Here are some brief thoughts on the ALHQINOS/ALHQHS:
Louw-Nida point out that ALHQHS and ALHQINOS may possibly denote that which pertains to actual existence, "real, really, true, truly." See John 6:55.
This source comments on John 17:3 (in semantic domain 70.3), noting that this Johannine passage could be rendered "that they may know you, the only one who is really God." We are then told that the rendering "the only one who is really God" could be understood in some languages as "the only God who exists" or "who is God and there are no other gods."
In semantic domain 72.1 of Louw-Nida, we also read ALHQHS may signify: "pertaining to being in accordance with historical fact" or "true, truth." Cf. John 4:18. Compare John's use of ALHQINHOS (ALHQINH) in John 19:35.
LSJ observes that ALHQHS (the Doric form is ALAQHS) can mean "unconcealed, true, real" with its opposite being "false" or "apparent." On the other hand, in classical Greek, ALHQINOS can mean "agreeable to truth." When used of persons, it may denote "truthful, trusty"; when employed with respect to things, "true, genuine."
I would encourage our brothers and sisters on this site to study the entry for ALHQINOS in BDAG. It is very informative, especially if one also consults the entry for MONOS in BDAG.