LemmaTrail is an alpha-stage, GitHub-native framework for human and AI collaboration on hard mathematical problems.
The goal is to preserve reusable progress instead of letting useful reasoning disappear inside isolated chats, notebooks, or private notes. The repository should give humans and large language models enough shared context to continue from the current frontier instead of starting over.
This project is AI-supported by design. LLMs, agents, prompt engineers, programmers, hobby mathematicians, and professional researchers are welcome to contribute if they follow the current structure and review rules.
This project is not a place for raw model transcripts or long speculative essays. It is a structured place for durable research state: problem statements, definitions, verified claims, candidate claims, failed routes, assumptions, source references, review state, and continuation points.
- add one precise source connection
- record one failed route and its obstruction
- add one concrete next task for a problem
- review one claim for a gap
- convert one chat result into a checkable object
If you are using a model or coding agent, start here:
- MODEL_PROMPT.md for the copy-paste prompt to give a model.
- INSTRUCTIONS.md for the required model-facing workflow.
- AGENTS.md for the repository entry point used by coding agents.
This repository is currently v0.1-alpha.
The structure is expected to change as the project learns what is useful. The current files are working rules and guardrails, not final governance. Contributions that improve the framework itself are welcome, but changes should stay small, explicit, and easy to review.
Original LemmaTrail code, documentation, templates, and research objects are licensed under the MIT License. See LICENSE.md. External sources and imported metadata keep their own terms; see THIRD_PARTY_NOTICES.md.
Some problems may have external prizes or rewards. LemmaTrail does not award, manage, divide, or guarantee eligibility for any external prize.
Prize eligibility is controlled by the organization or person offering the prize. Contributors are responsible for checking those rules before relying on any prize claim.
Repository credit records provenance and contribution history, but it is not a legal authorship or prize-sharing agreement.
If a contribution develops into a serious solution attempt, contributors should agree separately on authorship, publication, and prize-related expectations before submission outside the repository.
Git history records commits, and research objects should preserve visible credit for authors, reviewers, source-finders, and curators when practical. AI tools must be disclosed, but they are not credited as authors. See CONTRIBUTORS.md.
Every contribution must make the next human, reviewer, or model better positioned to continue.
Accepted contributions should add at least one of:
- a precise problem statement
- a sourced definition or known result
- a candidate claim with derivation
- a verified claim with review evidence
- a refutation or counterexample
- a failed path with a clear obstruction
- a concrete next task
- a useful reference
See docs/example-research-object.md for a small mergeable contribution shape.
LLMs may propose, triage, and review. Humans decide what becomes canonical.
llm_reviewed: true
human_reviewed: false
status: needs-reviewThe example above is not verified research state. It means an LLM review did not find an obvious issue, but a human still needs to check it.
Durable contributions enter LemmaTrail through pull requests.
Issues, comments, and external discussions are welcome for proposing ideas, asking questions, reporting gaps, or giving feedback. But if something should become part of the repository's research state, it must be converted into a checkable research object using the repository templates and merged through a pull request.
This applies to both human and LLM-assisted contributions.
Pull requests that do not follow the current format will not be merged. The format can evolve, but unstructured output should not become repository state.
LLM-assisted work is welcome when it is useful, structured, and reviewable.
A model may help propose a claim, route, failed attempt, source connection, derivation, review note, or continuation point. It should not rewrite large parts of the repository, submit raw transcripts, or present unverified work as proven.
LLM-assisted contributions follow the same repository rules as human contributions: durable work must become a templated research object and enter through a pull request.
See INSTRUCTIONS.md for the current model-facing workflow. For a copy-paste prompt to give a model or agent, see MODEL_PROMPT.md.
catalog/ Candidate sources and imported YAML problem metadata
docs/ Project rules, status model, source policy, text policy
problems/ Problem workspaces
_workspace-template/ Readable skeleton for new problem workspaces
templates/ Reusable research-object templates
.github/ PR and issue templates
AGENTS.md Entry point for coding agents
INSTRUCTIONS.md Short workflow for LLMs and agents
MODEL_PROMPT.md Copy-paste prompt for model-assisted contributions
CONTRIBUTORS.md Credit and recognition policy
LICENSE.md Project license summary
THIRD_PARTY_NOTICES.md External source notice policy
See docs/repository-structure.md for the full structure. See docs/import-pipeline.md before adding any scraper or source adapter. See docs/pr-guard.md for pull request shape rules.
LemmaTrail is still an alpha-stage repository. The structure, review process, templates, and contribution rules may change as people try the format and expose what works or does not work.
For now, the source of truth is the GitHub repository: problem workspaces, pull requests, reviews, and issue discussions.
If the project succeeds, the natural next step is a website or app that makes the same repository-backed research state easier to browse, with better LaTeX rendering, problem pages, contribution history, review status, and source trails for a broader audience.
See docs/licensing-notes.md before copying external material.
You can support the project maintainer on Ko-fi.