When did Earth's solid inner core begin to grow?

In plain words

Estimates of the inner core's age range from about half a billion to several billion years. The answer depends on how fast the core loses heat.

Precise statement

Determine the inner-core nucleation age $t_{ic}$. Thermal models give $t_{ic}$ of roughly 0.5 to 1.5 Gyr for high core conductivity and much older values for low conductivity; paleomagnetic candidates include the Ediacaran ultra-weak field near 565 Ma and a Mesoproterozoic intensity rise near 1.3 to 1.5 Ga. An answer is $t_{ic}$ with uncertainty below about 0.2 Gyr consistent with core energetics and the paleointensity record.

What would settle it

A resolved core conductivity and heat budget combined with a dense, reliable Precambrian paleointensity record showing a unique nucleation signature.

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