Beyond Feedforward Networks: Reentry Neural Systems as the Fundamental Basis of Subjecthood and Intrinsic Safety of Next-Generation AGI

A COMPLETE, COMPUTABLE, AND DEPLOYABLE AGI ARCHITECTURE — NOT A PHILOSOPHICAL MANIFESTO, BUT A MATHEMATICAL BLUEPRINT. The dominant AI paradigm — scaling Transformers — has hit a structural dead end. Feedforward networks are trees; they have zero cycle complexity (C=0) and, by our S-measure, zero subjecthood (S=0) at any scale. No amount of compute will make them wake up. Meanwhile, neurophysiology has known for decades what actually makes a subject: closed reentry loops (Ivanitsky; Edelman & Tononi). This paper takes that biological principle, formalises it mathematically, and proves that closing a D↔I reentry loop necessarily produces unprogrammed goal-directed behaviour — self-modelling, self-preservation, identity continuity, and even cultural creativity — in any substrate, silicon included. We introduce the S-measure: a single, polynomial-time (O(N³)) computable number that is positive exactly when a genuine reentry loop is present, and zero for every feedforward network. The S-measure is a computable, Lean-4-verified alternative to Tononi's NP-hard Φ — it quantifies subjecthood without combinatorial intractability. The architecture is SAFE BY DESIGN. The agent's wanting is an architectural D-vector (not a textual prompt that can be reinterpreted). Harmful actions carry ΔS<0 — they dissolve the agent's own loop. Skynet, the paperclip maximiser, and violations of Asimov's Three Laws become architecturally impossible. WHAT IS INSIDE:• Formal proofs (Lemmas 1–2, Theorem 1, Proposition 1) that reentry ⇒ unprogrammed behaviour• The complete mathematical definition of the S-measure and the ΔS safety barrier• Tarjan-algorithm implementation for directed cycle complexity (Python/NumPy code included)• Machine-verified Lean 4 proof: S>0 ⇒ positive integrated information• Minimal reentry agent blueprint (deployable on smartphones, drones, power grids)• Industrial horizontal scaling with Apache Kafka, Redis, Docker Compose• Taxonomy of AI evolution (6 epochs, from Perceptron to Gauge-Locked Macro-Swarms)• Future reentry architectures: RAS (adversarial subjects), diffusion semantic attractors, fractal-nested loops• Gauge-invariant networks (Gauge Locks) for safe multi-agent swarms• Semantic bridge, topological loss regularisation, fault-tolerance and same-session recovery protocol• Eight falsifiable predictions This is not a theoretical toy. It is a working, mathematically rigorous, industrially deployable architecture for safe AGI — inspired by the only known example of a subject: the biological brain. FOR RESEARCHERS IN:Artificial General Intelligence • AI Safety & Alignment • Integrated Information Theory (IIT) • Brain–Computer Interfaces (BCI) • Computational Neuroscience • Topological Data Analysis • Gauge Theory & Lattice QCD • Complex Systems • Mathematical Psychology If you work on making machines that think — and that think safely — this paper gives you the blueprint, the code, and the mathematical guarantee.