---
name: co-math-init
description: Initialize a new AI co-mathematician research project. Use when the user wants to start a new math research investigation with AI agent support, or types "/co-math-init", "start a co-math project", "new research project", or similar. Scaffolds a directory with paper.tex, goals.md, decisions.md, workstreams/, and per-project hooks/config that enforce the co-mathematician discipline (no hand-waving, reviewer approvals required for completion).
author: Moran Koren <korenmor@bgu.ac.il> (Ben-Gurion University of the Negev)
---

> **Author:** Moran Koren, Ben-Gurion University of the Negev (korenmor@bgu.ac.il). Part of the [Theorist Toolbox](https://github.com/morankor/theorist-toolbox).


# co-math-init

Bootstrap a new research project for the personal AI co-mathematician system, modelled after the Google DeepMind AI Co-Mathematician paper (Zheng et al., 2026-05-07).

This skill creates the directory layout, copies the LaTeX template, initializes the per-project hook configuration, and sets up the workstream registry. After init, the user can spawn workstreams via the `project-coordinator` sub-agent.

## When to invoke

Trigger phrases:
- `/co-math-init`
- "start a new co-math project"
- "init a research project"
- "new mathematician project"

## Steps

### 1. Gather inputs from the user

Ask via `AskUserQuestion`:

1. **Project name** — short, lowercase-kebab-case (e.g., `ambidextrous-sofa`). This becomes the directory name.
2. **Initial research question** — one sentence. Goes into `goals.md`. The user can refine later.
3. **Strict mode** — strict (default) or pragmatic. Strict means the prover sub-agent must mark every gap with `\unproven{...}` and never hand-wave. Pragmatic allows informal prose for minor steps. Default is **strict** unless the user explicitly says otherwise; this default is recorded in user memory and must be respected.
4. **Parent directory** — where to create the project. Default: current working directory.

### 2. Create the directory structure

Inside `<parent>/<project-name>/`:

```
paper.tex
goals.md
decisions.md
PROJECT_README.md
co-math-config.json
workstreams/
  .gitkeep
references/
  .gitkeep
failed-explorations/
  .gitkeep
.co-math/
  approvals/
    .gitkeep
  workstream-registry.json
.claude/
  settings.json        # per-project hooks (Phase 3 — empty for now)
```

### 3. Populate files from templates

Templates live in this skill's `templates/` directory. For each entry below, Read the template, do placeholder substitution, then Write to the project path:

| Template | Destination in project |
|---|---|
| `templates/paper.tex` | `paper.tex` |
| `templates/goals.md` | `goals.md` |
| `templates/decisions.md` | `decisions.md` |
| `templates/PROJECT_README.md` | `README.md` |
| `templates/co-math-config.json` | `co-math-config.json` |
| `templates/claude-settings.json` | `.claude/settings.json` |

Placeholders to substitute in each file:

| Placeholder | Replace with |
|---|---|
| `{{PROJECT_NAME}}` | the project name |
| `{{RESEARCH_QUESTION}}` | the user's initial question |
| `{{DATE}}` | today's date in YYYY-MM-DD |
| `{{STRICT_MODE}}` | `true` or `false` (lowercase, JSON literal) |

### 4. Initialize the workstream registry

Write `.co-math/workstream-registry.json`:
```json
{
  "project": "<project-name>",
  "created": "<DATE>",
  "strict_mode": <true|false>,
  "next_id": 1,
  "workstreams": []
}
```

### 5. Print next steps to the user

After scaffolding, output a concise message:
- Confirm the directory was created (with absolute path).
- Explain the files: `goals.md` for refining the question, `paper.tex` is the living working paper, `workstreams/` will fill up as the project-coordinator spawns work.
- Tell them to invoke the `project-coordinator` sub-agent (once Phase 2 ships) to start the first workstream, OR — if Phase 2 isn't built yet — to manually edit `goals.md` and start drafting in `paper.tex`.
- Note the verification ladder available to the coordinator: an informal `prover` proof (`\unproven{}` for any gap), or — for results worth machine-checking — a `lean-prover` workstream that formalises the lemma in Lean 4 and verifies it with `lake build`, closing the theorem with `\leanproved{W{NNN}}`. After any proof is APPROVED, a `proof-readability` pass can polish the exposition without touching the mathematics.
- Note that hooks are not yet wired up (Phase 3 deliverable).

## What this skill does NOT do

- It does not start any workstream itself. That is the `project-coordinator` sub-agent's job.
- It does not invoke any agent. Pure scaffolding.
- It does not modify global Claude Code settings, only writes a per-project `.claude/settings.json`.

## Notes on respecting prior user decisions

The default strict_mode value is **always strict**. If the user has previously asked to relax this for a specific project, that is recorded in that project's `decisions.md`, not as a global default. Each new project starts strict.