Math MCP Learning Server vs Oraclaw

optimize_contextual

Select the best option given a numeric context/feature vector, using a LinUCB contextual bandit that learns per-context preferences from optional history. Use when the best choice changes with situational features that vary call-to-call (user/segment attributes, time of day, current regime). Returns the chosen arm with its LinUCB expected reward and confidence width. If you have no per-call features, use optimize_bandit.

optimize_cmaes

[Premium] Optimize N continuous parameters against a weighted-sum objective using CMA-ES, suited to non-convex/noisy/gradient-free landscapes. Use for hyperparameter search, simulator calibration, or control-policy tuning where you supply per-dimension objective weights. Returns the best parameter vector, its objective value, iteration/evaluation counts, and a converged flag; stochastic init means repeated runs may differ. Use optimize_evolve for discrete spaces and solve_constraints for linear/MIP constraints. Premium: needs an ORACLAW_API_KEY OR a per-call x402 payment (no signup).

solve_constraints

[Premium] Solve a linear / mixed-integer / quadratic program with the HiGHS solver and return a provably optimal assignment. Use when your objective and constraints are linear (or quadratic) over named continuous/integer/binary variables: budget allocation, supply or capacity planning with integer counts, allocation with hard caps. Returns solver status (optimal/infeasible/unbounded), the objective value, and the solved value per variable. Use optimize_cmaes for black-box objectives and solve_schedule for task-to-slot assignment. Premium: needs an ORACLAW_API_KEY OR a per-call x402 payment (no signup).

solve_schedule

Assign tasks to time slots to maximize total score by matching each task's energy requirement to a slot's energy level (and respecting duration). Use for deep-work blocking, shift or session planning, or any task-to-slot fit where high-energy work should land in high-energy slots. Returns the assignments, any unassigned task IDs, and a total score. For arbitrary linear constraints use solve_constraints; for routing use plan_pathfind.

analyze_graph

[Premium] Compute structural metrics of a directed weighted graph: PageRank centrality, Louvain community clusters, an optional critical path between two given nodes, and bottleneck nodes. Use to find the most influential nodes, cluster a dependency/knowledge graph, or locate chokepoints in supply or process networks. Returns per-node PageRank and community index, cluster summaries, the critical path with its weight, and bottlenecks. For a single source-to-goal route, use plan_pathfind (free). Premium: needs an ORACLAW_API_KEY OR a per-call x402 payment (no signup).

analyze_risk

[Premium] Compute portfolio Value-at-Risk and Conditional VaR (Expected Shortfall) from a historical [asset][time] return matrix and portfolio weights, accounting for cross-asset correlation. Use to size downside risk on a weighted multi-asset book, attribute risk, or run drawdown scenarios with auditable inputs. Returns VaR and CVaR (loss as a positive number) at the requested confidence, plus expected return, volatility, and the horizon used. To sample outcomes from a parametric distribution instead, use simulate_montecarlo. Premium: needs an ORACLAW_API_KEY OR a per-call x402 payment (no signup).

score_convergence

Score how strongly multiple independent sources agree on a single event's probability, using Hellinger-distance agreement plus penalties for dispersion/uncertainty and a freshness weight (recency, source volume, and confidence). Use to fuse 0..1 estimates from polls, prediction markets, or model outputs into one number. Returns a 0..1 convergence score, the volume-weighted consensus probability, source count, and component breakdown. To combine N point predictions instead, use predict_ensemble.

predict_forecast

[Premium] Forecast the next N values of one evenly-spaced numeric time series using ARIMA (non-seasonal trend) or Holt-Winters (additive seasonal, set seasonLength). Use for short-to-medium horizon point forecasts of demand, KPIs, or capacity. Returns the point forecast array plus lower/upper confidence bands and the fitted model description. ARIMA requires at least 20 observations; Holt-Winters needs at least 2 x seasonLength. To flag outliers instead of projecting, use detect_anomaly. Premium: needs an ORACLAW_API_KEY OR a per-call x402 payment (no signup).

detect_anomaly

[Premium] Flag outlier points in a numeric series using a Z-score test (parametric, assumes near-normal) or IQR test (robust to skew/heavy tails). Use for metric monitoring, fraud/abuse signals, sensor noise, or quality control. Returns each anomaly's index, value, and score, plus the underlying statistics (mean/stdDev/threshold for Z-score; q1/q3/IQR/bounds for IQR) and an anomaly count. To project a series forward instead, use predict_forecast. Premium: needs an ORACLAW_API_KEY OR a per-call x402 payment (no signup).

plan_pathfind

Find the shortest path (or k-shortest paths) between a start and end node in a weighted directed graph using A* with selectable heuristic (zero=Dijkstra, time, cost, risk, weighted) and Yen's algorithm for alternatives. Use for routing, dependency resolution, or 'how do I get from X to Y' over a graph; set kPaths>1 for alternatives. Returns the path node IDs, total cost, a time/cost/risk breakdown, nodes explored, and a found flag. For centrality/communities use analyze_graph; for task-to-slot assignment use solve_schedule.

simulate_montecarlo

Draw N samples from one parametric distribution (normal, lognormal, uniform, triangular, beta, or exponential) and summarize the resulting spread. Use to quantify uncertainty around a single random factor: an NPV under an uncertain growth rate, a latency tail, or a reserve estimate. Returns the mean, standard deviation, p5/p25/p50/p75/p95 percentiles, a histogram, and the iteration count; each call re-samples (non-deterministic) and is capped at 2000 iterations. For correlated multi-asset risk, use analyze_risk.