BGS Triple Architecture: Heterogeneous Triple Modular Redundancy (HTMR) 144+144+160 = 448 bit

This technical note serves as a critical supplement to the EGESB-G₂ unified framework (v6. 3), detailing a major architectural evolution in numerical stability for G₂-equivariant systems. It addresses two primary objectives: the analytic correction of the QCD string tension derivation (OP-25b) and the introduction of the BGS Triple Architecture, a 448-bit Heterogeneous Triple Modular Redundancy (HTMR) system designed for distributed coherence in high-precision physics simulations. Physical Corrections (OP-25b) The document reports the formal correction of the G₂-Ricci flow soliton integral from 2/9 to 4/15. This refinement leads to the derived QCD warp scale k₂ ₐ₂₃/2. 04, effectively resolving the 12-order magnitude gap between the Electroweak and QCD scales through the Double-Warp Architecture. Computational Architecture: BGS-T3 To mitigate inter-process decoherence in parallel environments, we propose a 448-bit 144+144+160 HTMR configuration: Groups A & B (144-bit each): Dual-parallel registers employing a 64+64+16 format for double-double arithmetic and internal G₂ root-phase monitoring. Group C (160-bit Verifier): A structurally distinct supervisor that monitors first-order AB drift and second-order G₂ coupling terms. Crucially, the Group C verifier is designed to map onto native FP32 registers on modern GPUs, minimizing hardware overhead for real-time applications. Applications The BGS Triple architecture provides a robust path toward: Orbital Mechanics: Detecting base-12 harmonic residuals in Near-Earth Object (NEO) trajectories (Prediction P-1). Plasma Physics: Real-time stability control in Tokamak reactors via multi-channel ₆₋ estimation. Artificial Intelligence: Ensuring forward/backward coherence in G₂-invariant manifolds for geometric deep learning pipelines.