CL5D Phase-Dynamic Framework Applied to Earth's Interior: Gravitational Anomaly, Benchmark Score Topology, and the D′′ Layer Conjugate Balance Condition

We apply the CL5D Hybrid Model — a deterministic multi-phase mathematicalframework (Papers 1–6, Chakraborty, 2026) — to the geophysical structure of Earth’smantle and core–mantle boundary region, using two observational datasets: thePreliminary Reference Earth Model (PREM; Dziewonski & Anderson, 1981) and theSEISGLOB1 global seismic shear-wave tomography model (57 depth levels, 179×360global grid, δVs = S-wave velocity deviation from PREM). We define a FractalHeterogeneity Coefficient α(z) = stdδVs(z)/σmax and a CL5D BenchmarkScore BS(z) incorporating skewness and kurtosis penalties, and compute bothquantities at each of 57 depth levels from 50 to 2,850 km.The resulting BS(z) profile reveals a three-basin topology: Basin 1 (asthenosphere,50–200 km, BSmin = 0.129, Phase III confirmed), a micro-basin at the670 km seismic discontinuity (α: 0.176–0.270, Phase I–II), and Basin 2 (D′′ thermalboundary layer, 2,200–2,850 km, BSmin = 0.711, Phase I–II). A linear depth projectionplaces the Phase III threshold crossing at z∗ ≈ 3,908 km — approximately1,017 km beyond the Core–Mantle Boundary (CMB) at 2,891 km. This depth barrierdemonstrates that the D′′ layer cannot achieve Phase III singularity throughdepth alone: its dynamical endpoint is Phase II Conjugate balance, consistentwith the CL5D finding in Paper 6 that Black Hole singularity resolves as Conjugateequilibrium rather than a true mathematical singularity. The asthenosphere is confirmed as a pluripotent-analogue Phase III zone— a region of maximum mathematical potentiality within the CL5D framework.We further introduce the Gravity Bridge: a Phase-Dynamic Potential metric gCL5D(z) = gPREM(z) · 1 + α(z), which quantifies how the gravitational profileis weighted by heterogeneity-driven density asymmetry. Δg reaches ∼2.0%(∼194 mm/s2) in Basin 1 and ∼0.5% in the D′′ zone. These results position CL5Das a phase-dynamic complement to PREM: while PREM describes the averagegeophysical state, CL5D reveals the underlying mathematical structure that governswhere and why Earth’s mantle departs from thermodynamic equilibrium.