Structural Closure Multiplicity and the Isospin-Symmetric Island of Inversion: a PDL Analysis of ⁸⁴,⁸⁶Mo

This document (D41) confronts the Projective Dynamic Logo (PDL) framework with the experimental results of Ha et al. (Nature Communications 16, 10631, 2025), which reports the first lifetime measurements of the first 2⁺ states in ⁸⁴Mo and ⁸⁶Mo, revealing an abrupt structural transition between an intruder-dominated nucleus (8p-8h configuration, N=Z=42) and a configuration-mixed nucleus (N=Z+2=44), with a measured B(E2) ratio of approximately 2.45. Within the PDL framework, this ratio is shown to be a direct consequence of the structural identity T ≈ (Δn+1)² = 25, where T = R_surf(p)²/R_sea(n) = 25.26 is the nuclear binding unit derived in D22 and D40, and Δn = n_d − n_u = 4 is the valence-core asymmetry of the proton. Three independent observables extracted from the published source data (MOESM3) of Ha et al. are each consistent with the factor-of-two prediction arising from this identity: (i) the B(E2) ratio (22% discrepancy, within experimental uncertainty); (ii) the ratio of DNO-SM wave-function component counts, N_comp(⁸⁶Mo)/N_comp(⁸⁴Mo) = 1.962 vs. the PDL prediction of 2.000 exactly (2% discrepancy); and (iii) the Shannon entropy difference ΔS_WF = 0.868 nats vs. ln 2 = 0.693 nats (25% discrepancy). The closure multiplicity conjecture H_B is introduced: for a nucleus at the boundary of an island of inversion dominated by a kp-kh configuration, the number of accessible partial closures scales as N_comp(k) ~ k, yielding N_comp(8)/N_comp(4) = 2 exactly. The B(E2) ratio pattern along the N=Z and N=Z+2 lines shows that the factor-of-two signal appears only at the two boundaries of the isospin-symmetric island of inversion (Z=32 and Z=42), not in the deformed bulk region, in structural agreement with the conjecture. A structural correspondence is conjectured between the ZBM3 model space (pseudo-SU(3) ⊕ quasi-SU(3)) used by Ha et al. and the two-type valence-core architecture (n_u = 24, n_d = 28) of the PDL proton. Two falsifiable predictions are formulated for ⁸⁸Ru/⁹⁰Ru and ⁹²Pd/⁹⁴Pd (B(E2) ratio ≈ 2.02 ± 25%), testable at FRIB and RIKEN.