Genre and place in the book. The close of the anti-fame series (after 04-19), but now at the level of value-theory: beauty and the good are self-valued (ἐξ ἑαυτοῦ); praise adds nothing to them. This is the foundation under 4.19: if the good is self-valued, posthumous repute is nothing it needs.
καλὸν ἐξ ἑαυτοῦ — beautiful of itself. The main thesis: everything καλόν is beautiful from itself and "terminates in itself" (ἐφ’ ἑαυτὸ καταλήγει); praise is no part of it (οὐκ ἔχον μέρος ἑαυτοῦ τὸν ἔπαινον). The praised is made no better, the blamed no worse. Value is intrinsic; repute is external and indifferent.
Two levels of καλόν. (1) "commonly called beautiful" — material things, works of art; (2) "the truly beautiful" (ὄντως καλόν) — law (νόμος), truth (ἀλήθεια), benevolence (εὔνοια), TERMmodesty / reverence (αἰδώς). Neither needs praise.
The emerald and the descending list. σμαράγδιον — an emerald is made no worse for being unpraised; nor gold, ivory, purple, a lyre, a little knife, a flower, a shrub. The list deliberately "descends" from the precious to the trivial: the argument grows stronger — if even a trinket loses nothing for want of praise, all the more the truly beautiful.
The link with self-sufficiency. The truly beautiful (= virtue) is self-sufficient: praise is no part of its good (cf. DOGMAvirtue-is-sufficient). Hence 5.6 (the good deed, like a vine bearing grapes, seeks no onlookers) and 7.73 (having done a good act, do not look for a "third thing" — recognition or a return).
The disciplines. The principal one is assent: the judgement that value is intrinsic and that praise or blame do not touch it. The secondary is desire: from it follows not craving praise (a continuation of 04-19).
Parallels. The good is self-valued, repute indifferent — 04-19; Med. 5.6; 7.73. The truly beautiful needs no praise — 03-06; cf. DOGMAvirtue-is-sufficient. Praise comes from others' opinion, not the thing's worth — 02-12; cf. the Stoic doctrine that the good is καλόν (beautiful) and choiceworthy for its own sake (DL 7.100–101).