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In our neck of the woods, you're more likely to find composted/aged pine bark. And it's an excellent growing media. One of the best I've ever used, in fact.
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That's exactly right. Phosphate takes time to break down in soil. And there's more biomass, hence more microbial colonization, and more biodiversity. You will literally not in a thousand years get rock phosphate to break down in a container, short of making the media so acidic, that it won't grow a plant.
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Mushroom compost is composted horse manure. (along with bedding) It's too heavy to use straight, because you get too much rain. If you lived in a desert, I'd say go for it.
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Calcium is totally unnecessary for soil anywhere on the East Coast. For containers, different story. What is your current pH?
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Calcium nitrate is not readily available. Useless. You'll have better results with Epsom or calcium acetate. (vinegar and eggshells)
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BER is commonly caused by heavy rain, and disruption of nutrient uptake. But I can't say that authoritatively, without knowing your story. What have you fed it so far? (for calcium supplementation) Containers, right?