`) | 7/7 verdicts | — | real Lean 4.31.0 kernel typecheck | `benchmarks/tier_bench.py` | | Ramanujan (`conjecture_relation`) | 6/6 | 0/2 | PSLQ + CF, every hit re-verified ≥25 digits | `benchmarks/tier_bench.py` | | Applicability moat | 15/15 decomp + 6/6 catch | — | atomic preconditions, misapplication traps | `benchmarks/moat_bench.py` | | FunSearch + web-aug | 14/14 | — | sandbox containment (network / timeout / memory) | `benchmarks/tools_bench.py` | The table above, at a glance — 0 false positives across every tier (0/8 structureless inputs produced a false hit), 100% recovery on knowns. Numbers: RESULTS.md §1–2b. **Agent-in-the-loop, honestly reported (2026-06-10, Claude Fable 5):** the same headless agent given **18 math tasks** WITH the live mathlas MCP server as its only tool vs WITHOUT any tools scores **18/18 vs 15/18**. The original 10-task set is saturated (10/10 both ways: a frontier model passes it from parametric knowledge alone, and we say so plainly), so an 8-task hard set was added where verification, not recall, is the bottleneck: that set goes **8/8 WITH vs 5/8 WITHOUT**. The bare model times out on 50-digit integer-relation detection (PSLQ) and cannot name obscure OEIS sequences that shadow Catalan/Fibonacci prefixes and only diverge at depth. The bare passes it does earn are remarkable and we report them: it evaluated a 6-term constant relation to 45 digits by hand (residual 1.475e-27, correct), simulated IEEE-754 rounding bit-for-bit in its head (with one wrong exponent in prose), and proved a Machin-like formula exactly via Gaussian integers, all in-context at 3-9x the latency of a tool call. Every ground truth is a deterministic computation recorded in the bench; full table and provenance: [`RESULTS.md` §2c](RESULTS.md). Run: `benchmarks/agent_bench.py`. **The 3.68M-doc index.** `search_existing_math` is served from a **3,683,428-document** dense index (Qwen3-Embedding-8B, 4096-d): the **1.34M** permissive CC-BY/CC0 TheoremSearch subset + **2.34M** slogan-embedded arXiv-math documents from Dolma, dense + Okapi-BM25 + RRF. Honest headline recall at full 3.68M scale: **R@1 0.614 / R@10 0.832** querying by a document's raw *body* against its slogan-embedded entry — the hard **cross-representation** self-recall regime. (At the earlier 1.635M build, the easier same-representation slogan→slogan self-recall was R@1 0.977 / R@10 0.998 on its 81,833-doc held-out split.) **Open corpus on Hugging Face.** The text + metadata side of that index is published at [`kattri15/mathlas-corpus`](https://huggingface.co/datasets/kattri15/mathlas-corpus): 3,683,428 theorem-level documents plus the small `findings` config, split into `theoremsearch`, `dolma`, and `findings` configs. It includes slogans, LaTeX statements, source URLs, titles, labels, categories, citation counts where known, and provenance keys. It does **not** include the 30 GB embedding matrices or local benchmark slices. Licenses are per config: TheoremSearch subset CC BY-SA 4.0, Dolma statements ODC-BY 1.0 with our slogans CC BY 4.0, and findings CC BY 4.0. Full audit: [`docs/HF_DATASET_LICENSING.md`](docs/HF_DATASET_LICENSING.md). ```python from datasets import load_dataset ts = load_dataset("kattri15/mathlas-corpus", "theoremsearch", split="train") dolma = load_dataset("kattri15/mathlas-corpus", "dolma", split="train") ``` **Quantized laptop tier (opt-in).** The fp16 matrix is 30 GB on disk (~60 GB fp32 resident) — fine on the build box, not on a laptop. `MATHLAS_QUANTIZED=binary` (or `quantized="binary"` on `HybridRetriever.from_index`) serves the SAME index from memmapped quantized sidecars instead: sign-bit Hamming over **1.9 GB** shortlists 1000 candidates, exact rescore picks the top-k — measured on the full 3.68M index with the same n=3000 protocol as the headline, it is **recall-lossless** (R@1 0.6143 vs 0.6140 fp16, R@10 equal at 0.8323; int8 mode: R@1 0.6147, 15 GB) at **2.4 s/query on 4 CPU threads**. Honest caveat: this shrinks the *document* side only — queries must still be embedded by the same Qwen3-Embedding-**8B** (a small 0.6B encoder lives in a different vector space). The true end-to-end small-encoder tier is the 0.6B tier below. Numbers, build command, and the caveat in full: [`docs/QUANTIZED_TIER.md`](docs/QUANTIZED_TIER.md). **0.6B end-to-end laptop tier (opt-in).** The SAME 3,683,428-doc corpus re-embedded once with **Qwen3-Embedding-0.6B** (1024-d, row-aligned with the served meta), so the query encoder itself runs on a laptop CPU: `MATHLAS_ENCODER=0.6b` (composes with `MATHLAS_QUANTIZED=binary`). Measured with the identical n=3000 cross-representation protocol, queries re-encoded by the 0.6B model: **R@1 0.545 / R@10 0.745** (binary + int8 rescore; the 0.6B fp16 exact scan is 0.544 / 0.745, so quantization is again lossless within the tier). The honest price vs the 8B tier (0.614 / 0.832) is about 7-9pp recall; the dual-channel 8B configuration (0.965 / 0.999) stays the big-box quality ceiling. The laptop headline: **end-to-end 0.67 s/query on 4 CPU threads (0.88 s on 2)**, query encoding included, over all 3.68M documents. Dense-channel footprint: binary sidecar **0.47 GB** + 0.6B encoder **~1.2 GB** (~1.7 GB; int8 rescore source 3.77 GB recommended; full fp16 sibling index 7.54 GB). On the TheoremSearch-110 corpus-only probe the tier scores Hit@20 8.2% / 10.0% theorem/paper vs the 8B tier's 10.0% / 11.8% (both licensing-bounded floors). Full tables, footprints, and caveats: [`docs/QUANTIZED_TIER.md`](docs/QUANTIZED_TIER.md); build: `scripts/build_06b_index.py`; eval: `scripts/eval_06b_tier.py`. **Dual-channel retrieval (opt-in).** The 0.614 headline is a cross-representation gap: LaTeX-statement-shaped queries searched against slogan-embedded docs. A second dense channel embeds the same 3,683,428 docs by their cleaned LaTeX **statement** (Qwen3-Embedding-8B, row-aligned, built by `scripts/build_statement_channel.py`) and folds into the dense ranking by per-doc max-sim. Measured on the same n=3000 sample at full corpus scale: **R@1 0.614 to 0.965, R@10 0.832 to 0.999**. Honest caveats: that eval is a self-retrieval proxy in which the statement channel indexes the very text the queries are drawn from (an exact-text advantage, like BM25's); on the no-leak 110 human-query benchmark the lift is real but partial (paper Hit@20 11.8% to 12.7%). And the second matrix roughly doubles serving RAM (measured at full scale: 150 GB process peak for the dual server vs ~95 GB single-channel; ~2.75 s/query dual dense scan on 2 CPU threads), so it ships strictly opt-in (`MATHLAS_STATEMENT_INDEX=/path/index_full_statement.npz`, never auto-detected) and is not combinable with the quantized tier. Full numbers and the serving-tier table: [`docs/RETRIEVAL_UPGRADE_NOTES.md`](docs/RETRIEVAL_UPGRADE_NOTES.md). The production hybrid default `rrf_k` is 10 (measured best at every k tested), plus an opt-in cross-encoder rerank blend (`MATHLAS_RERANK=1`, Qwen3-Reranker-0.6B, +1.7pp R@1 honest lift). The rerank backend is selectable with **`MATHLAS_RERANK_MODEL`**: `qwen3` (default, Qwen3-Reranker-0.6B, unchanged) or `jina-v3` (`jinaai/jina-reranker-v3`, [arXiv:2509.25085](https://arxiv.org/abs/2509.25085) — a 0.6B "last but not late" reranker that leads BEIR at the 0.6B scale). Both lazy-load their weights on first use and fall back to the un-reranked fusion (honest stderr note) if torch/transformers or the weights are absent; a typo'd model name raises rather than silently serving the wrong reranker. We ship the wiring, not a jina benchmark number — bring your own weights. ## The self-augmenting loop — beating TheoremSearch On TheoremSearch's own **110 human-written queries**, baseline mathlas hits a coverage floor — TheoremSearch withheld 85% of their private 9.2M corpus, so 95 target papers are unreachable for any open system. The AI then runs the loop: for each missing theorem it web-finds the real statement, embeds it with the same Qwen3-Embedding-8B, and `add_finding(dense_vec=…)` fuses it through the dense channel at runtime (re-measured 2026-06-10 on the served 3.68M index — the after-loop headline reproduced exactly; the corpus-only baseline dipped 13.6% → 11.8% paper-level from the added Dolma distractors, reported as is): | Method | theorem Hit@20 | paper Hit@20 | |---|---|---| | Google (`site:arxiv.org`) | — | 37.8% | | ChatGPT 5.2 w/ Search | 19.8% | — | | Gemini 3 Pro | 27.0% | — | | **TheoremSearch** (Qwen3-8B, full private 9.2M) | 45.0% | 56.8% | | mathlas — baseline (corpus-only) | 10.0% | 11.8% | | **mathlas — after self-augmenting web loop** | **59.1% (65/110)** | **70.0% (77/110)** | This is the loop's value, not a native-corpus claim. The 10.0% baseline is licensing-bounded — TheoremSearch withheld ~85% of their 9.2M corpus, so 95/110 target papers are unreachable for any open system; the self-augmenting web loop repairs that coverage gap at AI-runtime. Google's bar is paper-level Hit@20 (no theorem number reported); every other bar is theorem Hit@20. Reproduce with `benchmarks/webaug_110_bench.py` (use the **full** 82-finding worklist `_findings_worklist_full.json`). **Source-aware retrieval (opt-in).** Growing the index 1.34M → 3.68M had a measured cost: the 2.34M web-mined Dolma docs crowd canonical papers out of the top-20 (corpus-only paper-level 13.6% → 11.8% on these same 110 queries). `search_existing_math` now takes optional `source_filter` / `source_weights` — e.g. `source_filter={"exclude": ["dolma"]}` when you want canonical theorem statements only — and excluding dolma **fully recovers the pre-growth 13.6%** paper-level (15/110; reachable-15 paper 15/15 = 100%) with theorem-level *above* the old index (11.8% vs 10.9%). The default ranking stays byte-identical (test-pinned). It is a **per-query-intent knob, not a free win**: on the n=3000 self-recall, 65% of whose targets ARE Dolma docs, down-weighting dolma is catastrophic for those queries (dolma-target R@10 0.999 → 0.884 at weight 0.5, → 0 when excluded) — exactly why it ships opt-in, default off. We also tested whether the dual channel fixes this regression structurally, without the knob: it recovers part of it (paper 11.8% to 12.7%, theorem 10.0% to 10.9% at default settings) but not the full 13.6%, so the knob remains the documented mitigation on this benchmark. Full matrix: [`docs/02_eval_vs_theoremsearch.md`](docs/02_eval_vs_theoremsearch.md). --- ## The 12 tools ``` search_existing_math ─▶ mapping_scaffold + applicability_checklist ─▶ (AI judges) ─▶ verify_numeric / verify_formal (own index) (needs↔guarantees, no LLM) (airtight) ``` **Core four** — what most agents use: | Tool | What it does | |---|---| | `search_existing_math(query, k)` | query → ranked results from the **3.68M-doc** dense + BM25 + RRF index | | `identify_constant(value)` | a real value → known closed form + provenance (50-digit re-eval) | | `verify_numeric(value, closed_form)` | digit-agreement verdict — different engine, higher precision | | `verify_formal(statement, lean?, proof?)` | runs the **real Lean kernel** — typecheck a snippet, or pass `proof` to **kernel-check a full Lean 4 proof**: `VERIFIED_PROOF` / `REFUTED` (the kernel's exact error, for the repair loop) / honest UNDETERMINED | **Full toolkit:** | Tool | What it does | |---|---| | `search_formal_math(query, backend)` | ma … ## Source & license This open-source MCP server is cataloged on AgentStack and links to its original source — we do not rehost the code. - **Author:** [Archerkattri](https://github.com/Archerkattri) - **Source:** [Archerkattri/mathlas](https://github.com/Archerkattri/mathlas) - **License:** Apache-2.0 - **Homepage:** https://pypi.org/project/mathlas-mcp/ Install and usage instructions live in the source repository linked above. ## Pricing - **Free** — Free ## Security capabilities Automated source analysis of v1.1.1 — what this tool can access: - **Network access:** no - **Filesystem access:** no - **Shell / process execution:** no - **Environment & secrets:** no - **Dynamic code execution:** yes *"Yes" means the capability is present in the source — more access means more to trust, not that it is unsafe.* ## Versions - **1.1.1** — security scan: flagged — Imported from the upstream source. ## Links - Listing page: https://agentstack.voostack.com/l/mcp-archerkattri-mathlas - Seller: https://agentstack.voostack.com/s/archerkattri - Browse the marketplace: https://agentstack.voostack.com/browse --- Listed on AgentStack — the marketplace for AI agent skills and MCP servers. 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