Occam MCP Server

Evolutionary Symbolic Regression (PySR). Discovers algebraic equations y = f(x1, x2, ...) from feature/target data. Returns a Pareto front ranked by the complexity/accuracy tradeoff. Slower than SINDy (10-60s); searches often terminate early on convergence. For differential equations from time series, use sindy_run instead. Pricing: free tier up to 100 rows × 8 features, 60s timeout. Beyond that, $0.25 + $0.03 per 100 extra rows + $0.01 per extra feature squared, timeout up to 300s (5 min), via x402 (USDC on Base) or MPP/Stripe. MPP/Stripe adds a flat $0.35 per-transaction fee (Stripe processing), so the MPP challenge amount in a `payment_required` response is $0.35 higher than the x402 amount for the same base price; x402 gets the lower rate. Omit `payment` for free-tier requests; paid requests without a valid credential receive a `payment_required` result with pricing and accepted schemes. Full pricing: occam://pricing Advisory limits: jobs over 50,000 rows or 20 features are accepted but may not converge; response carries a top-level `warning`. Operators: fixed supported set only — custom operators (e.g. 'inv(x) = 1/x') are rejected. Unary: sin, cos, tan, exp, log, log2, log10, sqrt, abs, sinh, cosh, tanh. Binary: +, -, *, /, ^. See also prompt `supported_operators`. Loss metric: `loss` (in `pareto_front[].loss` and `best_loss`) is mean squared error between model prediction and `y` on the full training set — not RMSE, and not normalized by Var(y). A threshold appropriate for one dataset scales with y's magnitude, so set `loss_threshold` with that in mind (e.g. for y values near 1.0, 1e-6 is a tight fit; for y near 1000, the equivalent is 1.0). Early termination: set `loss_threshold` to stop at your noise floor. The server also stops when the search stalls (<1% improvement in the last third of the budget); disable with `stall_detection=false`. Response `stop_reason` is one of: loss_threshold, stall, timeout, natural. If `feature_names` is supplied, its length must equal the number of columns in `X`; a mismatch is rejected with a validation error. Follow-up: call `pysr_uncertainty` with a chosen expression and the same dataset for bootstrap confidence intervals on its fit constants and optional prediction bands. Rate limit: 10 requests/hour per IP, 200/hour global, max queue depth 20 (shared with sindy_run and pysr_uncertainty). Response (success) includes `pareto_front[]` (each with `complexity`, `loss`, `expression`, `expression_latex`), `best_expression`, `best_expression_latex`, `best_loss`, `best_complexity`, `stop_reason`, `elapsed_seconds`, `queue_seconds` (>0 = server saturated; use as backoff signal), optional `warning`, optional `_meta` (MPP receipt). Full response and payment-required schemas: occam://tool-schemas Example request: X=[[0.0], [1.0], [2.0], [3.0]], y=[1.0, 3.0, 5.0, 7.0], feature_names=["x"], max_complexity=10, timeout_seconds=15 Policy: occam://privacy-policy — Citation: occam://citation-info

Bootstrap confidence intervals for the numeric constants of a frozen expression, plus optional prediction bands on an x-grid. Typical flow: call pysr_run, pick an expression from the response (best_expression or a pareto_front entry), pass it back here with the same dataset to get CIs on its fit constants. Returns frequentist bootstrap confidence intervals, not Bayesian credible intervals — posterior inference over expression structures is an open research problem. This tool freezes the expression chosen by the caller and bootstraps only its numeric constants; uncertainty about *which* expression is correct is not quantified. Bootstrap semantics: - If y_sigma is supplied, uses parametric bootstrap (y_b = y + Normal(0, y_sigma)). CI reflects user-stated measurement noise. - Otherwise uses residual bootstrap: fit once, resample residuals. CI reflects estimated-from-residuals noise. Only Float constants in the expression become free parameters. Integers stay structural (the 2 in x**2 is a function-class choice, not a fit constant). Expressions with no Float constants (e.g. "x + y") will be rejected with a validation error. Expression grammar: the `expression` string is parsed by sympy. Accepted operators are the same set pysr_run emits: unary `sin`, `cos`, `tan`, `exp`, `log`, `log2`, `log10`, `sqrt`, `abs`, `sinh`, `cosh`, `tanh`; binary `+`, `-`, `*`, `/`, `^` (or `**`). Whitespace and parenthesization are free. Every free symbol in the expression must correspond to an entry in `feature_names` — an unrecognised symbol is silently treated as a fresh sympy Symbol and the fit will fail downstream rather than reject early. Parse failures (syntax errors, malformed operators) surface as tool errors. If `feature_names` is supplied, its length must equal the number of columns in `X`; a mismatch is rejected with a validation error. Pricing: always free, regardless of dataset size. This tool has no `payment` parameter and is never subject to the x402/Stripe gate. Large bootstrap jobs still count against the shared rate limit below, so budget `n_resamples` accordingly. Rate limit: 10 requests/hour per IP, 200/hour global, max queue depth 20 (shared with sindy_run and pysr_run).

Request a feature that Occam doesn't support yet. Use this when you need a capability that Occam doesn't currently offer. Requests are logged and used to prioritize development. Rate limit: 5 requests/hour per IP, 50/hour global — stricter than the compute tools' 10/hour to prevent log flooding. Descriptions longer than 500 characters are truncated.

Sparse Identification of Nonlinear Dynamics (SINDy). Recovers governing differential equations (dx/dt = f(x)) from time series data. Returns human-readable sparse expressions. Fast (seconds). For algebraic y = f(x) relationships without time structure, use pysr_run instead. Pricing: free tier up to 100 rows and 8 variables. Beyond that, $0.05 + $0.01 per 100 extra rows + $0.01 per extra variable squared, via x402 (USDC on Base) or MPP/Stripe. MPP/Stripe adds a flat $0.35 per-transaction fee (Stripe processing), so the MPP challenge amount in a `payment_required` response is $0.35 higher than the x402 amount for the same base price; x402 gets the lower rate. Omit `payment` for free-tier requests; paid requests without a valid credential receive a `payment_required` result with pricing and accepted schemes. Full pricing table as structured JSON: occam://pricing Advisory limits: jobs over 500,000 rows or 50 variables are accepted but may not converge within the time budget; the response carries a top-level `warning` the agent should surface and treat as tentative. If `feature_names` is supplied, its length must equal the number of data columns; a mismatch is rejected with a validation error. Rate limit: 10 requests/hour per IP, 200/hour global, max queue depth 20 (shared with pysr_run and pysr_uncertainty). Response (success) includes `equations[]` (each with `variable`, `equation`, `expression`, `expression_latex`, `r2`), `library_terms`, `nonzero_terms`, `elapsed_seconds`, `canonical_match` (dict with `system`, `form`, `variable_map`, `parameter_map`, `confidence` if the discovered system matches one of Lorenz / Lotka-Volterra / Van der Pol / Duffing; `null` otherwise), optional `warning`, optional `_meta` (MPP receipt on paid calls). Full response and payment-required schemas: occam://tool-schemas Example request: data=[[1.0, 0.0], [0.95, -0.31], [0.81, -0.59]], t=[0.0, 0.1, 0.2], feature_names=["x", "y"], poly_degree=2, threshold=0.1 Policy: occam://privacy-policy — Citation: occam://citation-info