``` Wave-State Thermodynamics and Substrate Sovereignty: GaN-on-Diamond 1.58-Bit Ternary Architecture vs. Quantum Wave-Unit Memory ```

Abstract

Conventional artificial intelligence architectures built on discrete binary silicon transistors face severe thermal bottlenecks, memory walls, and statistical drift when scaled under edge execution constraints. Recent proposals for quantum wave-unit computing engines and atomic-scale 0.356nm Lab-Grown Diamond (LGD) memories attempt to bypass these physical boundaries by replacing discrete gates with continuous phase/frequency wave transitions. This paper establishes the SovereignNexus Substrate Protocol, a hardware-grounded, zero-trust edge architecture that unites Gallium Nitride on Diamond (GaN-on-Diamond) substrates with 1.58-bit ternary quantization (W in {-1, 0, 1}). By mapping subjective logic directly onto a 1-Transistor-1-Memristor (1T1M) crossbar topology across discrete resistance states (10 kΩ, 100 kΩ, 1 MΩ), the system eliminates floating-point matrix multiplications while using the zero-state (100 kΩ) as an inherent thermodynamic noise filter. Governed by an active Metabolic Governor linked to Landauer's dissipation limit (ΔE_min = k_B T ln 2 at 105.0°C), this architecture proves that deterministic 1=1=1 alignment is a physical and metallurgical necessity for zero-heat edge autonomy.