# SR-MCP

> Symbolic regression as a service via Model Context Protocol (MCP)

SR-MCP exposes two symbolic regression tools to MCP-compatible AI clients:

## Tools

### sindy_run
Sparse Identification of Nonlinear Dynamics. Discovers differential equations from time series data.
- Input: time series array + timestamps
- Output: sparse governing equations as human-readable expressions
- Speed: seconds
- Free tier: 100 rows, 8 variables (no payment needed)
- Paid tier: up to 500,000 rows, 50 variables
- Advisory: jobs exceeding 500,000 rows or 50 variables will be accepted but
  are unlikely to converge within the time budget

### pysr_run
Evolutionary symbolic regression via SymbolicRegression.jl.

Supported operators (fixed set; custom operators NOT supported):
- Unary: sin, cos, tan, exp, log, log2, log10, sqrt, abs, sinh, cosh, tanh
- Binary: +, -, *, /, ^

- Input: feature matrix X + target vector y
- Output: Pareto front of expressions (complexity vs accuracy tradeoff),
  plus a `stop_reason` field ("loss_threshold", "stall", "timeout", or "natural")
- Speed: 10-60 seconds; often less when the search converges early
- Optional `loss_threshold`: stop once best loss ≤ this value (useful if you
  know your noise floor)
- Optional `stall_detection` (default true): stop if best loss has not improved
  by more than 1% during the last third of the timeout budget
- Free tier: 100 rows, 8 features, 60s timeout
- Paid tier: up to 50,000 rows, 20 features, 300s (5 min) timeout
- Advisory: jobs exceeding 50,000 rows or 20 features will be accepted but
  are unlikely to converge within the time budget

### pysr_uncertainty
Bootstrap confidence intervals for the numeric constants of a frozen
expression returned by pysr_run, plus optional prediction bands.

**Frequentist bootstrap CIs, not Bayesian credible intervals.**
Posterior inference over expression structures is an open research
problem — this tool fixes the expression chosen by the caller and
bootstraps only its numeric constants.

- Input: expression string (from pysr_run), X, y, optional y_sigma,
  n_resamples, alpha, x_grid
- Output: per-parameter CI + optional prediction band at x_grid points
- Speed: 1-10 seconds depending on n_resamples and expression size
- Parametric bootstrap when y_sigma is supplied; residual bootstrap otherwise

## Pricing

Free tier: both tools accept up to 100 rows and 8 variables/features at no charge.

Beyond the free tier, pricing is:
  baseline + $row_price × (rows − 100) / 100 + $var_price × (vars − 8)²

| Parameter      | sindy_run | pysr_run |
|----------------|-----------|----------|
| Baseline fee   | $0.05     | $0.25    |
| Per 100 rows   | $0.01     | $0.03    |
| Per extra var² | $0.01     | $0.01    |

Payment methods:
- x402: USDC on Base (on-chain, lower rate)
- MPP/Stripe: card payment via Shared Payment Tokens (adds $0.35 surcharge)

When payment is required, the tool returns a `payment_required` result with
pricing details and payment options. Retry with the `payment` parameter.

## Integration

Remote endpoint (streamable HTTP):
```
https://occam.fit/mcp/
```

Add to Claude Desktop `claude_desktop_config.json`:
```json
{"mcpServers": {"occam": {"type": "streamable-http", "url": "https://occam.fit/mcp/"}}}
```

## Links

- Full reference (parameters, response schemas, examples): https://occam.fit/llms-full.txt
- Repository: https://github.com/codereclaimers/sr-mcp
- MCP Protocol: https://modelcontextprotocol.io