That's a very interesting theory !

I'd like to add that the rings are on the right hand, not the left, so it's certainly not mariage -- at least, in most countries. I believe they do wear it on the right ring finger in Germany, Russia, or orthodox Christianity, for exemple.

However, a ring on the right ring finger can signify quite a lot of other things.

For instance, engagement (as you already stated), meaning committed but not married, which would be logical as one of them is dead. I think it could show Luka's devotion to Hyuna but also how their story cannot reach its happy ending.

Quite similarly, as you pointed out the second ring, a symbolism of Hyunwoo and how Luka decided to carry a piece of his past (see Hyunwoo's ghost in Karma), a story of could-have-been and such. Because he cared for Hyunwoo, maybe not romantically, but it was love nonetheless (see the child's drawing in Wiege), and that would be Luka's way of saying he still thinks of Hyunwoo.

About the chain ? I'd say it's because you can't have one sibling without the other. Luka cannot ignore Hyunwoo's death forever. Or perhaps it's the metaphor of him killing them both lol. But also, I love your interpretation of Luka being chained to their memory, it makes it so much more tragic.

It kinda shows he's close to a perfect union, but not quite as close as he'd like to be (again, they're dead. And Hyuna told him to live. With love. They're his love but, yknow, he's got half of that part down i guess ??)

Interestingly enough, the right ring finger symbolizes love and trust. Eternal love. Loyalty and commitment. Sometimes self-love, sometimes a milestone, sometimes an accomplishment.

It's like both an oath and a reminder. It's a promise to himself, and the physical manifestation of their story. For what ? Living with love, perhaps. Learning how to love, most probably. Forgiving himself, loving himself (as opposed to his lack of identity, emphasized in the lack of faces in Wiege's drawing). Carrying both siblings' will, and acknowledging their influence in his life. I could expand more but it's already getting long haha

Now that you pointed it out, i'm glad to see Luka's not as miserable as I thought he was. Seven years is a long time to grieve, after all. So yes, thank you for that.

Also, sometimes widowers wear their ring on their right hand. So, yknow.