Residual-Rank Entanglement of Conjugate Weil Pairs in the Spectral Admissibility Cascade

We compute the entanglement entropy of a closed conjugate Weil pair ,q-c\ along the spectral admissibility cascade of the Cosmochrony programme, where entanglement is the infra-projectable invariant of a non-decomposable joint fibre of the non-injective projection. The bipartite state lives on the residual fibre-level support of the Gram–Schmidt span of Weil fingerprints on the Heisenberg Cayley graph. We show that the normalized admissibility residual of each newly admitted independent direction equals unity: the admitted Weil fingerprints are mutually orthogonal (proved analytically in the companion paper ), so the reduced Schmidt spectrum is flat and the reduced entropy is exactly Sₑₙₜ(n)=log rₚₐᵢᵣ(n), the logarithm of the residual Gram–Schmidt rank. No Born–Infeld spectral correction survives: the admissibility-weight deficit is identically zero. Because the cascade only adjoins independent directions, rₚₐᵢᵣ(n) is non-increasing structurally, so the residual conjugate-pair entanglement is maximal at the earliest admissible stage and decreases monotonically as correlated capacity is stabilized into projected structure. The capacity-level statement (non-negativity of the stabilization rate) is established numerically. The entropy computed here is the full residual-rank observable on the complete Gram–Schmidt basis; its relation to the minimal admissible pair sector, whose entropy is log 2 conditional on two explicit hypotheses (H-carrier) and (H-inv), is established separately. The remaining finite-q task is to measure the contraction law of rₚₐᵢᵣ(n) and compare its exponent with the pair-capacity exponent δₚₐᵢᵣ.