# Project GPE: proof maps of OpenAI's openai/math papers (373 families catalogued, 5 digested) [openai/math](https://github.com/openai/math) is a collection of 721 machine-written math manuscripts in 373 result families. Project GPE catalogues all of them (title, abstract, discipline, PDF, Lean status) and turns some into browsable proof maps: every definition, lemma and theorem, plus the major claims inside long proofs, each with a plain-English statement, an explanation of why it is in the paper, a standard/routine/novel classification, and the dependency edges between them. This page tells an agent how to read the catalog and the maps. Everything is read-only, needs no key, and returns JSON. Two ways in, same tools and same answers: - **HTTP GET** (works with any fetch or curl): `https://project-gpe.vercel.app/api/v1`, described below. - **MCP** (streamable HTTP): `https://project-gpe.vercel.app/api/mcp`. Add it as a remote MCP server; the tools are the ones below, each with an extra `paper` argument (the slug). The catalog endpoints are HTTP only. ## How to use it 1. `GET https://project-gpe.vercel.app/api/v1/papers` lists the papers with a map. Pick a slug. (To find a result that has no map yet, search the catalog: `GET https://project-gpe.vercel.app/api/v1/families?q=…`.) 2. `GET https://project-gpe.vercel.app/api/v1/papers//get_overview` gives the summary, main results and the section layout. 3. Drill in with `get_node` (the explanation and direct edges) and `read_node` (the verbatim LaTeX statement and proof). 4. For "how does X lead to Y", call `trace`; a node's own edges are only its direct uses, so don't assemble chains by hand. `ancestors` gives everything a node rests on or supports. 5. Answer from what the tools return, and cite nodes with their `url` so the user can open them in the map. Node ids look like `lem-greedy-hashes`; the paper's LaTeX labels (`lem:greedy-hashes`) work too. An unknown id comes back as an error that lists close matches. Errors are `{ "error": "…" }` with status 400 (bad arguments) or 404 (unknown paper, node, figure or family). Example: `GET https://project-gpe.vercel.app/api/v1/papers/intmult/trace?from=&to=` ## Catalog Every openai/math result family, built from the repository's own index (no model involved). A family has a 3-digit code (`049`), a title and description, a discipline, its manuscripts, Lean status, and `digested`: the maps made from its manuscripts (slug and counts), `[]` when none is mapped yet. ### list_families `GET https://project-gpe.vercel.app/api/v1/families?…` Families, filtered and paged. Each has number, code, title, description, discipline, members, has Lean, reasoning-trace PDF (when there is one), and `digested`. - `q` (string, optional): case-insensitive text match against family titles and descriptions and manuscript titles and abstracts - `discipline` (string, optional): a discipline slug from list_disciplines, e.g. `combinatorics` - `digested` (`1` \| `0`, optional): only families with (or without) a map - `lean` (`1` \| `0`, optional): only families with (or without) a Lean formalization - `sort` (`flagship` \| `number` \| `title` \| `members`, optional): default `flagship` (featured families first, then mapped, then by number) - `limit` (integer, optional): default 50, max 400 - `offset` (integer, optional) ### get_family `GET https://project-gpe.vercel.app/api/v1/families/` One family (`049` or `49`) with every manuscript: title, abstract, publication date, PDF, source and README links, Lean status, and the map's slug when one exists. ### list_disciplines `GET https://project-gpe.vercel.app/api/v1/disciplines` Catalog totals (families, manuscripts, disciplines, digested, Lean, the indexed commit) and each discipline's slug, name, family count and digested count. ## Papers - `intmult`: Integer multiplication below n log n (OpenAI), 95 nodes, family 109 (Theoretical computer science). https://project-gpe.vercel.app/intmult - `logspace`: Exact Derandomization of Logarithmic Space: L = RL = BPL (OpenAI), 164 nodes, family 103 (Theoretical computer science). https://project-gpe.vercel.app/logspace - `unit-distance`: A power saving for planar unit distances (OpenAI), 96 nodes, family 167 (Combinatorics). https://project-gpe.vercel.app/unit-distance - `noncoordinate`: An explicit noncoordinate polynomial with affine three-space zero fibre (OpenAI), 12 nodes, family 049 (Algebraic and complex geometry). https://project-gpe.vercel.app/noncoordinate - `eth`: The Exponential Time Hypothesis is False, 89 nodes, family 378 (Theoretical computer science). https://project-gpe.vercel.app/eth ## Tools ### list_papers `GET https://project-gpe.vercel.app/api/v1/papers` Every paper that has a proof map: slug, title, authors, source, node count and link; for openai/math manuscripts also `family` (number, code, title, discipline), `pdf_url`, `has_lean` and a one-line `headline` when the map has a summary. ### get_overview `GET https://project-gpe.vercel.app/api/v1/papers//get_overview` A paper's summary and main results (with plain-English statements), its openai/math family and manuscript (PDF, Lean status), its sections with node counts, counts by kind, and its figures. Start here. ### list_nodes `GET https://project-gpe.vercel.app/api/v1/papers//list_nodes?…` One line per node (id, kind, name, headline, section, classification) in paper order. Filter by section id or kind; pages of 50 by default (max 200), follow next_offset for more. - `section` (string, optional): Section id from get_overview - `kind` (`definition` \| `lemma` \| `proposition` \| `theorem` \| `corollary` \| `claim` \| `remark`, optional) - `offset` (integer, optional) - `limit` (integer, optional) ### get_node `GET https://project-gpe.vercel.app/api/v1/papers//get_node?…` One node as the map explains it: plain-English statement, why it is in the paper, standard/routine/novel classification with its reason, friction notes, what it uses and what uses it, and a link. - `id` (string, required): Node id, e.g. lem-greedy-hashes, or a LaTeX label like lem:greedy-hashes ### read_node `GET https://project-gpe.vercel.app/api/v1/papers//read_node?…` One node's verbatim LaTeX statement and proof (or claim span) from the paper's source with file and line numbers, plus the equations it references. Use it to quote a proof or check an exact step or constant. - `id` (string, required): Node id, e.g. lem-greedy-hashes, or a LaTeX label like lem:greedy-hashes ### search_paper `GET https://project-gpe.vercel.app/api/v1/papers//search_paper?…` Case-insensitive search over the paper's LaTeX source, ignoring LaTeX punctuation (\sqrt{\log n} matches "sqrt log n"). Returns file:line, section, the node containing the line, and ±2 lines of context. - `query` (string, required): Words or a LaTeX fragment - `max` (integer, optional): Hits to return (default 10, max 15) ### trace `GET https://project-gpe.vercel.app/api/v1/papers//trace?…` Up to 3 shortest dependency paths from a supporting node to a result that rests on it. Use it for "how does X lead to Y"; says when no path exists and whether the reverse holds. - `from` (string, required): The supporting node - `to` (string, required): The result ### ancestors `GET https://project-gpe.vercel.app/api/v1/papers//ancestors?…` Everything a node rests on (direction "supported_by") or everything that rests on it ("supports"), grouped by distance. - `id` (string, required): Node id, e.g. lem-greedy-hashes, or a LaTeX label like lem:greedy-hashes - `direction` (`supports` \| `supported_by`, required) - `depth` (integer, optional): Levels to follow (default 3) ### view_figure `GET https://project-gpe.vercel.app/api/v1/papers//view_figure?…` One figure: LaTeX caption, description, data summary for charts, page, section, the nodes it supports, and a link to the figure image when one was rendered (over MCP the image itself is attached). - `ref` (string, required): Figure id or label from get_overview, "Figure 2", or 2 ### get_friction `GET https://project-gpe.vercel.app/api/v1/papers//get_friction?…` Places where the map is uncertain about the paper: dependencies inferred from prose rather than cited, unresolved references, structure the pipeline was unsure of. Worst first, at most 100. - `severity` (`info` \| `warn` \| `high`, optional) - `kind` (`inferred_dep` \| `unresolved_ref` \| `structure_uncertain`, optional)