Rom 8:1: Is the KJV correct, and all other versions incorrect?

In the KJV, we read in Rom 8:1: "There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit."

The translators of the KJV added the last phrase, "who walk not after the flesh, but after the Spirit", apparently basing it on verse 4 of the same chapter, which reads in Rom 8:4, "That the righteousness of the law might be fulfilled in us, who "walk not after the flesh, but after the Spirit".

Rom 8:1 does not contain the last phrase in any other version of the scriptures.

Does including the last phrase in the KJV modify the meaning of the verse? Let's investigate the context, and original Greek words used by Paul. In verse 1, the word "condemnation" is translated from the Greek word, "Katakrima", which is used only three times in the scriptures: Rom 5:16, Rom 5:18, and Rom 8:1. "Condemnation" is used in these three instances to describe the consequences of Adam being told "for dust thou art, and unto dust shalt thou return" (Gen 3:19). Thus, Adam and all his descendants (the entire human race) are sentenced (condemned) to die, and return to dust to remain for eternity. That is what Paul is saying in Rom 5:16 & 18. In the remainder of Rom 5, Paul tells of a remedy for this situation, salvation offered through Jesus Christ. Baptism into Christ (in this dispensation) provides us with the remedy.

Paul, in Romans chapters 5 & 8, makes a distinction of the human race's situation before and after being baptized into Christ:

Before: like the entire human race, we are condemned, under condemnation (Katakrima) (Rom 5:16, 18).

After: we are in Christ, no longer under condemnation (Katakrima) (Rom 8:1).

In Rom 8:1, Paul is telling us that the condemnation (Katakrima) is removed by being baptized into Christ, gone forever, never to return. Its removal is not dependent on how we behave in the future. This is not to say that our behavior does not have any bearing on whether, or not, we receive eternal life. This is what Paul means when, later in Rom 8, he makes reference to "walking after the flesh", contrasted to "walking after the spirit". If, at the judgement seat of Christ, one is found to be "unfaithful", the individual will be "condemned with the world" (I Cor 11:32). This condemnation will not be "Katakrima", reimposed, but another condemnation "krima", brought on by their own actions.

Understanding this, the KJV's introduction of the "conditional" statement in the latter phrase of Rom 8:1 actually changes the meaning of what Paul is telling us - "Adamic Condemnation, (Katakrima) is removed by being baptized into Christ" - and should be discarded.