D-exp-f7/2 — PDL Structural Analysis of the f₇/₂ Mirror Nuclei: ⁴⁷Cr–⁴⁷V and ⁴⁹Mn–⁴⁹Cr — Confrontation with the Escudeiro–Recchia–Lenzi et al. (2026) B(E2) Data

We apply the Projective Dynamic Logo (PDL) framework to the f₇/₂ mirror nuclei ⁴⁷Cr–⁴⁷V and ⁴⁹Mn–⁴⁹Cr, motivated by the experimental measurement of quadrupole transition probabilities by Escudeiro, Recchia, Lenzi et al. (Phys. Rev. C 113, 044304, 2026). All four nuclei are located in the PDL harmonic-oscillator shell 4f₇/₂ (cumulative range 21–28), as established by the unconditional theorem of D47, and the Mirror Lemma (D47) is satisfied for both pairs. The proton number Z = 25 of ⁴⁹Mn occupies position 5/8 within the shell, 3 units below the magic closure Z = 28; this structural asymmetry is absent in the ⁴⁷Cr/⁴⁷V pair at position 4/8. Under the conjectural hypothesis H_B (D41, B(E2) ∝ k) and its further conjectural extension to mirror-nucleus ratios, the PDL prediction for the ⁴⁹Mn/⁴⁹Cr ratio is R_PDL = 2.021. The observed mean ratio is R̄ = 2.118 ± 0.57, lying 0.58σ from R_PDL; the coherent scenario (k² scaling) is disfavoured at 2.04σ. The ⁴⁷Cr/⁴⁷V pair yields R̄ = 1.44, consistent with the absence of structural tension at the symmetric shell position 4/8. The formal gap between the PDL structural facts and a derivation-level B(E2) prediction is identified as open problem OP-E2-PDL: the identification of the E2 transition operator within the PDL signed-graph formalism. All results are stratified by epistemic status; this document is exploratory.