The first point is that Arrian does not mention a reform where the ‘forces’ are organised into thousands at all; he notes a reform of the Companion cavalry, dividing the ilia into two lochoi of probably 128, or at least establishing a command level here.That units of 500 or so (called lochoi) existed prior to this re-organisation cannot be disputed.
OK....I’ll do my best. The re-organisation occurs in Arrian at III.16.11 into ‘thousands’ of the ‘forces/numeri’ - not just Hypapists. (Curtius). However, ‘lochoi’ don’t disappear from the ‘orbat’ –for example at Arrian IV.2.1 each company of infantry [pezoi kata lochois] is ordered to prepare a set number of scaling ladders each; at VI.27.6, the march through the Gedrosian desert, camels are distributed at the rate of one per 100 cavalry, and to the various ‘lochoi’ of infantry; at VII.11.3 the Makedones complain about imitation units, including Persian ‘lochous’; at VII.24.4 we have sacrificial meat and wine distributed, again to cavalry “100’s/ekatostuas" and 'lochous'.Well I dispute it and defy you to give the references.
As to prior to the re-organisation we have Alexander at Issus addressing “Ilarchs and lochagoi” – and that these were Macedonian is confirmed because the mercenaries etc are addressed separately[Arrian II.10.2]
Another occasion prior to reorganisation is before Gaugemala [III.9.6] when once again Alexander addresses his ‘lochagoi’, ‘ilarchai', ‘taxiarchs’, and ‘leaders/hegemons’ of that part of the phalanx entrusted to them.
Clearly sub-units of ‘lochoi’ continued throughout.....
I will leave IV 2 I, for the moment; VI 27 vi, however is not an instance of distribution by ‘hekatostyes’ and ‘lochos’ the quote is
that is ‘by ile and hekatostyas and by lochos’ ; the distribution is to the cavalry by ile, the Macedonian infantry by hekatostyes and the other infantry by lochos (the size being uncertain). Otherwise the cavalry receive two distributions. It thus follows that, if nothing has fallen out at VII 24 iv the distribution is to the Macedonian infantry by hekatostyes and Macedonian cavalry by lochos (the very lochoi established at III 16 xi).τοῖς δὲ κατ᾽ ἴλας τε καὶ ἑκατοστύας, τοῖς δὲ κατὰ λόχους,
VII 11 iii is Arrian’s own confection and evidence of little but his own uncertainty
‘lochoi’ is here used in much the same way that Arrian normally uses ‘taxis’ each unit here is caught under the umbrella term ‘lochos’, even the ‘ taxis’ of Argyraspides who exist side by side with two agemata, clearly one one foot and one mounted, and pezhetairoi and asthetairoi (bit of a blow for those who wish these to be Upper Macedonians, unless they want there to be a Persian settlement in Upper Macedonia!) the intrusion of the later term ‘argyraspides’ is a bit of a clue that this passage is just Arrian displaying the terms he knows. Nor is it likely that the complaints are actually those that moved the troops, they were really concerned about the disparate treatment of those being dismissed and those being retained and the criteria for belonging to each group, the anti-Orientalism seems to be grafted on by the sources.3] ὡς δὲ τὰ Περσῶν τε καὶ Μήδων αὐτοῖς ἐξηγγέλλετο, αἵ τε ἡγεμονίαι Πέρσαις διδόμεναι καὶ ἡ στρατιὰ ἡ βαρβαρικὴ ἐς λόχους τε καταλεγομένη καὶ τὰ Μακεδονικὰ ὀνόματα ἄγημά τι Περσικὸν καλούμενον καὶ πεζέταιροι Πέρσαι [καὶ ἀσθέτεροι ἄλλοι] καὶ ἀργυρασπίδων τάξις Περσικὴ καὶ ἡ τῶν ἑταίρων ἵππος καὶ ταύτης ἄλλο ἄγημα βασιλικόν, οὐκέτι καρτεροὶ σφῶν ἦσαν,
But when the news was reported to them about the Persians and Medes, that the military commands were being given to Persians, that the barbarian soldiers were being assigned to lochoi, and those given Macedonian names, a so-called Persian agema, Persian foot Companions and asthetairoi besides, a Persian taxis of silver shields, as well as the cavalry Companions, and another royal agema, they were no longer able to restrain themselves…
The various addresses at Issos and Gaugamela follow neatly from this;
II 7 iii
Which is paralleled by III 9 iiiὁ δὲ συγκαλέσας στρατηγούς τε καὶ ἰλάρχας καὶ τῶν ξυμμάχων τοὺς ἡγεμόνας
He called together the generals and the ilarchs and the leaders of the allies
Although the list has expanded at Gaugamela the picture is broadly the same as is the construction; certainty is impossible but I would venture Arrian found this grouping in his source. He then develops the theme,τούς τε ἑταίρους καὶ στρατηγοὺς καὶ ἰλάρχας καὶ τῶν συμμάχων τε καὶ τῶν μισθοφόρων ξένων τοὺς ἡγεμόνας ἐβουλεύετο
He summoned the Companions and the generals and ilarchs and the leaders of the allies and the foreign mercenaries
At III 9 v
But he then has III 9 vi]τοὺς αὐτοὺς ἡγεμόνας,
These same officers (as at 9 iii)
This is problematic, we should expect the taxiarchs to be the very ‘infantry leaders’ ‘pezwn hegemones’ ordered to encourage the men of their phalanx! Arrian seems to be collating his sources clumsily here, Ptolemy seems to have used ‘taxis’ when describing the individual phalanx units whereas Aristoboulos preferred ‘phalanx’. Nor is the construction logical, it seems to go infantry, cavalry, infantry, same infantry. I would venture this is one of Arrian’s own lists and that he has intruded the later cavalry ‘lochoi’; we then have small cavalry unit, larger cavalry unit, undefined infantry unit (taxis can encompass any size of unit), large infantry unit. Somewhere the officers of the Allies and mercenaries should be included, the choice lies between the initial ‘lochagoi’ or the general ‘taxiarchs’, either way these’lochagoi’ are not among the Macedonian infantry.τοὺς κατὰ σφᾶς δὲ ἑκάστους ἐξορμᾶν ἠξίου, λοχαγόν τε λοχίτας καὶ ἰλάρχην τὴν ἴλην τὴν αὑτοῦ ἕκαστον καὶ ταξιάρχους τὰς τάξεις, τούς τε ἡγεμόνας τῶν πεζῶν τὴν φάλαγγα ἕκαστον
…each was to encourage his own men, the lochagoi their lochoi, the ilarchs their ilai, the taxiarchs their taxeis and the infantry leaders their own phalanx…
II 10 ii reads
We cannot say for sure that these lochagoi are not Macedonian and, on the face of it, it does seem possible, but if they are they are not exalted individuals, they are less important than the ‘hegemones’ , less important than ilarchs, but more important than individual mercenaries. They unlikely to be commanding 500 men, the ilarchs command 250, they ought to represent a lower echelon, c 125 would be possible. Considerations of status seem not to effect this list, the ‘hegemones’ might be the named phalanx commanders, but they are usually ‘taxiarchs’ or ‘strategoi’, hegemon’ is reserved for lesser officers, one might posit ‘pentekosiarchoi’.ὡς δὲ ὁμοῦ ἤδη ἦν τὰ στρατόπεδα, ἐνταῦθα παριππεύων πάντῃ Ἀλέξανδρος παρεκάλει ἄνδρας ἀγαθοὺς γίγνεσθαι, οὐ τῶν ἡγεμόνων μόνον τὰ ὀνόματα ξὺν τῷ πρέποντι κόσμῳ ἀνακαλῶν, ἀλλὰ καὶ ἰλάρχας καὶ λοχαγοὺς ὀνομαστὶ καὶ τῶν ξένων τῶν μισθοφόρων, ὅσοι κατ᾽ ἀξίωσιν ἤ τινα ἀρετὴν γνωριμώτεροι ἦσαν
When the two armies were close, Alexander rode all along the front and bade them be worthy men, calling aloud with all proper distinctions not only the names of the leaders but even those of ilarchs and lochagoi, as well as any foreign mercenary who were distinguished by status or glory.
Which brings us to IV 2 I, where the infantry are ordered to make ladders, each ‘lochos’ for its own use. I have to concede that, if this comes from a source rather than Arrian, and that seems likely, the Macedonian structure DID include units called ‘lochoi’ but from the foregoing I would place then at a lower level than the pentekosiarchs.