of the currently proposed LG mirror models are modelled on the so called *Hori-Vafa recipe*, the previous observation introduces possible re-parameterizations of all these LG models, which should be compared with the known ones from the point of view of Homological Mirror Symmetry (HMS) (see considerations given in §\[ssez:iperellittica\]).

More deeply, by observing a natural Landau-Ginzburg/Hypersurface correspondence, conjecturally extending the LG/CY correspondence studied by [@Chiodo-Ruan] (see §\[sssez:LG/Hyp\]), a framing turns out to be the hypersurface counterpart of the “anchoring at infinity” of the compactified LG models proposed by Katzarkov, Kontsevich and Pantev [@KKP] (see \[ssez:KKP-compct\]), so opening the door to conceivable connections with the log-geometry of the Gross-Siebert Intrinsic Mirror Symmetry [@GS-IMS].

Moreover, $f$-duality explains quite well why, passing from a framing to a weak framing, that is, loosing positivity properties, in terms of Kodaira dimension, of the hypersurface (complete intersection) we are considering, translates in loosing completeness properties of the associated mirror partner, so well justifying a description of mirror symmetry in terms of a duality between associated LG models (see Remark \[rem:negKod\]).

A further important remark, is that, since $f$-duality is a duality between framed toric varieties, that is, between pairs given by a complete toric variety and 