Right with the standard
Dikaiosynē is being right — with the law, with the covenant, with God. In the Hebrew behind it (tsedaqah), God's righteousness is not merely his justice but his saving faithfulness: he sets things right. Paul seizes this: the gospel reveals 'the righteousness of God.'
Counted, or infused?
The verb in the same family — dikaioō, 'to justify' — drives the Reformation debate. Does God justify by declaring the believer righteous (a verdict, Christ's righteousness reckoned to faith — Rom 4:5; 2 Cor 5:21), or by making the believer righteous (grace infused, transforming)? Protestants read dikaioō forensically ('declare just'); Catholics read it transformatively ('make just'). The whole disagreement turns on what this one word-family does — count, or change.
Where This Word Decides Debates
Dikaiosyne (and the verb dikaioō) is the hinge of justification — imputed/forensic vs infused/transformative righteousness.
When This Word Study Proves Too Much
Don't reduce the OT 'righteousness of God' to bare courtroom acquittal — tsedaqah includes saving faithfulness. And don't settle the imputed/infused question by the English split between 'righteousness' and 'justice'; it's one Greek root.