Execute auditable quantitative research across preregistered study design, statistical inference, numerical verification, dimensional analysis, uncertainty propagation, counterexample search, and formal proof. Use when a scientific or mathematical question…
Compare finite actions under uncertainty with explicit states, loss, utility or risk-neutral payoff, priors, experiment likelihoods, and a declared decision criterion. Use for Bayes risk, expected utility or payoff, pure-action minimax, minimax regret,…
Compare finite actions under uncertainty with explicit states, loss, utility or risk-neutral payoff, priors, experiment likelihoods, and a declared decision criterion. Use for Bayes risk, expected utility or payoff, pure-action minimax, minimax regret,…
Start or continue a task-scoped scientific workbench in Codex. Invoke when the user explicitly uses $codex-science or asks to start, activate, enable, load, or enter Codex Science, including "Codex Science 시작" or "Codex Science 활성화". Also invoke automatically…
Inspect and use the local computer as a reproducible scientific workbench across shell, Python, R, Julia, Jupyter, containers, CPUs, and GPUs. Use when a scientific task needs local files, code execution, package or environment setup, data conversion,…
Audit equations, models, conversions, scales, and limiting cases with explicit dimensions and units, plus executable SI dimensional-consistency and conversion receipts. Use for physical quantities, empirical correlations, nondimensionalization, scaling laws,…
Quantify and review measurement or model-input uncertainty with explicit measurands, calibration, Type A and B components, covariance, linear sensitivities, seeded Monte Carlo propagation, nonlinear disagreement, and machine-readable uncertainty receipts.
Formalize mathematical statements and produce auditable kernel-check receipts in an existing Lean 4 workspace. Use for theorem-statement audits, proof repair, definition design, tactic or term proofs, dependency minimization, axiom inspection, and…