Resource-Constrained Stabilization in Neural Architectures: From Brain-Inspired Topology to Brain-Isomorphic Dynamics

Intelligence is not knowledge retrieval; it is relationship activation. Knowledge consists of concepts embedded in data; intelligence emerges when those concepts are connected, traversed, and stabilised into a coherent response. Current artificial intelligence (AI) systems conflate the two, encoding knowledge as static vectors and retrieving answers by proximity. This produces hallucinations as a structural inevitability: the system has no mechanism to distinguish a well-grounded conceptual pathway from a statistically similar but meaningless one. The Hydrogen Interpretation (HI) (Ghisleni, 2026) establishes that any system whose stabilisation is governed by sustained local access to required resources belongs to a class of physical systems described by a single master equation, validated from atomic structure to galactic rotation. The human brain is such a system: its cognition is stabilised by the same class of dynamics. A knowledge graph designed as a deliberate abstraction of the brain's cognitive architecture is therefore such a system too. The master equation's three terms give the constraints directly: (1) sustained access: any reasoning transaction requires continuous local availability of activation throughout its full duration; (2) coalescence: activation propagates preferentially through stronger and denser relational pathways; and (3) a density limit: no single concept may monopolise the activation field, forcing contextual breadth or refusal to answer. We calibrate this master equation to knowledge graphs, where nodes represent concepts and weighted edges represent explicit relationships. Stability analysis yields a single critical condition: the density limit must equal the spectral radius ρ(W) of the weight matrix. At this critical point the system sustains a stable oscillation, the breathing cycle, and delivers the following concrete improvements over current architectures: (a) structural elimination of hallucinations: a query lacking a stable relational attractor is detected as a convergence failure and refused without any separately trained confidence classifier; (b) immunity to semantic collapse: knowledge grows as graph topology, not as vectors in a fixed-dimensional space, so retrieval precision does not degrade with scale; (c) continuous local learning without backpropagation: a Hebbian update rule derived from first principles reduces memory overhead from O(E × T) to O(E); (d) fully derived parameters: the density limit, activation sharpness, initialisation, and input timing are all determined by ρ(W). The framework is brain-isomorphic (reproducing the governing physics of biological cognition, not merely its topology) and yields four falsifiable predictions, two of which are empirically validated on synthetic graphs.