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Is there any intention by the respective author or by Bitcoin.org to edit, improve or re-write the white paper for absolute clarity?

Among others I do not understand the value of repetitive manipulation of the message, until a hard-to-find number can be added to the message, that then forces the digest into an arbitrary format to show a given number of starting zeros.

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Is there any intention by the respective author or by Bitcoin.org to edit, improve or re-write the white paper for absolute clarity?

The pseudonymous author (Satoshi Nakamoto) has not been present online for many years; I suspect we will not see Satoshi return for a whitepaper update.

You can learn more about the contributors of bitcoin.org on this page.

Updating the whitepaper is not a priority in any sense. It is a technical paper that lays out the fundamentals of the Bitcoin Network, and it does that job well. Further, I don't believe any person or party would be capable of doing so in a way that everyone can agree on. Bitcoin has no leader, and the whitepaper is an artifact of Bitcoin's history- which is not to say it is irrelevant, just that it had its place in time. It is a great resource and starting point to learning about the Bitcoin protocol, but the modern Bitcoin network has advanced beyond what is laid out in the whitepaper, and as such there are now many other additional resources available to learn from. This website is one such resource, if you search through the history of questions you'll find there is a lot of good information available here.

With so many other resources available online, there really isn't a need to rewrite the whitepaper, at least not in any 'official capacity', even if such a thing were to exist.

Among others I do not understand the value of repetitive manipulation of the message, until a hard-to-find number can be added to the message, that then forces the digest into an arbitrary format to show a given number of starting zeros.

You may be interested to read the answer I wrote here, I think it may answer your question.

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There are many explanations of Bitcoin online, but the whitepaper is a historical document, and it is important, for one, in order to understand the inventor'(s) initial design and intentions.

Among others I do not understand the value of repetitive manipulation of the message, until a hard-to-find number can be added to the message, that then forces the digest into an arbitrary format to show a given number of starting zeros.

It is important because it gives everyone on the distributed network something to agree on. If the data is easily changed or forged, it is difficult to agree on. One of the main purposes of Bitcoin, as a currency, is that it is decentralized. Thus, participants on the network have to agree on supply and ownership, since there is no trust authority. Rather, users trust in the irreversibility and unforgeability of the cryptography, which includes the hash function (for mining and consensus) and the digital signing algorithms (to prove ownership).

The hash function (two rounds of SHA256) is a one-way function, so it is not reversible, i.e. you cannot calculate an input for a given output other than brute forcing (guessing). So, if you find a solution that meets a value threshold, it proves that a certain amount of work was done, on average. This acts as a way for the network to stamp transaction data as irreversibly accepted.

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