Μη in this sentence is not explained either in Smyth or any commented editions available online κελευει μείναι επι του ποταμού μη διαβαντας. It does not appear to be conditional, nor can it be generalizing. Or can it be explained by 2737a μη after imperative?
Although the verbal idea is expressed as a participle, it’s a prohibition; therefore μη.
This is what my Greek grammar in Russian of 1888 says but Smyth does not have it.
Smyth 2737:
Where μή is used when we expect οὐ the negative expression usually depends on a verb that either has μή or would have it, if negatived.
a. After imperatives. Thus, σάφ᾽ ἴσθι μή με θωπεύσοντά σε know well that I shall not fawn upon thee E. Heracl. 983, ““νόμιζε μηδὲν εἶναι τῶν ἀνθρωπίνων βέβαιον εἶναι” consider nothing in human life to be secure” I. 1.42 ( = μὴ νόμιζέ τι κτλ.), ““ὡς οὖν μὴ μόνον κρί_νοντες, ἀλλὰ καὶ θεωρούμενοι, οὕτω τὴν ψῆφον φέρετε” cast your ballots then in the belief not only that you are passing judgment but also that the eyes of the world are upon you” Aes. 3.247 (cp. 2732). See also 2086 b.
b. After conditional expressions. Thus, ““εἰ δέ τις . . . νομίζει τι μὴ ἱκανῶς εἰρῆσθαι” but if any one thinks some point has not been sufficiently mentioned” And. 1.70, λύ_σετε δὲ οὐδὲ τὰ_ς Λακεδαιμονίων σπονδὰ_ς δεχόμενοι ( = ἐὰ_ν δέχησθε) ἡμᾶς μηδετ<*>´οων ὄντας ξυμμάχους and by receiving us, who are allies of neither, you will not be violating the treaty with the Lacedaemonians either T. 1.35. Cp. 2736 a.
c. > Other cases: ““κελεύει μεῖναι ἐπὶ τοῦ ποταμοῦ μὴ διαβάντας” he ordered them to remain by the river without crossing” X. A. 4.3.28 (here μεῖναι, if negatived, would take μή, 2720)> , ““ὑπέσχετο εἰρήνην ποιήσειν μήτε ὅμηρα δοὺς μήτε τὰ τείχη καθελών” he promised that he would bring peace about without giving hostages or destroying the walls” L. 12.68 (here ποιήσειν, if negatived, would take μή, 2725).
N.—But οὐ may assert itself even under the above circumstances; as μὴ ὅ γε οὐ χρὴ ποίει don’t do what is really wrong P. Eu. 307b, ““ἢ ἀφίετέ με ἢ μὴ ἀφίετε ὡς ἐμοῦ οὐκ ἂν ποιήσαντος ἄλλα” either acquit me or do not acquit me in the knowledge that I should not act otherwise” P. A. 30b (cp. 2732), ““εἰ νομίζεις οὐχ ὑφέξειν τὴν δίκην” if thou thinkest not to suffer the penalty” S. O. T. 551 ( = οὐχ ὑφέξω), εἰ γνωσθησόμεθα ξυνελθόντες μέν, ἀμύνεσθαι δὲ οὐ (some Mss.) ““τολμῶντες” if we shall be known to have come together, and yet not to have the courage to avenge ourselves” T. 1.124 (it would be said of them: ξυνῆλθον μέν, ἀμύ_νεσθαι δὲ οὐκ ἐτόλμων, a contrast, cp. 2690).
d. On μή in questions where we might expect οὐ, see 2676 b.
It’s difficult to find this point in Smyth, especially if you’re using the on-line version, and Smyth’s explanation is perverse. μεῖναι is not, in fact, negatived – it’s a positive command – and the reason for μὴ really has nothing to do with μεῖναι: the reason for μὴ is that μὴ διαβάντας represents a prohibition. And Smyth’s general point under which this appears, "[w]here μή is used when we expect οὐ . . . " is framed in terms of the expectations of an English-speaker, not in terms of how the Greek works.