Matter-Induced CPT Violation and Earth-Density Stratification Effects in Long-Baseline Neutrino Oscillation Experiments

We present a unified analysis of two matter-potential systematics in long-baseline (LBL) neutrino oscillation experiments. Matter-induced extrinsic CPT violation produces a non-zero asymmetry $A_{\mu e}^{CPT}=(P_{\mu e}-P_{\bar{\mu }\bar{e}})\mathrm{/}(P_{\mu e}+P_{\bar{\mu }\bar{e}})$, computed here with exact three-flavour matrix-exponentiation propagators for T2K, NO$\nu$A, DUNE, and Hyper-Kamiokande; values range from 0.022 to 0.180 at the respective peak energies and differ by up to 9% between normal and inverted mass orderings. The three-dimensional surface $A_{\mu e}^{CPT}(E,{\delta }_{CP})$ at the DUNE baseline reveals an entanglement between extrinsic CPT violation and intrinsic CP violation in the high-$L\mathrm{/}E$ regime that requires joint statistical treatment. Concurrently, replacing the Preliminary Reference Earth Model (PREM) with a constant path-averaged density introduces a ${\delta }_{CP}$-reconstruction bias below ${0.3}^{\circ }$ for $L\le 5000$ km but growing to ${17.8}^{\circ }$ at $L=7000$ km and ${172.2}^{\circ }$ at $L=12000$ km. Since both effects share the same matter-potential Hamiltonian they must be modelled jointly; a Poisson log-likelihood ${\chi }^2$ statistic with nuisance-parameter pull terms is used to quantify the bias.