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Let's assume that there is an unbreakable Adamantium strand interwoven with Uru, Promethhium, Vibranium and also strengthened by mystical energy attached to the GL ring and Mjolnir as the line. Now the Ring is attempting to find a new host, while Mjolnir is attempting to return to Thor.

Which one gets pulled?

Before anyone suggests it, the line reinforces the strap on Mjolnir.

Mjolnir wins. I just saw Guy stop a ring from finding a wielder. I can't recall an incident where Mjolnir is prevented from returning to Thor that doesn't involve Odin.

No GL ring, alone, is powerful enough to fight Mjolner.

Mjolner: 9/10 (the 1 ring-win comes from narrative/circumstanstial rationales: the Guardians add their power, directly, to will it so; other GL's add their power/will to the endeavor... and take a *long* ass time; Batman uses the Batkick; et al...)

Guy is part of the GL Honor Guard. I'm thinking that may be part of the reason he could stop the ring since he was able to DL the ring's data. He's also a god level being! biscuits

But yeah, I don't see a GL ring's directive to find a replacement Lantern beating Odin's enchantment on Mjolnir.

GL ring runs out of energy there for Mjolnir wins

Mjolnir wins.