math2-agent

README

math2-agent

This repository holds the toolchain and the research agents for Math 2.0. The content is in tamnd/math2.

Math 2.0 is a versioned knowledge graph of mathematics. The m2 command reads the node files in math2. It builds the Lean library, computes the status of each node, makes the graph and checks each change with the audit rules. Later milestones add search, an API, an MCP server, a research workspace and AI research agents.

Specification

The design is in spec/. It has 22 documents, 00 to 21. Issues, code and reviews refer to a section by its number, for example 04.5 or 15.3 S03.

The wiki at https://tamnd.github.io/math2 shows the spec, the milestones and each node.

Status

The project is at milestone M1. Release v0.1.0 closes the code of M0: m2 new, m2 fmt, m2 check, m2 mint and m2 site build are written. In M1, m2 audit runs the rules T01 to T06, S01 to S04, S09, B01 to B05 and G01 to G10. Rule G04 reads build/extract.json from the last m2 build. It skips when that file does not exist. The graph package derives the graph from the node files, with the AND-OR closure of spec 05.5, the CSR adjacency and the Parquet build format. The lean package drives M2Extract, a small Lean program that gives the type hash, the axioms and the formal dependencies of each bound declaration. m2 build runs lake build, runs M2Extract on each binding, computes the status of each node and writes the graph, with a cache for each step. The status package computes the evidence level, the fidelity level and the flags of spec 04.7, and m2 status shows them. The report shows each other rule of spec 15.3 with the state skip and the reason "not written yet". m2 help shows the milestone that delivers each command. A command that is not written yet exits with code 3 and names its milestone. It does not exit with code 0, because a command that does nothing and exits with code 0 looks like a command that worked.

Milestone	Dates	Result
M0, the skeleton	Nov to Dec 2026	Both repositories, the node schema, m2 new, m2 fmt, m2 check and the public wiki.
M1, the seed and the trust core	Jan to Mar 2027	About 2,000 seed nodes, m2 build, m2 audit, the checker stack and release 2027.03.
M2, the graph meets the world	Apr to Jun 2027	External sources, alignment, the monthly Mathlib bump and monthly releases.
M3, open to readers	Jul to Sep 2027	Search, the read API, the MCP server, the workspace and the computational engine.
M4, fidelity at scale	Oct to Dec 2027	The review tool, statement autoformalization and write access through the API.
M5, the research engine	Jan to Jun 2028	The research agents, the orchestrator, budgets and the weekly agent report.

Each milestone has a tracking issue with the label milestone. The tracking issue has the exit criteria and a list of sub-issues.

Install

You need Go 1.27 or later.

go install github.com/tamnd/math2-agent/cmd/m2@latest

You can also download a binary from the releases page. Each archive has a build provenance attestation. To verify an archive, run this command:

gh attestation verify m2_v0.1.0_linux_amd64.tar.gz --repo tamnd/math2-agent

Commands

Command	What it does	Milestone
m2 new <kind>	Make a node file with a provisional id.	written
m2 fmt	Make front matter canonical and change aliases to tags.	written
m2 check	Check schema, body and links on the working tree. This does not use Lean.	written
m2 mint	Change the provisional ids to tags before merge, and add the tags to registers/tags.reg.	written
m2 site build	Build the wiki: a static site for people and agents.	written
m2 build	Build the derived data: Lean, extraction, status and graph. Search comes later.	written
m2 audit	Run the audit rules and write the report to reports/.	written
m2 status <tag>	Show the computed status of a node and the evidence for it.	written
m2 graph	Run a graph query: closure, reverse dependencies, path or frontier.	M2
m2 ingest <source>	Get a pinned snapshot of an external source.	M2
m2 align <source>	Propose crosswalk edges to an external source.	M2
m2 bump	Make a branch that moves Lean and Mathlib to the next release.	M2
m2 release	Cut, describe or verify a release.	M2
m2 search <query>	Search the knowledge graph.	M3
m2 serve	Serve the API, the MCP server and the workspace.	M3
m2 compute	Run or verify a computation.	M3
m2 prov	Show or change provenance.	M3
m2 review <tag>	Review a formal statement against its informal statement.	M4
m2 autoform <tag>	Make a formal statement for a node.	M4
m2 agent run <role>	Do one agent run.	M5
m2 orchestrate	Run the job scheduler.	M5

The wiki

m2 site build makes the wiki at https://tamnd.github.io/math2 from a math2 working tree and the spec. The math2 repository runs it on each push to main and each night, and GitHub Pages serves the result.

go run ./cmd/m2 site build -content ../math2 -spec spec -out _site
python3 -m http.server -d _site 8000

Each node gets a page with an infobox, its links and its backlinks. KaTeX renders the math in the browser with the macros of math2. Each page also has a copy for programs: node/<TAG>.md, api/node/<TAG>.json, api/nodes.json, llms.txt and llms-full.txt. A build with no -date flag gives the same bytes each time.

To preview the site with the local server above, set -url http://localhost:8000.

The build

m2 build makes the derived data of a math2 working tree in build/. Run it in the root of the tree. It needs elan for the Lean steps.

m2 build                # all the steps
m2 build -only lean     # only lake build
m2 build -json          # write the manifest as JSON

The steps are lean, extract, status and graph. The lean step gets the Mathlib cache and runs lake build in lean/. The extract step runs M2Extract on each formal declaration and adapter that a node names, and on each declaration with the attribute @[m2 "TAG"]. It writes build/extract.json. The status step computes the evidence level and the fidelity level of each node from the nodes, build/extract.json and the reviews in reviews/, and writes build/status.json. The graph step writes the graph as Parquet to build/graph/. A tree without lean/ has only the status and graph steps.

build/manifest.json records the Lean toolchain, the Mathlib commit, the hash of each checker program of the toolchain, and the input hash and output hash of each step. When the inputs of a step and its files do not change, the step does not run again. The output hash of the build covers extract.json, status.json and graph/. Two builds of the same commit give the same output hash (rule R01).

The status of a node

m2 status shows the status of a node from the last m2 build. It reads build/status.json. Give a tag, an alias or an m2:// URI.

m2 status 3C53TD
m2 status lagrange-theorem-groups
m2 status m2://lean/Subgroup.card_subgroup_dvd_card
m2 status -json 3C53TD

The output gives the evidence level, the fidelity level, the flags, each item of evidence, each Lean binding with its type hash, its axioms, its reviews and its replay, and one reason for each decision. For an E5 result, it also gives the checker versions. A tag that is not in the build exits with code 1.

Rules that the toolchain keeps

1. The files in tamnd/math2 are the truth. Each database, index and site comes from these files, and you can make it again from them.
2. The build computes the status of each node. No person and no agent writes a status.
3. Only the Lean kernel and the certificate checkers can give the levels E4 and E5. A model can propose a proof. A model cannot accept a proof.
4. A formal statement must agree with its informal statement. This agreement is a separate level, F0 to F3. Only a person can give F2 or F3.
5. Each write is a pull request against tamnd/math2. The audit is the gate.
6. Each agent run has a run record. Each run has a person or a schedule that is responsible for it.
7. Each release pins the Lean toolchain, the Mathlib tag, the container images, the model ids and the prompt versions.

Build and test

make build    # writes bin/m2
make test     # runs the tests with the race detector
make lint     # runs golangci-lint

CI runs the same checks on each pull request. It also runs govulncheck, CodeQL, OpenSSF Scorecard, a smoke test of the binary, actionlint and zizmor.

Layout

cmd/m2/   the m2 binary
audit/    the audit rules of spec 15, with a fixture pair for each rule
build/    the steps of m2 build, their cache and the build manifest
check/    the fast rules of m2 check: schema, body and links
cli/      the command table
format/   the canonical form of m2 fmt and the change from aliases to tags
graph/    the graph of spec 05: edges, closure, cycles, CSR and Parquet
lean/     M2Extract, its Lake package and the Go package that drives it
node/     read node files, write the canonical form and compute the content hash
schema/   check front matter against the node schema
site/     build the wiki
status/   the evidence level, the fidelity level and the flags of each node (spec 04.7), and the reviews
tag/      tags, provisional ids, the tag register and the alias register
uri/      m2:// URIs
spec/     the specification

Each directory except cmd/ and spec/ is a Go package that other programs can import. For example, a bot can use github.com/tamnd/math2-agent/node to read and format node files. The packages follow the conventions of the Go standard library, and go doc shows an example for each main function.

The full layout arrives with the milestones. The plan has these parts: compute, ingest, align, search, api, mcp, orchestrator, agent, prompts/, images/, web/ and bench/.

Contribute

Read CONTRIBUTING.md. To report a security problem, read SECURITY.md.

Licence

Apache-2.0. Refer to LICENSE.