Metasignal is an open-source Python package for signal detection theory (SDT) and metacognitive measurement. It implements the 17 metacognitive measures evaluated by Rahnev (2025), together with the reference variables d' (perceptual sensitivity), response criterion c (response bias), and mean confidence. The 17 measures comprise three meta-d' family estimates, meta-d', M-ratio, and M-difference; four nonparametric Type-2 measures, the Type-2 area under the receiver-operating-characteristic curve (AUC2), Gamma, Phi, and delta confidence, together with their eight SDT-normalized ratio and difference forms; and two model-based measures, meta-noise and meta-uncertainty. A single function computes the complete set from trial-level stimulus, response, and confidence arrays. `metasignal` currently supports binary (two-alternative) discrimination tasks, in which each trial's stimulus and response are coded with exactly two categories. The package also provides a command-line interface, group summaries, bootstrap confidence intervals, permutation tests, optional hierarchical Bayesian models, and information-theoretic measures. `metasignal` unifies these measures in a single platform to encourage broader metacognition research and adoption in decision-making studies.
Physical sensing and actuation noise floors should inform how much belief resolution a decision-making system can reliably use. We introduce Finite Reliability Representations (FRR), a framework for covering belief spaces by reliability cells: regions within which the optimal action-value function Q*(b,u) varies by at most a tolerance epsilon, uniformly over actions. The framework is formulated on beliefs rather than states and uses a cover rather than an equivalence quotient, because approximate decision-closeness is not transitive in general. A central technical point is that noisy Bayesian updates should not be treated as globally contractive on arbitrary beliefs. We therefore separate three objects: the fixed-observation filter map, the predictive observation law, and the controlled belief-transition kernel. For nonlinear continuous-state systems, FRR is obtained under a reachable-set Lipschitz modulus for the belief-transition kernel. For finite-state POMDPs, the same construction becomes exact on the belief simplex: prediction is linear, Bayesian correction is a normalized positive linear map, sensor noise enters through observation-distribution distinguishability, and actuation uncertainty enters through an action-execution channel. Under the corresponding action-value Lipschitz condition, an FRR cover supports a cell-constant policy whose suboptimality is bounded by 2 epsilon/(1 - gamma). We also introduce reliability entropy, the logarithm of the minimal number of reliability cells, as a measure of certified decision-relevant belief complexity. The framework distinguishes representation sufficiency from fundamental performance floors imposed by sensing, process, and actuation noise. It applies to finite POMDPs, linear-Gaussian filters, locally linearized nonlinear filters, and particle-filter implementations through analytic or empirical certification of reliability cells.