Livia is a browser-based workbench for building and running quantitative models in Perceptual Control Theory, in the tradition of Powers (1978), Quantitative analysis of purposive systems. A model is written as explicit equations with units and stated assumptions. Livia runs it under matched interventions, shows every signal separately, and stores each run as an immutable record that can be exported, checked for tampering and recomputed by someone else.
It is part of the QPCT project. Perceptual Control Theory is the work of William T. Powers (1926–2013); Livia is a tool for testing models in that theory, not an extension of it.
| 1 · Model | Write the controller as equations: perception, reference, comparator, output, environment. Every relation has units, a meaning and an assumption record. Livia checks dimensions and refuses an algebraic loop rather than inserting a hidden delay. |
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| 2 · Experiment | One run computes three conditions, each with a matched undisturbed counterpart: the loop live, the output held, and the feedback held. All three share the same state at the moment of the intervention, so the only difference is the cut. |
| 3 · Observe | Actual perception, comparator input, internal error, controller state and applied output are plotted separately, and any moment can be inspected with the equation that produced it. |
| 4 · Compare | Branch the model, change one assumption, and run it under the same protocol. Earlier runs stay unchanged; the comparison shows the structural difference and the pointwise difference in behaviour. |
| 5 · Export | Download the whole notebook as one bundle: models, protocols, trajectories, metrics, figures and the exact source code that ran them, with a script that recomputes every run without the browser. |
Reproducing a run recomputes it from its stored inputs and compares the two records under six named checks: run status, model and protocol, source and dependencies, trajectories, metrics, and criterion evaluation. A run recomputed with a different engine version is labelled a cross-version comparison, never a strict reproduction.
Exported bundles are tamper-evident. Every file must match the manifest, nothing may be missing or added, and every file that duplicates the project data must match it exactly. Change one number and Livia refuses the bundle. Between version 0.1.0 and 0.1.1 the equations and the solver did not change, and the calibration model reproduces the earlier results exactly.
Losing regulation when the loop is cut is reported in neutral words, regulation criterion met or not met, because in Perceptual Control Theory that loss is often exactly what the model predicts.
Livia computes the consequences of a model you write. It does not import participant data, fit parameters, or validate a psychological mechanism. A model that regulates well in Livia shows what the equations imply, not what a person does.
Version 0.1 supports up to three scalar controllers, three environmental quantities and six dynamic states, deterministic non-stiff equations, and one-parameter sensitivity runs of at most 25 values. There is no stochastic mechanism and no model of reorganisation.
Hashes show that a bundle has not changed since it was exported. They are not a public preregistration and not a third-party certificate.
Livia runs at its own address, qpct.perceptualcontroltheory.org, behind a password while a small group of testers works with it. Public access will follow once their feedback is in.
If you work with control models in research or teaching and want to try it, write to [email protected].
The software is free for noncommercial use under the PolyForm Noncommercial License 1.0.0, including research, teaching, personal study, and use by universities, public research organisations and non-profits. Documentation and example models are licensed under CC BY 4.0. Commercial use, including deployment inside a company or in a paid product or service, requires a commercial licence from the author.
This release. Diener, Ł. (2026). Livia: a computational workbench for Perceptual Control Theory (version 0.1.1) [Software]. Zenodo. https://doi.org/10.5281/zenodo.23589119
All versions. https://doi.org/10.5281/zenodo.23541392 · version 0.1.0, 21 October 2026: https://doi.org/10.5281/zenodo.23541393