PNMS Mode B — General Relativity Branch: Φ_R Coupled to Einstein's Field Equations

Branch document connecting the PNMS constructive operation (Mode B) to general relativity. The document defines how the PNMS projection operator Φ_R is applied to systems governed by Einstein’s field equations. It specifies the active quantities used in the analysis — mass, energy, temperature, entropy, length scale, horizon area, and time scale — and identifies their corresponding rows in the PNMS reference basis. The document establishes the constraint relation (E / E_p) · (T / T_p) = 3.9789 × 10⁻² which defines the general-relativistic constraint surface for Schwarzschild systems in PNMS signature space. It also defines the constructive operation used to generate and verify relativistic states and introduces the general-relativity case study series associated with this branch, including Schwarzschild, Kerr, Reissner–Nordström, de Sitter, and gravitational-wave systems