Infrastructure That Learns: Network Neuroplasticity and Graph-Theoretic Growth in Autonomous Cellular Adaptive Infrastructure

This paper presents the long-term adaptive learning capacity of the Adaptive Matrix Ecosystem (AME), modelled on biological neuroplasticity and Hebbian learning principles. AMW maintenance missions permanently deposit IPS passages as they operate, causing the network to strengthen frequently-used pathways and accumulate redundant routing over operational time without any explicit learning algorithm or centralised design. Four convergence theorems establish formal guarantees: monotone graph growth, speed-of-healing convergence, monotone reachability growth, and expected redundancy non-decrease. Biological analogies — Hebbian synaptic potentiation, Physarum slime mold, fungal mycelium, trabecular bone remodelling, and immunological memory — illuminate the mechanism. A 500-mission simulation on a 168-node AME-500 hexagonal substrate quantifies all four properties. Fourth and final paper of the AME Autonomy Tetralogy. This paper is part of the AME Hexalogy, the third collection in the AME research series by J.O. Danenberg, Aveotto LLC. Prior collections: AME Physics Trilogy (Papers 1–3, January 2026) and AME Education Pentalogy (Papers 5A–5E, February 2026), both available on Zenodo under ORCID 0009-0003-9549-2107. The Hexalogy comprises the AME Autonomy Tetralogy (Infrastructure That Feels, Heals, Strengthens, and Learns) and the AME Ethics/Construction Duology (Infrastructure That Judges and Fortifies).