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Logically, an argument with an AND has to have all its premises true to make it valid. So... the Arkenstone can't be a Silmaril, it just isn't valid at least logically. Even if we take the argument that the world has been remade by the fall of Numenor.
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I don't quite follow you. Forgive the completely irrelevant foray into logic, but meseems that this quote:
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‘And they knew that those jewels could not be found and brought together again, unless the world be broken and remade.’
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. . . would be parsed thus in sentential logic:
~(Br & R) -> ~(F & BT)
. . . where 'Br' is 'The world is broken', 'R' is 'The world is remade', 'F' is 'The Silmarils are found', and 'BT' is 'The Silmarils are brought together again'. Strictly speaking, the statement allows the Silmarils to be found (even if the world is not broken and remade) as long as they are not brought together again. And if the world was indeed 'broken and remade' then nothing whatsoever is ruled out.
Of course, that kind of literal-minded reading is rather out of place here.
Anyway, I still haven't finished
Return to Bag-End, but I look forward to what Rateliff has to say about the Arkenstone.