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Earth’s diameter is around 13000km, if there is an inner core with a 600 km width, you will find this core around 6000km below your feet, which is more than 1600 km below your feet (as the article correctly stated…)

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Yes, I also noticed it. It's too large a difference to be some miles to km conversion mistake. There is nothing 1600 km wide inside [1], not even the distance between the inner core and this new inner-inner core boundaries.

[1] https://en.wikipedia.org/wiki/Core%E2%80%93mantle_boundary

I do think conversion is involved in generating these odd figures somehow. May not be the sole part, but the figure in the title is definitely an conversion that's sprouted additional sigfigs.

644 km is 400,000 miles (within 0.04% error).

Typo there: 400 miles. The actual paper's abstract [1] says "~650-km". In a skim through I didn't see anything that might correspond to the strange 1600km depth.

[1] https://www.nature.com/articles/s41467-023-36074-2

And if I was asked, I would have guessed it would have been around 1000km.

You'd have guessed from a horizontal position in that case.

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