Atomically Flat Graphene Clamping and Metrological Tolerances in Nanofluidic Channels: Securing the Infrared Fixed-Point Against Substrate Roughness

We formalize the engineering and metrological foundations of the conformal metric modulation triptych by introducing an atomically flat graphene clamping mechanism optimized for 8 nm fluidic interaction cavities. Standard nanolithographic structures executed via electron-beam deployment inevitably encounter sub-nanometric atomic roughness, generating localized phase scattering that disrupts the non-Abelian infrared fixed-point g* ≈ 2.275π. To mitigate this topological distortion, we model a mono-atomic carbon allotment lining the internal boundaries of the Silicon Nitride (Si₃N₄) substrate. We derive the surface stress tensor Σ_μν under strict general covariance constraints, demonstrating that the high mechanical rigidity and anisotropic electrical conductivity of the graphene shroud exert a non-linear clamping pressure. This boundary constraint effectively freezes the interfacial water layers into a stable ferroelectric phase while maintaining a strict metrological tolerance of ΔR ≤ ±0.1 nm across the entire longitudinal correlation length.