Quantum Geometry–Matter Entanglement with a Compactness-Dependent Sector in Effective Loop Quantum Gravity

We study a single-object effective construction that retains the frozen Relative Gravitational Matter–Energy Confinement (RGMEC) selector, preserves its explicit quantum-mechanical phase–momentum sector, and places the construction alongside a concrete spherically symmetric loop-quantum-gravity (LQG) stellar Hamiltonian. For the LQG sector we use the gauge-fixed effective perfect-fluid Hamiltonian of Wilson-Ewing, based on improved-dynamics holonomy corrections. The compactness-dependent quantum sector is kept distinct: a reduced density matrix defines a state expectation value of the momentum dyad, while the frozen control remains Δp = ℏ/R, β = 0, and α = 1. The selector yields seven algebraic consequences, including Cpeak = 0.2391463117 and (ξGE/R)max = 0.5493420567. For PSR J0740+6620, Cpeak corresponds to Rpeak = 12.8003 km at M = 2.073 solar masses and lies between the central compactness values inferred in two separately published 2024 NICER/XMM analyses that use related data sets and differing inference pipelines. A direct scale audit of the effective-LQG exterior gives a surface holonomy factor of approximately 2.4 × 10⁻⁷⁹ for the standard area gap, placing the star extremely deep in the semiclassical regime of this specific LQG realization. Thus the neutron-star comparison tests the frozen selector at the level claimed here; it is not evidence for a detectable LQG correction, geometry–matter entanglement, or a nonzero quantum residual. We state the tensor-to-Hamiltonian interface condition, conservation and covariance requirements, rotation limitation, no-retuning rule, and falsification criteria explicitly.