Use when your human partner has explicitly opted into exploratory or feasibility mode - a compute-heavy simulation, an unproven pipeline, an unbenchmarked solver, an untested cluster job - or when whether the work can run at all is still unknown, when a plan's largest configuration has never been executed, when a…
You MUST use this before any data analysis or investigation - before exploring a dataset, loading or profiling data, running a model, computing a statistic, or testing an idea, and before any outcome data is touched.
Use before running any confirmatory analysis or looking at outcome data, when testing a hypothesis, computing a p-value, or about to claim an effect - locks predictions and decision rules before results are seen.
Select and configure nonlinear solvers for root-finding f(x)=0, optimization min F(x), and least-squares problems — choose among Newton, Newton-Krylov, quasi-Newton (BFGS, L-BFGS), Broyden, Anderson acceleration, and Levenberg-Marquardt methods, configure line search or trust-region globalization, diagnose convergence…
Analyze numerical stability for time-dependent PDE simulations — check CFL and Fourier criteria, perform von Neumann stability analysis, detect stiffness, evaluate matrix conditioning, and recommend explicit vs implicit time-stepping schemes. Use when selecting time steps, diagnosing numerical blow-up or solver…
Extract, analyze, and summarize simulation output data — pull spatial fields at specific timesteps, compute time-series trends and detect steady state, extract line profiles through the domain, generate statistical summaries and distributions, calculate derived quantities (gradients, fluxes, volume fractions…