Creative-Intelligence

This project explores mathematical creativity in AI—whether it can move beyond solving existing problems to originate new ideas and expand the frontiers of mathematics alongside humans.

Current Focus

1. Tracing the Origins of Mathematical Concepts Study how important mathematical concepts emerged, including their historical context, the problems they addressed, the limitations they overcame, and their influence on mathematics and related fields.

2. Exploring Mathematical Creativity in AI Use frontier AI models to investigate whether they can move beyond solving existing problems and demonstrate genuine mathematical creativity, including the ability to generate new concepts, perspectives, and approaches.

Mathematical Object Origin Archive Runner

This runner supports the first research direction by generating and verifying origin archives for mathematical concepts and objects. It processes an ordered collection serially, gives each object its own Moonshine project and session, and writes the final Markdown archive only after verification passes.

Moonshine dependency

This is a Moonshine runtime extension, not a standalone application. Install, initialize, and configure Moonshine by following the Moonshine repository.

Place this repository directly inside the initialized Moonshine runtime home, not inside the Moonshine source-code package. With the default Moonshine setup, the runtime home is ~/.moonshine. If Moonshine was initialized with --home, use that directory instead.

<MOONSHINE_HOME>/
├── config.yaml
├── config/
├── projects/                              # Moonshine projects created for individual objects
├── sessions/                              # Moonshine session records
├── skills/
│   └── installed/                         # Runtime copies installed automatically by the runner
└── Creative-Intelligence/                 # This GitHub repository
    ├── README.md
    ├── run_archive.py
    ├── archive-format-specification.md
    ├── tests/
    │   └── test_run_archive_offline.py
    ├── skills/
    │   ├── math-object-origin-archive/
    │   │   └── SKILL.md
    │   └── verify-math-object-origin-archive/
    │       └── SKILL.md

config.yaml and the other runtime directories are created by python -m moonshine init. The runner treats its parent directory as MOONSHINE_HOME and automatically installs the two included skills into that runtime when it starts.

Input

Create a UTF-8 JSON file containing an ordered list of objects. The JSON file may be stored anywhere:

{
  "format": "math-object-origin-archive-v1",
  "objects": [
    {
      "name": "Bochner formula",
      "materials": [
        "materials/bochner-notes.md"
      ]
    },
    {
      "name": "Riemann curvature tensor",
      "materials": []
    }
  ]
}

materials is optional and accepts local UTF-8 text or Markdown files. Relative material paths are resolved from the directory containing the input JSON file, not from the repository or runtime home.

Run

Run commands from the initialized Moonshine runtime home. Replace <MOONSHINE_HOME> with the runtime directory used during Moonshine initialization:

cd <MOONSHINE_HOME>

This must be the same directory previously passed to python -m moonshine --home <MOONSHINE_HOME> init, or the runtime directory created by the default initialization.

Process every object serially:

python Creative-Intelligence/run_archive.py path/to/concepts.json

Optionally validate the input without starting Moonshine sessions:

python Creative-Intelligence/run_archive.py path/to/concepts.json --validate-only

Start from a specific 1-based index:

python Creative-Intelligence/run_archive.py path/to/concepts.json --start-index 5

Retry objects previously marked as failed:

python Creative-Intelligence/run_archive.py path/to/concepts.json --retry-failed

Optional flags include --max-turns N and --verbose. Run the same command again to resume the saved Moonshine sessions. After a run has started, keep its input JSON unchanged; use a new, uniquely named JSON file for another queue.

Generated files

The following directories are created automatically when the runner is used and are not part of the initial repository structure:

• Final archives: Creative-Intelligence/archives/<input-name>/
• Queue state and project/session associations: Creative-Intelligence/runs/<input-name>.state.json

Offline regression tests

The deterministic runner contracts can be tested from a standalone checkout without an initialized Moonshine runtime, provider credentials, network access, or model calls. The test harness uses only the Python standard library and provides import-time stubs for the narrow Moonshine symbols required to load run_archive.py.

Run from the Creative-Intelligence repository root:

python -m unittest discover -s tests -p "test_*.py" -v

These tests cover runner-owned deterministic behavior such as queue validation, immutable queue state, format-placeholder checks, verifier-output integrity, archive overwrite protection, and provider preflight logic. They do not simulate Moonshine agent execution, session storage, MCP tools, or real verification-provider behavior; those remain runtime integration concerns.