Whom did Plato Mean in the Parable of 'Gigantomachia over Being' (Sophist 246a4 ff.)?

The mythopoetic parable of 'Gigantomachia over being' in Plato's Sophist 246a4 ff. is neither a theoretical construction ad hoc of some general trends, nor a reference to a single contemporary debate, e.g., between Plato's Academy and atomists in 4th century BC. The controversy on the nature of being is described as a real battle on epic scale (alpha pi lambda epsilon tau omicron sigma mu alpha chi eta) between two camps, as a debate about fundamental problem of philosophy, that has always existed (alpha epsilon iota sigma upsilon nu epsilon sigma tau eta kappa epsilon nu) and is still going on. In favor of the identification of the two camps primarily with the Ionian and Italian traditions in the pre-Platonic philosophy speaks the juxtaposition of the 'Ionian and Italian Muses' (Iota alpha delta epsilon sigma kappa alpha iota Sigma iota kappa epsilon lambda iota kappa alpha iota Mu omicron upsilon sigma alpha iota) in the preceding context Soph. 242de. The 'unreformed giants' are the Ionian physikoi from Anaximander to Democritus, while their 'divine' adversaries, who reduce being (ousia) to immaterial forms, are the Pythagoreans, Eleatics and Platonists, as well as Socrates, who dismisses the Ionian pi epsilon rho iota phi upsilon sigma epsilon omega sigma iota sigma tau omicron rho iota alpha in Plato's Phaedo and who upholds the theory of ideas in the Republic and Phaedrus. The 'improved' giants of the second generation are metaphysical dualists like Anaxagoras and Empedocles who admit incorporeal causes like Mind and Love alongside with matter, as well as Heraclitus, the Ionian Sophists and Antisthenes who combined ontological naturalism with teaching arete. The general scheme of the development of theories of archai in Aristotle's Metaphysics is very similar: from those who recognized only material causes to those who admitted incorporeal moving cause (Anaxagoras and Empedocles).