Did Jesus Die on The Cross for The Just/Elect/Saved Whose Names Are Written in The Book of Life OR

No, He died only for those who will inhabit the world to come, not everyone. Had He not died for them, then there wouldn't
be a world to come.

I agree. I was using them to see what they said is all.

Bed time. TTYL.

Good Night Brother!

Using the Greek translation

The word kosmos refers to the universe or the whole of creation.

kosmos is the word the Apostle John used in 1 John 2:2

2 He is the propitiation for our sins, and not for ours only but also for the sins of the whole world = kosmos or the universe or the whole of creation

So John is saying not just the saved, but Jesus died for EVERYONE!

kósmos
κόσμος = kosmos or the universe or the whole of creation

That's ALL people, not just the saved. John, the Apostle is saying Jesus died for every human being that "ever" lived.

1 John 2:2
And he is the propitiation for our sins: and not for ours only, but also for [the sins of] the whole world.
και
and

αυτος
he

ιλασμος
-

εστιν
he is

περι
about

των
of the

αμαρτιων
of errors

ημων
of us

ου
not

περι
about

των
of the

ημετερων
of our

δε
-

μονον
only

αλλα
but

και
and

περι
about

ολου
of whole

του
of the

κοσμου
of world-universe

Yep, Jesus died for everyone, the saved, and the ones who reject Him.

And so you forced the word forced into the equation

The Gift of repentance comes with the New Birth, a new heart and inner man. This is the New Man that has repentance, his actions have been ordained by God to walk in, not forced

That scripture pertains only to the saved, they have Christ as their Advocate and Intercessor, even if they sin 1 jJn 2:1-2

My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous:

2 And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.

Christ isnt the advocate for lost people, He never knew them Matt 7:23

23 And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.

You think Hes their advocate and propitiation ?

Mathew 21:32
For John came to you in the way of justice, and you did not believe him. But the publicans and the harlots believed him: but you, seeing it, did not even afterwards repent, that you might believe him.

The New Testament commandments of God do not testify to what you have written here. The New Testament commandments are still binding on everyone.

Can you name a New Testament commandment/commandments from God which you believe are no longer binding on anyone.

The elect are saved because they believe and obey Jesus Christ.

A person who does not obey Jesus Christ is not holy and without blame.

Christ did not shed His blood for heathens; Christ only shed His blood for the elect.

The Holy Bible and the correct scholars are in 100% agreement.

Whatever was intended by God to be covered by Christ's offering can neither die nor be destroyed. If either could, then His offering didn't achieve what God had intended it to achieve. But we know it wasn't a failure and perfectly achieved what it was intended for because God had fully accepted it - hence Christ's title of Saviour. It can't be both ways: that He is the Saviour and yet all covered by it don't become saved - that would be a logical contradiction of the highest order.
This current "kosmos" (world) is to be destroyed by God but two are mentioned in the Bible not one: this one, along with its unsaved, which will be destroyed, and a new one with those saved by Christ who will inhabit it - both eternal. Christ is the Saviour and as Saviour, whatever was covered by His offering, can neither die nor be destroyed but must live/exist eternally.
Now, I cannot speak to what the new one will be like - it might just be Christ together with His saved in the air (see 1 Th 4:17 below), and not a world as we know it today.

[2Pe 3:7, 10-12 KJV]
7 But the heavens and the earth, which are now, by the same word are kept in store, reserved unto fire against the day of judgment and perdition of ungodly men. ...
10 But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up.
11 [Seeing] then [that] all these things shall be dissolved, what manner [of persons] ought ye to be in [all] holy conversation and godliness,
12 Looking for and hasting unto the coming of the day of God, wherein the heavens being on fire shall be dissolved, and the elements shall melt with fervent heat?

[1Th 4:17 KJV]
17 Then we which are alive [and] remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.
[Mar 10:30 KJV]
30 But he shall receive an hundredfold now in this time, houses, and brethren, and sisters, and mothers, and children, and lands, with persecutions; and in the world to come eternal life.
[Luk 18:30 KJV]
30 Who shall not receive manifold more in this present time, and in the world to come life everlasting.
[Heb 2:5 KJV]
5 For unto the angels hath he not put in subjection the world to come, whereof we speak.
[Heb 6:5 KJV]
5 And have tasted the good word of God, and the powers of the world to come,

By the fact that Christ shed His blood for them, is what makes them not heathens - but not because of anything they might do.

I don't understand your point. Can you explain it in your own words.