Analogy is good but I don’t like the idea that the value exists before issuance. The bitcoins exist, but their value is yet to be decided because they haven’t touched a market. But their quantity has already been fixed.

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That's a valid concern, and it's not a perfect analogy. Authorized stock is not a hard limit in the way not yet mined bitcoin is. Perhaps it's better to think of Bitcoin not yet mined as existing, but belonging to an entity who has published its schedule of "spending them" on the labor and resources used by the mining network. That entity being the network itself.