Project Janus: From Buffer to Brain (Thickened Fractal Interlayers as Three-Dimensional Functional Architectures for Non-von Neumann Computing)

Quantum computing seeks to exploit superposition states that collapse upon measurement—the act of observation destroys the very property being exploited. This work takes a fundamentally different approach: rather than pursuing unstable quantum coherence at −273◦C, we engineer stable continuous analog states at room temperature within a thickened rare-earth oxide inter layer, achieving multi-state non-von Neumann computation without cryogenic infrastructure. Project Janus establishes the physical and materials foundation for transforming the Angelica-series buffer layer from a passive stress absorber into an active three-dimensional functional device. The core contribution is the thickened fractal interlayer architecture: a 150nm (Eu,Pr,Y)2O3 ternary layer with threedimensional Angie’s Grading, C(x,y,z,t) = (1 − z)α × fMenger(x,y,z) × g(t), combining near-zero lattice mismatch (0.018%), isotropic fractal geometry (Hausdorff D=2.727), and Pr3+ ⇌Pr4+ memristive switching. Simulation results demonstrate: Matthews-Blakeslee critical thickness hc = 851nm providing 5.7× process margin over the 150nm design; 32 stable analog resistance states (= 5.8bits/cell); six-decade on/off ratio; I-V hysteresis loop (memristive signature); local Joule heating ∆T = 120K under non-equilibrium high-energy pulse injection, encoding deep analog states; in-memory VMM efficiency 20× that of GPU (A100-class); and backward RF compatibility (fT = 243GHz). Keywords: GaN-on-Si, memristive interlayer, Menger sponge, 3D Angie’s Grading, non-von Neumann, in-memory computing, Pr2O3, (Eu,Pr,Y)2O3, fractal architecture, analog memory. Version 2.0 — Release Notes Summary of Changes Bug Fixes (Required) Cross-reference resolved: Section 9.4 contained an unresolved LaTeX cross-reference (??) pointing to the Joule heating section. The {sec:joule} anchor has been correctly placed in Section 5.2, and all forward references now resolve correctly. Typographical correction: A misspelling (Standart) in the Fig. 3 memory technology comparison has been corrected to Standard. Thermal budget clarification: The aerospace self-healing entry in Fig. 3 previously listed ΔT=120K anneal, which could be misread as a 120 K cryogenic process. This has been corrected to Pulse→420K (<600°C limit) to make clear that the mechanism is a transient local Joule heating event (T_local = 300K + 120K = 420K), well within the 600°C process ceiling established in Section 8. Additions (Content) STDP simulation code: Appendix A now includes stdp_update(), a lightweight function implementing Spike-Timing-Dependent Plasticity via Pr³⁺/Pr⁴⁺ conductance switching. This provides the mathematical IP anchor for the STDP learning claim in Section 9 and establishes prior art for Project Raphael. New applications: Sections 9.2–9.6 now include four additional application directions with physical grounding: Janus-PUF (fractal hardware security), STDP on-chip learning, P-bit probabilistic computing, and radiation-hard self-healing aerospace memory. A bio-hybrid interface direction (Section 9.6) is introduced as a Future Direction toward Project Raphael.