I think righteousness is what Bible tells it is. and I have understood that it is basically right understanding, wisdom of the just, that comes visible in righteous actions. Like for example said in these:
…He who does righteousness is righteous, even as he is righteous. He who sins is of the devil, for the devil has been sinning from the beginning. To this end the Son of God was revealed, that he might destroy the works of the devil. Whoever is born of God doesn't commit sin, because his seed remains in him; and he can't sin, because he is born of God. In this the children of God are revealed, and the children of the devil. Whoever doesn't do righteousness is not of God, neither is he who doesn't love his brother.
1 John 3:7-10
Yahweh, who shall dwell in your sanctuary? Who shall live on your holy hill? He who walks blamelessly does what is right, And speaks truth in his heart; He who doesn't slander with his tongue, Nor does evil to his friend, Nor casts slurs against his fellow man; In whose eyes a vile man is despised, But who honors those who fear Yahweh; He who keeps an oath even when it hurts, and doesn't change; He who doesn't lend out his money for usury, Nor take a bribe against the innocent. He who does these things shall never be shaken. A Poem by David.
Ps. 15:1-5
The wicked borrow, and don't pay back, But the righteous give generously.
Ps. 37:21
The mouth of the righteous brings forth wisdom, But the perverse tongue will be cut off. The lips of the righteous know what is acceptable, But the mouth of the wicked is perverse.
Pro. 10:31-32
The thoughts of the righteous are just, But the advice of the wicked is deceitful… … A righteous man regards the life of his animal, But the tender mercies of the wicked are cruel… … A righteous person is cautious in friendship, But the way of the wicked leads them astray.
Pro. 12:5,10,26
A righteous man hates lies, But a wicked man brings shame and disgrace… … The light of the righteous shines brightly, But the lamp of the wicked is snuffed out.
Pro. 13:5,9
There are those who covet greedily all the day long; But the righteous give and don't withhold.
Pro. 21:26
The righteous care about justice for the poor. The wicked aren't concerned about knowledge.
Pro. 29:7
For a righteous man falls seven times, and rises up again; But the wicked are overthrown by calamity.
Pro. 24:16
I believe the righteousness can be achieved for example by hearing what Jesus told. His words can cause the change in persons innermost to righteous.
It is the spirit who gives life. The flesh profits nothing. The words that I speak to you are spirit, and are life.
John 6:63