What did Jesus accomplish on His cross?

What did Jesus accomplish on His cross? The light that will yet "lighten the earth with glory” (cf. Rev. 18:1-4) will make it clear to every honest heart. It's a self-humbling truth that is cataclysmic.
In John 12:47 He said He didn't come to pronounce condemnation on the world, "but to save the world.” "God sent not His Son into the world to condemn the world; but that the world through Him might be saved” (John 3:17). So the Father sent Him to save the world; that was His allotted task.
In 17:4 He claims He accomplished the work the Father gave Him to do. He did not say, Father, I tried to save the world, I did the best I could do, but they wouldn't let me do it! I gave everybody the offer of salvation, but the majority wouldn't have it! Sorry!
No, He said, "Father, ... I have finished the work which You have given Me to do,” I brought it to completion. And in His last breath on His cross He said, "It is finished, " the work is done, complete. To that last breath He had "condemned sin in the flesh,” said "No!” to self, as our "last Adam” (1 Cor. 15:45); He had reversed what the fallen "first Adam” did to the human race, and transformed his legal condemnation into a judicial "verdict of acquittal” (cf. Rom. 5:15-18, New English Bible).
Christ built a bridge over the chasm sin had made for the human race, and rejected the most awful temptation Satan could invent--the temptation to despair when He felt the curse of God to its uttermost, "My God, ... You have forsaken Me!” (read Psalm 22 all the way through--there's the story!). For every human soul Jesus made despair unnecessary and obsolete.
He (a) "saved the world,” or (b) He only tried to? Let's believe Him when He tells us what He did.
And if He did, then He saved you--five things, says Paul in Ephesians 1: "blessed” you, "chose” you, "predestinated” you, "adopted” you, "made [you] accepted in the Beloved” (vss. 3-6). The "us” means the whole world, you. When at the Jordan John baptized Jesus, the Father proclaimed Him "My beloved Son, in whom I am well pleased” (Matt. 3:17; fine). But you must believe that He also threw His arms around you! You can resist and reject all that He did for you through the awful sin of unbelief. Respond to Him, thank Him! Pray, "Lord, I believe; help Thou mine unbelief!” (Mark 9:24).