So I hope the necklace aka "Fractal Neuronic Cloning" is supposed to be a reference of Aristophanes, the playwright, tale in Plato's Synopsium. Aka Aristophanes says the origin of love (and also of culture) is than mankind was originally 3 sexes and each sex had four hands, four arms, two heads, etc. Well "the Gods" split the mankind into two for they were too powerful and thus we seek out one another aka our soulmates but also community in the greater culture itself.

Or to put it more poetically this song. https://www.youtube.com/watch?v=_zU3U7E1Odc

So like the ouroboros symbol of infinity representing you and your soulmate, but that ouroboros symbol of infinity is connected to the great circle that is the sun in alchemy (the circle of unity.) If this theory is true the necklace makes sense from a symbole perspective.

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Then again this theory is likely wrong. Afterall one of the four show-creators of Picard is Alex Kurtzman. Then again maybe my fears are wrong for Michael Chabon is also one of the show creators and to my understanding he is the opposite type of energy.