The stochastic nature of hashing is irrelevant to entropy modeling in Bitcoin. What matters is the finite, predetermined search space (a bounded entropy field) being resolved. Whether the valid hash is found on the first try or the trillionth, the total entropy being collapsed remains the same. The randomness is local; the structure is global. Bitcoin defines the cost of resolution, not the path to it. That’s exactly why entropy can be modeled: the space is known, the work is measurable, and the outcome is irreversible.

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Yes, good clarification and I think you're correct in a sense. Entropy would be a highly explanatory way to discuss hashing 'mattering'. There is still the question of 'mattering to what end'. Hashes 'matter to the end of building the chain' to the extent they successfully find a golden nonce. (e.g. THE successful hash submits a block to the chain to build upon.) Hashes that do not succeed to that end do not matter in that sense. BUT, from the perspective of entropy, yes, all hashes matter as a MORE descriptive illustration than the poisson example given above.... I'd have to look more into how entropy units function because I understand the idea of entropy units per satoshi, but would want to clarify entropy units as a function of searching the field and not entropy as a function of energy input into machines. Thank you!