Axiomatic Bounding of Thermodynamic Drift in Heterogeneous LLM Training via Operator-Theoretic Manifold Locking

The scaling of Large Language Models (LLMs) is fundamentally bottlenecked by the memory constraints of modern accelerators. While heterogeneous memory systems (e.g., CPU DDR5 to GPU VRAM) offer expanded capacity, maintaining mathematical coherence across distributed tensors during active optimization remains a critical challenge. In this paper, we introduce the WXY-8 Heterogeneous Manifold Hypervisor, a novel framework that enforces operator-theoretic spectral bounds on bare-metal silicon. By pinning a pristine "anchor state" in system memory and computing the orthogonal leakage (termed "Thermodynamic Drift") of the active weights in GPU VRAM, we apply a dynamic propensity penalty to restrict the model's physical geometry. We empirically demonstrate a fundamental "Spectral-Empirical Trade-off" on a 1.5-billion parameter causal transformer: Gradient-Level Projection (Soft Bounding): Allows for optimal loss minimization at the cost of linear momentum drift, as historical optimizer inertia pulls the model out of the permitted geometry. Absolute Weight-Level Projection (Manifold Lock): Bypasses the optimizer to permanently restrict the active model to a bounded Hilbert space. This completely flatlines the thermodynamic drift without causing catastrophic learning failure. Furthermore, we provide formal mathematical proofs for Hard Manifold Invariance and generalize the WXY-8 operator to support Multi-Anchor topological retention, laying the groundwork for continuous learning without catastrophic interference. Publication Notes: This upload serves as the official publication of Manuscript V for Phase 4 of the Emerald Apex Project. The empirical telemetry presented in this paper was generated using proprietary bare-metal Equinox/JAX infrastructure.