CALLIOPE · BCOM

We present a practical, falsifiable protocol for detecting algorithmic signatures of agenthood in artificial life systems. Building on the AIT Regulator framework, which formalizes the idea that good regulators must contain (algorithmic) models of the world'', we translate its single-episode, distribution-free theorems into an empirical test suite for Lenia and its mass-conservative variant Flow--Lenia. The central diagnostic is a contrastive compressibility gap $ $ between an ON condition (entity acts normally) and an OFF/null condition (entity's actuation replaced by a parameterized null operator). A sustained $ >0$ across tasks makes explanations with small mutual algorithmic information $ (W\!:\!R)$ exponentially unlikely under the universal prior, and thus operationalizes model content'' in the regulator. We specify readouts, null manipulations, compression proxies, and statistics, and we propose concrete assays (morphological homeostasis, disturbance rejection, chemotaxis, damage repair) in Lenia/Flow--Lenia.

A falsifiable compression test for whether a self-organizing pattern in a simulated world is genuinely doing something — regulating its environment — or just looks like it is.

The core idea is simple. Take a creature in Lenia (a continuous cellular automaton that produces lifelike, spatially localized patterns) and run it normally. Then run the same simulation again, but this time surgically disable or scramble the creature's behavior while leaving everything else identical. If the creature was actually regulating — maintaining its shape, chasing food, recovering from damage — then the normal run should produce a more predictable, more compressible sequence of outcomes than the disabled run. The difference in compressibility is called the compressibility gap Δ. A sustained Δ > 0 across multiple tasks is the proposed signature of agenthood.

This is grounded in the AIT Regulator framework (Ruffini 2025), which formalizes the classical "Good Regulator Theorem" — the idea that any system that successfully controls its environment must internally model it. The key move here is translating that structural claim into something measurable on a single episode, without assuming anything about probability distributions. The math says: if Δ is large, then explanations in which the creature shares little algorithmic information with its world become exponentially unlikely. In other words, a big gap is strong evidence that the creature encodes a model of what's happening around it. Kolmogorov complexity K(·) — the length of the shortest program that produces a string — is the theoretical quantity; in practice, off-the-shelf lossless compressors like lzma serve as proxies.

The paper specifies four concrete behavioral assays: morphological homeostasis (does the creature maintain its shape?), disturbance rejection (does it recover from perturbations?), chemotaxis (does it climb a resource gradient?), and damage repair (does it reconstitute itself after amputation?). For each assay, multiple "OFF" baselines are defined — freeze the creature, scramble its parameters, replay a mismatched actuation trace — and Δ is computed against all of them, with the minimum taken as the conservative estimate. This multi-null design is important: it guards against the pitfall where a readout looks compressible for trivial reasons unrelated to the creature's agency.

Flow-Lenia, a mass-conserving extension of Lenia where local parameter vectors travel with matter, is highlighted as the cleaner testbed. Its explicit species-identity embedding gives a sharp operational definition of which cells constitute the "regulator" R versus the "world" W, making the ON/OFF surgical intervention precise. The paper is honest about limitations: K(·) is uncomputable, compressors are approximations, and Δ > 0 is a necessary but not sufficient signature — poor readout choices or statistical synergy can muddy the picture. The recommended remedy is combining the compression test with behavioral assays and multiple nulls rather than relying on any single number.