One who fulfills their agreements is righteous or in the Hebrew Zaddiq. One who fails in their agreement has offended or sinned. Another way of looking at it is to say that the one who meets their agreement is innocent and the one who does not is guilty.
The word Pesh occurs 136 times in the Old Testament. Its basic meaning is "breach of a covenant." This type of sin is akin to breaching the stipulations of international treaties.
In scripture when God forgives sin he "Remembers it no more" or He bears it upon himself, He forgets it.
In the Greek of the New Testament there is a similar definition of sin being "to miss the mark" and the word was often used to describe archers who missed their targets. I have this definition from Strongs concordance:
Strong's Concordance hamartanó: to miss the mark, do wrong, sin Original Word: ἁμαρτάνω
Part of Speech: Verb
Transliteration: hamartanó
Phonetic Spelling: (ham-ar-tan'-o)
Short Definition: I sin
Definition: originally: I miss the mark, hence (a) I make a mistake, (b) I sin, commit a sin (against God); sometimes the idea of sinning against a fellow-creature is present. Cognate: 264 hamartánō (from 1 /A "not" and 3313 /méros, "a part, share") – properly, having no share in; to sin, which always brings forfeiture – i.e. eternal loss due to missing God's mark. Like 266 /hamartía, 264 (hamartánō) is regularly used in ancient times of an archer missing the target (Homer, Aesch., etc). Every decision (action) done apart from faith (4102 /pístis) is sin (Ro 14:23; cf. Heb 11:6). See 266 (hamartia).
My view of sin has been altered by the Biblical definitions of the words used to denote sin the the Old and New Testaments. To me righteousness is what brings us closer to God while sin is something that pulls us further from God. There are things that may move us from side to side and be mostly benign, neither good nor really bad but what is and is not a sin is not always clear so one should not apply black and white definitions in any given situation.
For example I know a couple and the husband became addicted to porn and stopped having sex with his wife, being that he was totally preoccupied by his addiction. So his wife turned around in response to him and began an affair with a married man. Whose sin is greater? They have both sinned and I think one sin begat the other and the greater point is not who is worse but that they are both guilty of sinning against each other.
And as another example if any of us were to see a man badly beaten on the side of the road and did not help him we would by most standards have committed a sin of omission, that is to say we sinned by doing nothing.
But in the parable of the Good Samaritan two priests pass by the Jew badly beaten and almost dead lying by the roadside. Most consider their lack of help to be sinful and they are right but there is more to the story, in the Old Testament there are a set of laws against touching corpses they say that doing so makes one impure and so they could not do their Temple work if they stopped to help him so they chose instead to do nothing and not even check to see if he was still alive.
The moral of the story is that we are all neighbors and to a degree responsible for one another, the idea of loving others as Christ loved us is very present in this parable but also present is the idea that we should not allow the letter of the law interfere with living out the spirit of it.
Helping this man and saving his life is more important that Temple work, if we pass by rather than helping then there is little good to be done in the Temple if we violate the essence of the Gospel, which according to an April 2014 conference talk by President Monson, love is the essence of the Gospel, and there is nothing loving about refusing to help one another.
It is odd to me that so many people consider some sins to be not that bad yet other sins are deal breakers and can't be forgiven. This denies the power of the Atonement to me. According to the Apostle Paul, all have sinned and fallen short of the glory of God. So we all sin, just not in the same ways, we all need the Atonement but we also are all deserving of the Atonement.
I think that if we view sin as missing the mark we can simply readjust and try again to see if we can make the grade. Yet if we view sin as a crime against God we give into fear mongering about God's wrath and give into the idea that we may be unforgivable.
Elder Russel M. Nelson once said "We all need to remember: men are that they might have joy—not guilt trips!"
Jesus simply told the adulteress to "Go and sin no more." There was no condemnation, no punishment, no guilt trips because the crowd that gathered to stone her to death was humbled into submission by Christ when He said "He who is without sin may cast the first stone."
None but Christ could have cast a stone but even though He could cast a stone, He did not. That is a very important lesson to us all regarding sin.