labyrinth-exploration

Labyrinth exploration

A skill for Codex and Claude Code, for open-ended research: mathematics, theoretical science, algorithms, anywhere the goal is to find out what is still unknown.

The skill treats a research programme as the exploration of a labyrinth. Your agent keeps an exact map of where you are:

• which corridors are charted (proved, or computed exhaustively);
• which are walled off (refuted, or impossible);
• which doors are visible but not yet entered (questions, conjectures);
• where it is still dark.

Every session starts from that map and leaves it changed. A refutation counts as progress: it turns a hoped-for corridor into a wall and usually reveals a new door.

• Proof stays apart from speculation. Every claim carries a tier, from T1 (proved in the literature) to T6 (a hunch). Nothing below T3 is ever cited as a fact, and hunches are kept on the board on purpose, clearly marked.
• "How much is left" becomes a number. For each size, every admissible value is classified as realized, impossible, conditional, conjecturally impossible or unknown. The dashboard shows the resolved share and how it moved over time.
• Nothing is used before it is checked. Results from agents or external models pass an independent referee, with its own code, before they enter the notes.
• It scales. For many open problems at once, it runs campaigns: attack agents, a literature agent, a referee for every report, writers who draft on a copy, and you (or the main agent) as the coordinator.

The method was developed on a research programme in pure mathematics in September and October 2026. The lessons from that programme are part of the skill.

Quick start

1. Install the whole repository for your client.

Codex (CLI, desktop app or IDE extension):

mkdir -p "$HOME/.agents/skills"
git clone https://github.com/nasqret/labyrinth-exploration "$HOME/.agents/skills/labyrinth-exploration"

For a project-scoped Codex installation, clone under .agents/skills/labyrinth-exploration in that project's repository instead. See the Codex guide for resource paths, native subagents, permissions and session handoff.

Claude Code:

mkdir -p "$HOME/.claude/skills"
git clone https://github.com/nasqret/labyrinth-exploration "$HOME/.claude/skills/labyrinth-exploration"

Run your client from the research project, not the installed skill directory. In Codex, invoke $labyrinth-exploration or describe a matching task; in Claude Code, invoke /labyrinth-exploration or describe the task. Codex detects new skills automatically; restart if it does not appear. Start a new Claude Code session after installing.

Both clients use the same SKILL.md, references, templates and data formats. No MCP server, client SDK or third-party Python package is needed for the engine or initial example.

2. See a complete map. The repository includes a small public example: how many triangles can a graph on n vertices have? It builds in seconds and needs only Python 3:

LABYRINTH_SKILL_DIR="$HOME/.agents/skills/labyrinth-exploration"  # Codex
# For Claude Code: LABYRINTH_SKILL_DIR="$HOME/.claude/skills/labyrinth-exploration"
LABYRINTH_DEMO_DIR="$(mktemp -d "${TMPDIR:-/tmp}/labyrinth-demo.XXXXXX")"
mkdir -p "$LABYRINTH_DEMO_DIR/labyrinth/dashboard"
cp "$LABYRINTH_SKILL_DIR/templates/lab.py" "$LABYRINTH_DEMO_DIR/labyrinth/"
cp "$LABYRINTH_SKILL_DIR/templates/dashboard.html" "$LABYRINTH_DEMO_DIR/labyrinth/dashboard/template.html"
cp "$LABYRINTH_SKILL_DIR"/examples/triangle-counts/{knowledge.json,events.jsonl,sota.json} "$LABYRINTH_DEMO_DIR/labyrinth/"
python3 "$LABYRINTH_SKILL_DIR/examples/triangle-counts/make_example.py" "$LABYRINTH_DEMO_DIR/labyrinth"
cd "$LABYRINTH_DEMO_DIR"
python3 labyrinth/lab.py check && python3 labyrinth/lab.py build
open labyrinth/dashboard/index.html        # or xdg-open on Linux

3. Use it on your own question. In either client, describe the programme, for example:

I want to understand which values the crossing number takes on cubic graphs of each size. Map what is known, set up the labyrinth for this project, and push the bounds.

The agent reads the skill and sets up labyrinth/ in your repository. It then works in the loop below and leaves a dashboard and a state-of-the-art table behind. More prompts are in examples/prompts.md.

How it works

Each iteration picks one to three doors and explores them with several tool families at once: literature sweeps in the background, small computations, extreme and named examples. It then states a bold conjecture with its test, runs the test, logs the outcome, has it refereed, and updates the map. A refuted claim becomes a dead end with a one-line lesson, followed by the modified statement. When the map stops changing, an escalation ladder takes over: change the tools, the parameter or the extremes, relax a hypothesis, invert the question, import from another community, or launch a broad attack.

The tutorial walks through all of this step by step, on the example.

The map

Tiers

Campaigns

When there are more open doors than one iteration can enter, the skill runs a campaign. One attack agent works on each conjecture, trying at least five perspectives. Each report goes to an independent referee, who returns a verdict per item and c