Pion’s valence-quark GPD and its extension beyond DGLAP region

We briefly report on a recent computation, with the help of a fruitful algebraic model, sketching the pion valence dressed-quark generalized parton distribution and, very preliminary, discuss on a possible avenue to get reliable results in both Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Efremov-Radyushkin-Brodsky-Lepage (ERBL) kinematial regions.This work has been partially supported by Spanish ministry projects FPA-2011-23781 and FPA-2014-53631- C2-2-P and French GDR 3034 PH-QCD “Cromodynamique Quantique et Physique des Hadrons" and ANR-12- MONU-0008-01 “PARTONS". We thank for their very valuable remarks to L. Chang, C.D. Roberts, F. Sabatié and S.M. Schmidt. H. M. and J. R-Q. are grateful for the chance to participate in the “21st Conference on Few-Body Problems in Physics", held in Chicago, and specially to C.D. Roberts for his warm hospitality at the Argonne National Laboratory