Two Thresholds for Consciousness¶

Consciousness has two necessary thresholds, free compute — Class-4 (universal-computation) capability recruited by the system for its own modeling — and the four-model architecture; neither is sufficient, and what is sufficient is a conjunction: the four model kinds under closure, with free compute, embodiment and at least one pain-pleasure axis.

The Four-Model Theory identifies two independent thresholds that any conscious system must cross, and states separately what is enough for consciousness. The master paper puts it in three sentences: "Free modeling is necessary but not sufficient; the four-model architecture is necessary but not sufficient. What is sufficient is a conjunction: a system that implements the four model kinds under closure, with free compute, embodiment and at least one pain-pleasure axis, is conscious." This framework answers the boundary problem — which systems are conscious and which are not — and grounds the engineering specification for artificial consciousness.

The Computational Threshold: Free Compute¶

The first threshold is computational. The substrate must have free compute: the capacity for Class 4 (universal) computation, actually spent on ongoing self-referential modeling rather than merely available. Criticality, the edge of chaos, is the dynamical signature this usually leaves in the human brain, not a separate condition, and the relation runs one way: "free modeling is necessary and not sufficient," while criticality "is neither necessary nor sufficient, and a conscious system may run subcritically." Below the threshold, the system cannot sustain the dynamic, self-referential computation the explicit models need.

The threshold is tested directly, not through the signature. The falsifier is "robust consciousness where the matched feedforward model keeps pace with the system on novel input as compositional depth grows." The probe trains an unrolled feedforward model of matched capacity (same parameters, exposure and memory) on the system's own history and compares the two on novel input of increasing compositional depth; the criticality statistics are recorded alongside, not as the test.

This threshold operates as a gate. Propofol suppresses complexity and abolishes free modeling, and the substrate turns subcritical with it. At propofol-induced loss of consciousness, frontal-to-parietal backward corticocortical effective connectivity fails while thalamocortical connectivity is preserved (Boly et al., 2012). At surgical depth reportable experience is absent, even though the four-model architecture remains physically intact in the synaptic connectivity. The architecture is still there; it simply cannot execute. (The gate is not a clean switch at every depth: dream reports after propofol anaesthesia are common, and participants repeatedly woken from deep propofol sedation gave experience reports on 24 of 52 awakenings.) In wakeable deep NREM sleep the architecture also stays, while the explicit models may be absent or run weakly; awakening reports cannot tell which.

A system can show the signature without crossing the threshold. A weather system has complex, near-critical dynamics; a turbulent fluid may sit close to a phase transition. Neither recruits its computation for modeling itself, so neither has free compute in the theory's sense. A laptop fails for the same reason from the other side: it is universal but heteronomous, and nothing in its own operation recruits that universality for self-modeling.

The Architectural Threshold: Four Model Kinds¶

The second threshold is architectural. The system must implement the four-model self-simulation: an Implicit World Model (IWM), an Implicit Self Model (ISM), an Explicit World Model (EWM), and an Explicit Self Model (ESM) arranged along the two axes of scope and mode. "With free modeling but without the architecture, there is complex dynamics but no consciousness."

A system can possess the architecture without being conscious. A brain under general anesthesia at surgical depth retains its synaptic connectivity — the implicit models (IWM, ISM) are stored intact in the topological architecture (Level 4 of the five-system hierarchy). With free modeling abolished, the explicit models are not generated. The architecture is present; the computation is not running.

Figure¶

quadrantChart
    title Both Thresholds Are Necessary
    x-axis "No Four-Model Architecture" --> "Four-Model Architecture Present"
    y-axis "No free compute" --> "Free compute recruited for self-modeling"
    quadrant-1 "Both thresholds met:\nconscious with embodiment\nand a valence axis\n(e.g., waking mammalian brain)"
    quadrant-2 "Free modeling,\nno four model kinds:\ncomplex dynamics,\nno consciousness"
    quadrant-3 "Neither threshold met\n(e.g., thermostat,\ncrystal, weather system)"
    quadrant-4 "Architecture present,\nnot running\n(e.g., brain under\nanesthesia)"

The two-threshold matrix. A system must be in the upper-right quadrant — free compute recruited for self-modeling AND the four-model architecture — to be conscious, and that quadrant becomes sufficient only with closure, embodiment and at least one pain-pleasure axis. Each threshold alone is insufficient.

What Is Sufficient¶

The sufficiency claim is the theory's strongest stated commitment, and it has four parts: the four model kinds under closure, free compute, embodiment, and at least one pain-pleasure axis. Two of the parts are easy to misread.

The valence axis may be engineered. "Presetting pain as aversive and pleasure as appetitive shortcuts what selection does by eliminating the creatures that get the sign wrong, so an engineered axis is compatible with substrate independence."
Embodiment is required for natural emergence, not for continued existence. "Embodiment is required for consciousness to emerge naturally, not for it to continue existing: the body is what gives the self model its content." A person locked in from birth would sit near the floor of minimal consciousness.

The conjunction yields a direct engineering specification: a substrate with free compute, the four model kinds with self-referential closure, an embodiment that supplies the self model's content, and a pain-pleasure axis. Building one is an implication of the theory, not yet a test of it — the engineering does not exist.

The conjunction also has diagnostic power. A base large language model lacks persistent implicit models, lacks an ongoing self-simulation (its autoregressive loop closes over the emitted text, not over a self-model), and lacks the real/virtual split. Post-trained models do carry a reportable representation of their own point of view inside a globally available workspace (Gurnee et al., 2026); what they lack is closure over it, persistence, and the Class 4 regime. The theory does not merely suggest LLMs are probably not conscious — it specifies exactly what they are missing and why.

Key Takeaway¶

Free compute and the four-model architecture are each necessary and neither is sufficient. What is sufficient is the conjunction of the four model kinds under closure, free compute, embodiment and at least one pain-pleasure axis, which gives both a boundary criterion and an engineering specification.