Half past arsed, n. An unspecified small hour of the night, at which it is pointless or undesirable to be conscious. Compare arsed; half-arsed; arsing about.
(1) "I've been up since half past arsed, and I'm sodding well shattered!" (The hour was so ridiculous, I can't be arsed to specify it. And possibly couldn't even be arsed to check it at the time.)
(2) "I rolled in at half past arsed and spent an hour surfing for cat videos." (The hour was so incapacitating, my options were limited to arsing about, or attempting constructive action in a futilely half-arsed fashion.)
And thus, with every humble brush-stroke each diligent artist adds, the great landscape of the English language grows a little more expressive and refined.