Project Mnemosyne: From Device to Field (Associative Memory and Selective Forgetting in Janus Fractal Crossbar Array)

Project Mnemosyne bridges the gap between Project Janus [1]—a single fractal memristive junction—and the neuromorphic computing systems envisioned in Project Raphael. Where Janus established a single synapse capable of 32-level analog storage and KWW stretched exponential forgetting (β = 0.6, τ = 720h), Mnemosyne asks: what emerges when many such synapses are organised together? The answer, demonstrated through software simulation grounded in confirmed Janus physical parameters, is associative memory with selective forgetting. A reservoir computing (RC) architecture using the Janus Butler Volmer activation and KWW memory kernel achieves R2 = 0.990 on Lorenz attractor prediction—a standard benchmark for nonlinear temporal computation. Critically, R2 remains above 97% across array sizes from 32×32 to 128×128, and falls only from 0.988 to 0.981 under 10% random junction failure. The selective forgetting mechanism (phase coupling γ = 0.4: strong signals consolidate to τeff = 1008h; weak signals prune to 432h) is not a limitation but the computational mechanism: it prevents state saturation and enables continuous adaptation without external weight updates. Important caveat: All results are software simulations. No hardware fabrication has been performed. The value of this publication is to establish prior art and demonstrate computational viability from confirmed Janus physical parameters. Keywords: reservoir computing; associative memory; KWW forgetting; Janus memristor; (Eu,Pr,Y)2O3; neuromorphic computing; Menger sponge; fractal crossbar; Lorenz prediction; selective forgetting v2 update: Acknowledgements clarified The Acknowledgements section in Version 1.0 contained an inaccurate attribution. During the development of this work, the author engaged in extensive discussions with Gemini (Google DeepMind) to work through specific challenges, and subsequently brought the outputs of those discussions to Claude (Anthropic) for implementation and synthesis. As a result, Claude's initial rendering of the Acknowledgements did not accurately reflect the origin of individual contributions. This version corrects the attribution. The scientific content remains unchanged.