https://en.wikipedia.org/wiki/Terra_preta
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I think charcoal's use in this context is more in terms of a structural matrix, rather than itself being of 'nutritious value'.
It is extremely absorbent to anything, specially nutrients in the soil so they don't get washed away by rain or irrigation. it releases them slowly.
I have done tests myself with very small quantities, 50 or so plants, half of those without, half with it, and plants certainly improve a lot.
We need scientific studies of thousands and thousands of plants for info about the combination of all those things.
It will require several disciplines, like genome extraction from soil, computer science to identify the microorganism present, lots of sensors for humidity, temperature, ph and so on.
I was at a soil management talk once, out in a paddock, and we dug a few holes looking at biomes and general soil quality. When we dug up bits of charcoal, the man said nothing has been burnt here for at least 50 years. It's my experience that wood is better at storing water: if interested have a look at hugelculture/ hugelkultur. It's a method that deliberately buries timber for nutrient and water retainment and as it composts it continues to feed the soil nearby.