In-Silico Tests of the Four-Model Architecture: Self-Referential Closure, Self-Modelling and Criticality in Model Systems
Abstract
The Four-Model Theory of Consciousness (FMT; Gruber, 2015, 2026e) specifies consciousness as ongoing self-simulation across two kinds of models — implicit (learned, substrate-level) and explicit (generated, phenomenal) — organized by scope (world vs. self) and mode (implicit vs. explicit), and it requires a substrate capable of open-ended (Wolfram Class 4) computation. Because the theory is an architectural specification, its functional commitments can be tested in silico. This paper reports the in-silico results the master paper points to, sorted by evidential kind. Two distinctions are needed to read them, both forced by model-system results: a built control closure (Closure-1) versus an emergent predictive closure (Closure-2); and a capability-first reading of criticality on which avalanche (σ ≈ 1) and edge-of-chaos (λ ≈ 0) statistics are candidate instruments for one underlying capability rather than competing definitions, and neither certifies it alone. The banked results are mechanism demonstrations at toy, reservoir, and gridworld scale: a self-model-gated planner scales with problem depth where a bracket of reactive policies fails (0.00–0.33); prospective self-modelling confers a survival advantage (0.29–0.33 vs. 0.17–0.25); a self/other model carries a transfer capability that removing its generating projection abolishes (0.98 vs. 0.78, Cohen's d = 2.44), reported as feasibility and pre-conceded as not unique to FMT. In a single, not yet replicated run on one rate reservoir, an edge-peak in computational capability appears only under sufficient task demand. One result is partial — a maintained-decodable representation is not, at spiking scale, computable-upon — and one is null (re-entry on a homogeneous reservoir adds nothing, FMT-consistent and diagnostic). Three further results price the architecture rather than demonstrate a capability: opening the global loop of a model connectome costs 14.0% of its synapses where making it acyclic costs 74.0%, so the cheap edit relocates closure and does not abolish it; closure's advantage is conditional on the driven subsystem carrying change the rest of the system cannot derive for itself, and falls but does not vanish when it can; and an argmin over 72 enumerated architectures selects a bottleneck exactly where content is low-dimensional, spans otherwise-separate subsystems, must be delivered near the achievable ceiling, and reads back over a short path — four conditions a self-model satisfies, with the word "self" nowhere in the derivation. These are structural and wiring-cost results: optimality, never necessity. The scaled, closure-driven test of the theory's central dependency is not attempted here. Keywords: consciousness; self-referential closure; criticality; edge of chaos; Wolfram Class 4; reservoir computing; world models; causal transfer; Four-Model Theory Changelog v3 **v3 (2026-10-02)** Supersedes v2 (2026-08-27). Companion to the Four-Model Theory v16. Retitled to *In-Silico Tests of the Four-Model Architecture: Self-Referential Closure, Self-Modelling and Criticality in Model Systems*. *Criticality.* The requirement is stated as Class 4 computational capability, with avalanche and edge-of-chaos statistics as instruments for it; every branching ratio is reported beside a rate-matched surrogate or marked as tracking firing rate. The demand-gated edge-peak (§4.4) is reported as a single run, not counted among the banked results; five further scans that found no edge-peak are described individually. *Structural priors.* §2 adds a paragraph on nature and nurture: which structural priors a model system may be given, the consolidation null that bounds them, and the scope of what the minimal rig shows. *Presentation.* Section headings and passages describe each experiment in plain terms; project-internal identifiers, run names and code paths are removed. Formulas are set as mathematics. No numerical result changed. The paper is 15 pages.