Axiomize

Reproducible scientific modeling that survives contact with reality. Axiomize turns a vague idea into an explicit, versioned mathematical model, validates it dimensionally and numerically, and exports an artifact someone else can re-run years from now.

This is not the numerical-methods library. That door is scientific-computing-system. Axiomize is the modeling layer: mandatory units, a versioned Model IR, and export to SBML, CellML, and Modelica. The MCP server is axiomize mcp.

mcp-name: io.github.Furox-Art/axiomize

Current package line: 1.12.5 on PyPI and npm.

Documentation: furox-art.github.io/axiomize · Changelog: CHANGELOG.md · Roadmap: ROADMAP.md · Security: SECURITY.md · Contributing: CONTRIBUTING.md · Code of conduct: CODE_OF_CONDUCT.md · Cite: CITATION.cff

Why

I got tired of scientific models that live in Jupyter notebooks and die there.

Someone writes a beautiful simulation, it works on their machine, they graduate or change jobs, and six months later nobody can run it. The dependencies are broken, the data is missing, and the "documentation" is a 47-cell notebook with no explanation.

Axiomize forces models to be explicit, versioned, testable code instead of exploratory spaghetti. Every assumption is written down. Every parameter carries a unit. Every result carries enough provenance that another person, on another machine, can reproduce it.

Related MCP server: SciMath MCP

Who it is for

Not a fit: if you want a black-box predictor with no inspectable assumptions, or if you need the engine to make scientific claims for you without a human in the loop.

Install

pip install axiomize

Optional extras: pip install "axiomize[full]" for PyMC/JAX Bayesian sampling.

The playground extra installs gradio and pandas but ships no UI: playground/app.py is not in the wheel or the sdist, so pip install "axiomize[playground]" alone leaves you with dependencies and nothing to run. To use it, get the file from the repository:

git clone https://github.com/Furox-Art/axiomize
pip install "axiomize[playground]"
python axiomize/playground/app.py

Python in five minutes

Declare the model, then let Axiomize check it. Units are mandatory, so dimensional mistakes fail loudly instead of producing a meaningless number. This block is the model in examples/quickstart_sir.py, field for field.

from axiomize.general_engine import simulate_model
from axiomize.model_ir import ModelIR

model = ModelIR.from_dict({
    "schema_version": "1.0",
    "name": "sir-outbreak",
    "domain": "epidemiology",
    "family": "ode",
    "independent_variable": "t",
    "independent_unit": "day",
    "variables": [
        {"name": "S", "unit": "person", "initial": 990.0, "bounds": [0.0, None]},
        {"name": "I", "unit": "person", "initial": 10.0, "bounds": [0.0, None]},
    ],
    "parameters": [
        {"name": "beta", "unit": "1/day", "value": 0.3, "bounds": [0.0, None]},
        {"name": "gamma", "unit": "1/day", "value": 0.1, "bounds": [0.0, None]},
        {"name": "N", "unit": "persons", "value": 1000.0},
    ],
    "equations": [
        {"target": "S", "expression": "-beta*I*S/N", "kind": "derivative"},
        {"target": "I", "expression": "beta*I*S/N - gamma*I", "kind": "derivative"},
    ],
    "constraints": [
        {"name": "cases_nonnegative", "expression": "I", "relation": "ge",
         "threshold": 0.0, "scientific_basis": "case counts cannot be negative"},
    ],
    "assumptions": ["closed population of 1000", "homogeneous mixing"],
})

result = simulate_model(model, t_span=(0.0, 30.0), points=4)
print(f"status: {result['status']}")
print(f"solver: {result['solver']['backend']} / {result['solver']['method']}")
print(f"days:   {result['time']}")
print(f"infected: {[round(v, 3) for v in result['states']['I']]}")
print(f"checks: {result['validation']['status']} ({len(result['validation']['checks'])} of them)")

Real output, and byte-identical to python examples/quickstart_sir.py:

status: PASS
solver: scipy / DOP853
days:   [0.0, 10.0, 20.0, 30.0]
infected: [10.0, 65.393, 239.869, 290.024]
checks: PASS (25 of them)

CLI in five minutes

Every command prints JSON you can pipe.

# What is actually installed, and is it usable? Backends report honestly.
axiomize capabilities

# Clarify a vague idea before any numbers get committed.
axiomize intake "Reduce traffic congestion in a mid-size city"

# Check a model against closed-form theory, not just vibes.
axiomize-validate --model sir --beta 0.3 --gamma 0.1

axiomize-validate output on those inputs:

=== SIR validation ===
horizon                = 180 days  (final-size theory is the t->infinity limit)
R0                     = 3.000  (outbreak)
Peak infected          = 300,465 at day 61.4
Final size (simulated) = 0.9404
Final size (theory)    = 0.9405
Theory match           = True

--- sanity checks ---
population_conserved                PASS
compartments_nonnegative            PASS
R_monotonic_increase                PASS

The two flags that matter once you leave the reference model are --input-json (the Model IR request as a file) and --approve-heavy (authorizes repeated refinement runs):

# Without --approve-heavy the study is refused rather than run silently.
axiomize model --action numerical-verify --input-json request.json
# status: APPROVAL_REQUIRED, study: solver_tolerance_refinement

axiomize model --action numerical-verify --input-json request.json --approve-heavy
# status: PASS, uncertainty_separation.numerical: 6.6100987239990846e-11

Step-by-step versions of all of this, with the request files, are in docs/quickstart.md.

Surface map

The engine is 68 public modules behind four interfaces. This README names the whole CLI and the shape of the two servers; the per-module detail belongs in docs/integrations.md.

Console scripts (8)

axiomize subcommands (14)

intake · policy · model · clean-data · compare-runs · solve · fit · validate · tools · capabilities · reproduce · benchmark · serve · mcp

tools and capabilities report backend availability; policy reports what the agent is allowed to spend; reproduce and compare-runs work on stored run directories.

axiomize model --action (16)

MCP and REST

The MCP server exposes 34 tools named axiomize.<verb>. axiomize.model_* mirrors the model --action values above; the unprefixed names (solve, fit_model, cross_validate, sensitivity_analysis, uncertainty_analysis, falsify, compare_models, intake, workflow_policy, clean_data, compare_runs, experiment_design, inspect_run, reproduce, get_capabilities, list_tools, select_tools) cover the surrounding workflow. Enumerate them rather than trusting a list:

axiomize mcp        # stdio transport; send tools/list over stdin

The REST server serves 30 route handlers (26 POST, plus GET /tools, /capabilities, /workflow-policy and /runs/{id}) under a /v1 prefix, on loopback by default:

axiomize serve --port 8765
curl -s http://127.0.0.1:8765/v1/capabilities

Both surfaces are larger than any README can enumerate honestly, which is why the naming convention matters more than the list. Both counts come from the installed handlers.

Model export formats

axiomize model --action export --input-json request.json dispatches on the "format" field. What actually returns PASS for a given model:

LaTeX is not in this dispatch chain. latex, tex and pdf raise ValueError: format must be json, python, yaml, sbml, or cellml. Use axiomize-to-latex on a written report instead.

Content in the repository

server.json is what the MCP registry reads to publish axiomize mcp; its mcp-name line is repeated at the top of this README for clients that scrape it.

Adoption path

1. Try it on something you already believe. Recreate a model you trust with axiomize-validate. If the engine disagrees with a result you can defend, stop here and open an issue.

2. Move one real question onto Model IR. Declare units and constraints explicitly. The dimensional checks are where the value shows up first.

3. Gate the expensive steps. Discretized families return APPROVAL_REQUIRED until you pass --approve-heavy. Approval authorizes compute; it never disables a resource ceiling.

4. Export something portable. axiomize model --action export emits canonical IR JSON, and SBML, CellML or Modelica for supported models, so the artifact outlives this library.

5. Wire it into review. Ship the exported IR and the validation record alongside the result, not just a figure.

What it actually does

• Validates dimensional consistency, so you cannot add meters to seconds

• Enforces scientific constraints as named, justified checks rather than prose

• Separates numerical error from stochastic variability before claiming convergence

• Compares candidate model families and records why one was chosen

• Exports to JSON, Python, YAML, notebooks, SBML Level 3, CellML 2.0, Modelica, GraphML, Graphviz DOT and a SHA-256 portable bundle; see the format table for which of those are conditional

• Converts written reports to LaTeX via axiomize-to-latex, which is a separate path

• Keeps an integrity-checked run ledger, so a stored result can be verified before use

Honest limits

• It does not make a bad model good. It makes a bad model fail loudly.

• Bayesian sampling needs the full extra (PyMC/JAX); FEM needs FEniCS/DOLFINx. Both are reported as unavailable rather than silently substituted.

• Benchmark results grade report structure in blind runs, not modeling correctness. Only the table carrying script, case-set and commit hashes is reproducible; the older waves are kept as history and cannot be rerun.

• Worked examples use illustrative parameter ranges labelled lit. / data / est.. No example cites an external source, so treat the numbers as reading material rather than literature-backed results.

• Generated-code execution and theorem elaboration are not an OS sandbox. See SECURITY.md.

Documentation

• Quickstart and workflow: furox-art.github.io/axiomize

• Worked examples: example gallery, or the 19 files in examples/

• Domain packs (which lenses matter per field): packs/domain-packs.md

• Agent integration (MCP, REST, CLI): docs/integrations.md

• Portable export formats: docs/portable-export.md

• Trust boundaries and reporting: SECURITY.md, docs/security.md

• Agent skill pack: skills/axiomize/SKILL.md, plus the 15 perspective lenses

npm

npx axiomize works and forwards to python -m axiomize.cli, so it needs Python and pip install axiomize underneath; it is not a standalone binary. npm 1.12.2 is published and broken (index.js had a syntax error); 1.12.4 is the first working release. PyPI 1.12.4 carries PEP 740 attestations, the npm tarball does not. Full detail, including verification commands and how to tell registry metadata signatures from provenance: docs/documentation.md.

License

MIT. Use it, break it, fix it.