# Mathematical proof that Craig S. Wright is Satoshi Nakamoto

# Introduction

British/Australian polymath Craig S. Wright is Satoshi Nakamoto, the inventor of Bitcoin.

**But he didn’t sign! And somebody else signed against him!** — Yes, but let’s leave this to a later section in this article, and let’s first look at the other facts and the math.

Despite a fabricated net of misinformation that has snared the public with widely spread narratives and propaganda, the truth is gradually breaking out. More and more people are able to overcome negative impressions and distractions and come to the objective and rational truth.

I started by accepting the then prevailing narrative that Craig Wright was a fraud, but reached an opposite conclusion after an independent study.

One has to study both the **history **and the **science **of Bitcoin to draw a reasonable conclusion. This could take books to explain (and books will be written and movies will be made), but one may start with the following (and also further follow through the links provided in the references):

How I know Craig Wright is Satoshi Nakamoto: Connor Murray.

Why I Believe Craig Wright is Most Likely Satoshi

Comments on Kleiman v. Wright verdict

Craig Wright is Satoshi, counter arguments

**While doing your research, try to evaluate the list of inquiries below. None of them standing alone can absolutely prove the identity of Satoshi, but all must be considered together with a proper mathematical model, most importantly the Bayesian probability theorem — see below.**

# Mounting Evidence and Attestations

1. Who has the *registered *copyright to the Bitcoin whitepaper and Bitcoin genesis database? (Answer: Craig Wright and no one else. The registered copyright has been put through an infringement lawsuit and held valid. And objections all come from infringers, not a single competing author. No one else has challenged the copyright by producing any evidence or even just a claim of being the true author instead. See Craig Wright’s Bitcoin Whitepaper Copyright Battle Continues, and Craig S. Wright’s copyright claim is a good “handicap signal”)

2. Who was sued in the court as a coinventor of Bitcoin for over a hundred billion dollars by a party alleging to be another coinventor, did not deny his identity and the ownership of over 1 million bitcoins belonged to Satoshi (doing which would have been an easy defense against any alleged liability to have the lawsuits dismissed quickly), but instead spent millions to go through the trial and won the case by proving in the court of law before the jury that he alone is the sole inventor of Bitcoin? (Answer: Craig Wright and no one else. See Comments on Kleiman v. Wright verdict, and In expectation of the historic Bitcoin trial: Kleiman v. Wright.)

3. *Update as of August 1, 2022*: Who in the world sued a libeler who made defamatory statements alleging his claiming to be Satoshi was fraudulent, and won in all accounts, by producing “a crazy amount of evidence” that he is indeed Satoshi? (Answer: Craig Wright and no one else. See, for example, Wright v. McCormack, and Dr Wright succeeds in libel action against podcaster Mccormack.)

4. How many people in the world have multiple high-profile witnesses, such as Gavin Andresen and Ian Grigg, who were the earliest prominent participants of Bitcoin and had intensive personal interaction with Satoshi Nakamoto, and were later convinced based on intimate personal knowledge that the person Satoshi they had interacted with matches exactly the person in question? (Answer: exactly one)

5. Who in this world have had **witnesses testifying under oath**, and many more expressly willing to testify under oath, that they knew the person had been working on something that was clearly and identifiably the subject matter of Bitcoin, before the Bitcoin whitepaper was released? (Answer: Craig Wright and no one else.)

6. Who in this world can produce evidence, any evidence, that they had some work products, before the Bitcoin whitepaper was released (the evidence has already been collected, but not presented in the recent Kleiman v. Wright trial due to Wright’s defense team’s tactic of reserving the evidence for the next occasion that has more direct relevance to Satoshi identity)? (Answer: Craig Wright and no one else.)

7. How many people in this world are known for reporting business activities related to creating Bitcoin in the tax return as early as your 2009, and, further, for being subsequently identified and attacked by the tax authority alleging tax liabilities due to his owning and running Bitcoin in those earliest years (including years preceding Bitcoin’s release in 2008)? (Answer: exactly one)

8. How many people in the world are known to have been involved in the earliest stage of Bitcoin development and are also skilled in the programming language Forth (the requisite language used for Bitcoin script designing)? (Answer: exactly one)

9. How many people in the world are known to have been involved in the earliest stage of Bitcoin and also had worked extensively on Bitcoin’s precursor tech and products such as digital cash, cybersecurity, and gaming systems for years before Bitcoin’s release? (Answer: exactly one, and he also happens to be the single most highly and extensively certified individual in the area of cybersecurity, including GSE CISSP, CISA, CISM, CCE, GCFA, GLEG, GREM, and GSPA certificates)

10. How many people in the world are known to have been involved in the earliest stage of Bitcoin and are also an expert on all the following key disciplines which are clearly a requisite expertise for inventing Bitcoin (if you have read the actual whitepaper you would agree): economics, monetary systems, law, computer sciences, cybersecurity, cryptography, and gaming theory? (Answer: exactly one, and he also happens to have multiple PhD degrees, one in computer science, one in economics, and another theology, plus more than 20 other academic degrees.)

11. How many people in the world knew that Bitcoin was **Turing complete** from the very beginning, when the Bitcoin gurus, including those that are still considered by the BTC community to be most likely Satoshi, were not only clueless but in fact adamantly claimed the opposite, all before it was rigorously proven both theoretically and empirically? (Answer: exactly one, and you should also understand that the question of Turing completeness of a computational system is not an ancillary question, but the most fundamental one, perhaps singularly most suited for testing the system’s creator-level knowledge.)

12. Who asked and then gave the answers to such questions about Bitcoin that even the question itself seemed strange at the time let alone an answer, but immediately became essential understanding about Bitcoin once they had been asked and answered by the person? These questions include: Why bitcoin is not a crypto? Why true Peer-to-Peer means the sender sends bitcoin directly to receiver without first submitting the transaction to miners? Why SWN for the miners? Why hashing is signaling? Why miner award is a necessary but temporary bootstrapping strategy? Why SPV? Why bitcoin is cash not gold? Why using Merkle Tree is not a security measure but rather for scalability? etc. (Answer: Craig Wright and no one else.)

13. Who showed understandings of Bitcoin scripts and gave explanations of their theoretical considerations and practical applications to a level that only the designer would and to an extent that no one else in the world comes even remotely close? (Answer: Craig Wright and no one else)

14. Who gave the original (the first ever) explanation for why Bitcoin is not encrypted, and why Bitcoin protects privacy but does not create anonymity, and why Bitcoin is designed to not only comply with the law, but in fact further enhance the rule of law, rather than be antigovernment (something that sounds counterintuitive but would become crystal clear with hindsight once one has learned about it and gone back to read carefully the whitepaper again)? (Answer: Craig Wright and no one else)

15. Who gave the original explanation for why Bitcoin’s security is not primarily based on a computational design, but rather on economic principles (again, something that sounds unnatural but becomes crystal clear with hindsight once one has heard about it and has gone back to read carefully the whitepaper again)? (Answer: Craig Wright and no one else)

16. How many people in this world have invented and filed hundreds of patent applications for technologies related to or derived from the original Bitcoin? (Answer: exactly one)

17. Who leads the building of the only platform in the world that is truthful to the original Bitcoin whitepaper, claims to be Satoshi Nakamoto, and has a world-class teams agreeing with his claims and devoted to building the Satoshi vision, even though they know quite clearly the whole crypto world is against them, and they’re going to lose opportunities of making quick money by not following those “number go up” Ponzi schemes? (Answer: Craig Wright and no one else)

The list can go on.

Again, this is not to argue that each piece of the above evidence standing alone would prove conclusively Craig Wright is Satoshi. But it is important to note the high level of objectivity (none of them are subjective opinions, but all are factual in nature, whether true or false), the independence of each from others among the listed pieces of evidence, and the unlikelihood that they are all a result of a concerted propaganda. Together they have a determinative impact if put together and evaluated under a proper mathematical model (see below).

In this light, **try to honestly and objectively study the above questions, plug your answers into the mathematical framework outlined in this article for a probabilistic determination** **(see below), and reach a rational scientific conclusion.**

**But, but, he didn’t sign! And somebody else signed against him!** — Yes, but let’s leave this to a later section in this article, and let’s first look at the math.

# What does math have to do with this?

The main point of this article is not to enlist all the evidence and attestations (which are mounting high, see above) supporting Craig Wright’s Satoshi identity, but to make a mathematical argument helping readers to weigh the evidence more scientifically and objectively.

A proper mathematical model is important to collectively evaluate the weight of evidence that has multiple attestation factors. It is so even if one assumes variable or partial credibility of each attestation (see below).

Fundamentally, this has to do with human psychology and how human minds work.

Human mind is usually good at measuring a single or linear factor, but becomes increasingly poor with a progression of multiple multiplications, which are typically **exponential phenomena**.

That’s why we must rely on math.

In the realm of investment, for example, people who trust math understand the compounding effect, while people who just trust their gut feeling tend to miss the profound compounding effect, not because they are stupid, but because our minds, or the “brain muscles”, are not made to naturally measure or cope with exponential phenomena.

Likewise, in the realm of evidence and testimonies, people’s minds are relatively good at evaluating the weight of each piece of evidence, but tend to fail to see the combined effect on the weight of the evidence, as human minds tend to look at each piece of evidence separately, not understanding that independent pieces of evidence corroborating together actually result in **exponentially **heavier weight in evidentiary value.

# The math

Let’s use the Bayesian methodology to estimate the probability of a hypothesis being true.

Bayesian method starts with specifying a prior probability of a hypothesis (H) given the initial evidence or when there is no specific evidence, and updates it to a posterior probability of the hypotheses using new evidence (E). There can be multiple consecutive updates, each using a new piece of evidence according to the Bayesian update formula. [1]

(Note [1]: to simplify the matter and focus on the most consequential concepts, we do not get into the difference between *likelihood *and *probability*, distributional statistics and fixed hypothesis, etc. In addition, the probability here, prior or posterior, is only numerically meaningful when the probabilities of two competing hypotheses are compared with each other. )

The Bayes’ Theorem Formula for updating from Prior Probability to Posterior Probability:

P(H|E) = P(H) x P(E|H)/P(E)

Where,

H = Hypothesis (in this case, that Craig Wright is Satoshi)

E = Evidence (not all evidence, but new evidence in the current iteration)

P(H) = Prior Probability of the Hypothesis (Probability that Hypothesis is true based on the prior evidence and independent of the Evidence in the current iteration)

P(E) = Prior Probability of the Evidence (Probability for the event in the Evidence to occur independent of Hypothesis)

P(E|H) = Posterior Probability of Evidence (Probability for the event in the Evidence to occur given that the Hypothesis is True)

P(H|E) = Posterior Probability of the Hypothesis (Probability that Hypothesis is true given that the Evidence is True).

Bayesian method starts with specifying a prior probability of the Hypothesis being **true** given the initial evidence or when there is no specific evidence, and updates to an exterior probability using new evidence.

For better numerical interpretation, one may do the same for two competing hypotheses respectively, and compare the results.

Let’s start conservatively by assuming the following:

P(H), *Prior probability* of Craig Wright being Satoshi = 10^-10

That is, one in 10 billion, a very small probability to be true. Roughly any random person living on earth has such a probability of being Satoshi without any relevant evidence attesting for the person.

(Or, if the hypothesis is that Craig Wright is NOT Satoshi, then *Prior probability* P(H) would be close to 1, because a random person with no supporting evidence is almost certainly not Satoshi. For simplicity, however, the following focuses on the first Hypothesis only. For a more specific numerical interpretation, should apply the same Bayesian method to the two competing hypotheses and compare the relative values.)

This *prior probability* P(H) is then updated to a *posterior probability* P(H|E) in the light of new, relevant data (evidence).

The *posterior probability* P(H|E), in turn, is then continuously updated with additional evidence.

Note that in every Bayesian update, the key is the ratio between P(E|H) and P(E), that is, the ratio between (i) P(E|H) — the Probability for the event in the Evidence to occur given that the Hypothesis is True, and (ii) P(E) — the Probability for the event in the Evidence to occur independent of Hypothesis . If this ratio is smaller than one, the posterior probability of the Hypothesis is **reduced **from the prior probability of the Hypothesis (that is, with the new evidence, Craig Wright is less likely to be Satoshi); but if this ratio is greater than one, the posterior probability of the Hypothesis is **increased **from the prior probability of the Hypothesis (that is, with the new evidence, Craig Wright is more likely to be Satoshi).

If after all updates based upon available evidence, P(H|E) — Posterior Probability of the Hypothesis — approaches zero (0) , the Hypothesis is proven to be False (that is, Craig Wright is not Satoshi).

If after all updates based upon available evidence, P(H|E) — Posterior Probability of the Hypothesis — becomes exceedingly large relative to the posterior probability of the company hypothesis, the Hypothesis is proven to be True (that is, Craig Wright is Satoshi).

# Bayes’ theorem? Really?

But I hear you protest: Who in the world brings Bayes’ theorem into a daily life problem? That’s too complicated. No one thinks that way.

The truth is that even if you don’t consciously think probabilities according to Bayes’ theorem, you unconsciously do it anyway, except that you are more likely to use Bayes’ theorem incorrectly than to do it correctly. Some fallacies can only be detected when one consciously exercises an objective and exact way of thinking.

Bayesian *posterior* *probability* update is essentially a series of multiplications. Our brain subconsciously carries out the multiplications but often with false inputs. The easiest and most consequential way to distort Bayesian probability estimate is to insert a ‘0’ into the multiplications. If you insert a ‘0’ into the series of multiplications, you make the overall outcome an perpetual ‘0’ no matter what. That is, if you insert just one ‘0’ at any point in a series of multiplications, nothing else matters because the outcome is always zero.

As will be shown in this article below, that is exactly how the deniers of Wright’s Satoshi identity reach their conclusion. They fixate on certain isolated scene, emotionally draw a ‘0’ from it, and insert it into their subconscious Bayesian posterior probability equation. Although people don’t explicitly reason that way, that is nonetheless how our brain processes the available information for assessing probabilities. The brain is a mathematical machine (and of course more than that). Be you aware of it or not, it needs to compute that mathematical logic to be convinced. That is its job. You usually cannot fool your brain in the logic itself, but you can fool it using false inputs. A ‘0’ is that false input as a convenient excuse to convince yourself because you emotionally feel the need.

But when you allow your brain to insert that big ‘0’ into the series of multiplications, you convert a meaningful continuous story into a single snapshot and have yourself stuck in that single point of the space-time.

That is a tragedy, because our universe is not a mere structure, nor just a series of snapshots, it is a story. How one interprets the story and plays one’s role in it, collectively constitute one’s life. Interpreting the story incorrectly, one not only misses the teaching of the story, but also misplays one’s role in it.

The matter of the Bitcoin inventor’s identity is a vivid illustration. See more below.

# Applying math to Wright’s case

With the case of Craig Wright, you would soon reach near certainty of the Hypothesis that is Satoshi Nakamoto, given the multiple pieces of evidence of high attestation values (see above).

A graduate student could do an actual Satoshi Nakamoto Bayesian modeling for a thesis, but I already know the result.

Again, the key is in ratio between P(E|H) and P(E). With each piece of evidence listed above, this ratio is extremely high because P(E|H) — the probability for the events in the evidence to be true if Wright is Satoshi — is close to 1, but P(E) — the probability of the event in evidence to be true to a random person (that is, independent from the hypothesis that the person is Satoshi) — is extremely small, almost close to 0.

For example, consider the probability for all the following to happen to a random person: (i) to have publicly claimed the registered copyright of the Bitcoin whitepaper; (ii) to have even gone to a court to assert the claim against an infringer and won a judgment, and (iii) at the same time not to face any challenge from anyone else who claims to be the author of the whitepaper. What is the probability for that?

I say that probability is around 10^-9 (one in a billion) based on the earth population.

That is, we have in this iteration a P(E) = 10^-9; at the same time, P(E|H) — the probability of the person who is Satoshi to have the copyright — is very much close to 1 (100%). Accordingly, the posterior probability of Wright being Satoshi is updated as follows:

P(H|E) = P(H) x P(E|H)/P(E) = (10^-10 x 1) / 10^-9 = 10^-1

(that is, 1/10th or 0.1).

Therefore, in the first iteration alone, the posterior probability of Wright being Satoshi is increased from 1 out of 10 billion to 1 out of 10.

And that’s only one piece of evidence, listed in the first item of the evidence and attestations.

Note that the above estimate is conservative. We don’t assert that because Craig Wright has demonstrated ownership of the Bitcoin whitepaper and Bitcoin original database, he is absolutely proven to be Satoshi with a P(H|E) = 1. Instead, we only conservatively estimated P(H|E) to be 0.1, in order to maintain an extreme level of rigorousness of our method. Satisfied?

If in doubt, let me put this in perspective: in a normal academic setting, the proof of authorship of the paper would be almost equivalent to the proof of inventorship, unless the assumption is seriously challenged and contradicted by alternative evidence. That is, normally, if we start with the authorship of the whitepaper and ownership of the database, the prior probability P(H) should already be very close to 1, instead of 0.1. But let’s all start with hating Craig Wright, and give him a meager 0.1 credibility after seeing the authorship of the whitepaper and ownership of the database. Happy?

But once all the independent evidence is applied with multiple Bayesian updates, the final P(H|E) — Posterior Probability of Hypothesis that Wright is Satoshi given all evidence — quickly approaches 1, meaning certainty.

**Let’s also take the negative factors** **into account in the patient updates:**

The only exception is the event that Wright did not sign but somebody else signed one of the addresses Wright listed in a lawsuit (but are not in the addresses that considered to be Satoshi addresses with high certainty). This is not an absolute negating event, but only one of the iterations. Different people may have different estimates of the ratio between P(E|H) and P(E) with regard to the signature event, but it would be irrational to assume this to be zero, because in this particular case P(E|H) cannot be rationally zero.

Asserting P(E|H) with regarding to the signature to be zero means that you are absolutely certain, it is **logically and physically impossible** that if Wright is Satoshi, he would not sign upon public demand. “That’s exactly what I think,” you say. But Really, how do you know? How can you be so sure? If you think that way, you are not a rational person. Please have a read of Craig Wright is Satoshi, counter arguments. And one needs to be minimally rational in analyzing these things. If one refuses to be even minimally rational, one should not touch these matters at all.

On the other hand, independent of the Hypothesis, P(E) — the probability that a random person would **not **sign a Satoshi address upon demand — is very much close to 1, because the random person is extremely unlikely to have access to a Satoshi address. This should not be controversial, because the number 1 is the highest possible and least favorable assumption against Wright in the estimate.

However, as explained above, **the probability that Satoshi would not sign the Satoshi address upon demand is not zero**. That is, P(E|H) may be less than one or even small, but it is not zero. You may believe that probability should be very small, that’s fine, but it is not zero. It is irrational to assume that would be zero, especially given the evidence in Craig Wright’s case he has rational and legitimate reasons refuse to sign publicly.

In fact, I could objectively give P(E|H) — the probability that Wright Satoshi would not sign a Satoshi address upon demand — as high as 90% (0.9) based on my analysis of his background, motivations and restrictions (see Craig Wright is Satoshi, counter arguments). If you disagree, you might give it a cynically low probability of 1% (0.01) and insist on your own understanding, but you cannot go as irrational as to assert P(E|H) to be zero (see above).

Therefore, this particular iteration concerning the signature may result in a reduction of the posterior probability P(H|E), but does not make it a zero. And this reduction will be easily overcome by the accumulative iterations of the other evidence to reach a final posterior probability P(H|E).

**Other math considerations:**

**Alternatively**, if you find Bayesian methodology hard to follow, let’s use a common sense method.

Assume N **independent **attestation factors, each factor having an attestation value measured to be 1/10 random probability (that is, given the credibility of the attestation itself, and if the subject matter satisfies the attestation, there would be only 1/10 of a chance for the subject matter to be false), then the subject matter that satisfies all N attestation factors has a probability P of being **untrue** as follows:

P= 10^-N.

P=10^-10 when N=10, which is one in 10 billion.

In real life, it is hard to have attestations that are truly completely (100%) independent, therefore P the probability (of being false) would be greater than the above estimate. But even if you increase the above probability by 1000 times, it is still only 10^-7, which is one in 10 million.

And remember the highest 5-Sigma standard of proving a fundamental physics discovery is 3×10^-7 (one in several million), at which level no reasonable mind could doubt.

In the case of proving that Craig Wright is Satoshi Nakamoto, there are far more than 10 such independent attestation factors, and many of these attestation factors have an attestation value higher than that equivalent to a 1/10 random probability (that is, given the credibility of the attestation itself, and when the attestation is applied alone, it results in less than 1/10 of a chance that Craig Wright is not Satoshi Nakamoto).

For examples of such attestation factors, see the above section “Mounting Evidence and Attestations”.

# Objections/Counterarguments

With regard to the above, I hear the following objection:

“I hear one million people claiming they saw Jesus, but that doesn’t mean I’ll accept that as truth with certainty.”

This objection may sound odd, but is highly representative in its underlying misunderstanding.

**First**, that is a different realm. Spiritual truth is established by a spiritual witness which speaks to one’s heart, not one’s mind. In contrast, with respect to Satoshi identity, we are not talking about spiritual truth here. It is mostly a material truth, which can only be based on objectivity and math.

**Second**, in the above objection, the premise is that the observer does not accept (rightfully or not) the objectivity of any personal testimony in the first place. The difference is in the premise, not in the math. The repeated multiplications of one million 1’s is still 1; or that of one million 0’s is still 0.

The math model in its simplest form assumes complete **credibility **of each attestation. But people assume variable credibility, which is why human reality is more complex than math. With partial credibility, one would need to adjust the probability of the respective individual attestation factor. If the credibility of a certain attestation is zero, you’d throw out that attestation factor completely.

However, one cannot simply assume that, just because a certain attestation is by another human being, it therefore has zero credibility. The more realistic model would estimate a partial credibility for each attestation.

In the math outlined above, the simple assumption that each attestation factor has an evidentiary value of only 1/10 (or 10%, instead of 100%) has already taken partial credibility of each attestation into consideration. If you disagree with the value(s), you may put in your own value(s), but you can’t deny the math logic.

**Third**, and more important, in the case of proving Craig Wright is Satoshi, each individual attestation is **not an expression of a personal opinion that they believe Craig Wright is Satoshi** (if that were the case, even 1 million people’s opinion that he is, or he isn’t, wouldn’t really matter ultimately), but to give personal testimony of certain **events or facts **that the person has actually witnessed firsthand.

There is a fundamental difference between the two. When it comes to an opinion, not only could people be wrong, but are in fact often wrong, especially when people are subject to certain propaganda. When it involves a propaganda, not only could people be wrong in the first place, but also their attestation further lacks the **requisite independence** (required in the math model), because they are a correlated result of an orchestrated scheme.

But when it comes to a fact for each event that was witnessed (just the fact or event itself, without reaching a conclusion, which could be a person opinion), a witness has to consciously lie knowing the truth in order to give a false testimony. Of course, people do lie about facts that they have supposedly experienced firsthand, but the likelihood for that to happen is far less than people being simply wrong or misled into forming an incorrect opinion.

This is especially so when it is a trial court witness under oath. There is a good reason that all common law based legal systems have very strict evidentiary rules with regard to witnesses, differentiating a first-hand witness from hearsay and factual evidence from an opinion.

The importance of this cannot be over emphasized. It is very common that people confuse the evidentiary value of the factual evidence and that of an opinion. “Factual” does not mean you must accept it. It means that the evidence is factual **in its nature**, in contrast to a mere opinion. For example, in an event of a fire at 10 AM, if a witness says that “I saw a man wearing a red jacket entering the building around 9:50 AM,” that testimony is called factual evidence. Whether you believe the witness is telling the truth or not, or whether this leads to the conclusion that the fire was caused by arson, is a different matter, but the testimony is factual in nature. In comparison, if another person says that “I believe John Smith probably started the fire because my friends told me he is a bad guy,” that is an opinion. The person could be very much right about John Smith, but what he said is not factual evidence.

Opinion can be created, manipulated, spread, and become codependent, and people don’t necessarily violate their conscience when they stand by the opinion. But factual evidence is independent. If it is false, it has to be manufactured by the witness himself in violation of the conscience.

And often, factual evidence is irrefutable, because it simply is there in eyes of the public (for example, a registered copyright). How you use the evidence to draw a conclusion depends on what prior and posterior probability model you use, but the evidence itself is factual, and you can’t simply brush it away as if it were somebody’s opinion.

On this point, compare the evidence called forth to support claims that any other individual is Satoshi with the evidence that support Wright’s Satoshi identity, there is not only a striking difference in terms of the *quantity *of the evidence, but also the *quality*, the former being mostly people’s opinion or sentiment, while the latter cold historical facts established through physical evidence and first-hand witness testimonies.

After all, there is an essential difference between claiming “I believe Nick is Satoshi because he seems to have an impressive technical background” and testifying “I know Craig is Satoshi because I saw him working on Bitcoin before it was made public.”

We all like to claim with pride that we only accept “objective” evidence, by which we usually mean evidence that is not subject to any third party’s subjective human mind. But problem is that other than the natural laws, very few important truths in this world can be established that way.

A lot of truth has to be based on personal testimonies. That’s how human society functions. One can’t blindly trust, but one can’t do without any trust either. For example, which part of the history is not relying on a personal testimony of somebody else (other than yourself)?

We are entering into a time where not only the history, but also even the contemporary happenings are becoming impossible to prove with absolute certainty, to an extent that every person will have to choose what he believes according to his own evidentiary model, which should give conscience, intuition, honesty room to work with objective math.

And coincidentally, that is also one of the major reasons that motivated Craig Wright to invent Bitcoin and Blockchain. His invention will be helpful if the true Bitcoin prevails. But even then, it won’t solve the problem completely.

For more related counter arguments, read Craig Wright is Satoshi, counter arguments.

# Why hasn’t he signed?

The question of signature has always ranked at the top in the inquiry of Satoshi identity. That is, if Wright is Satoshi, he could easily prove that by publicly signing a message using the private key of one of the bitcoin addresses known to be Satoshi’s.

I took the signature matter seriously, and investigated into it deeply, not only from a factual viewpoint, but also from a legal and a strategy viewpoint. I had previously written on this issue: Why doesn’t he just sign?, emphasizing the fact that he did sign it, multiple times, but only privately for key witnesses and partners, but not publicly. That article also discussed the argument of signaling theory made notorious by Vitalik Buterin.

But there is more to it. If I were Craig Wright, I too wouldn’t sign it *until *I have proven that legal ownership of bitcoin is more than just possession of a key. See Craig Wright is Satoshi, counter arguments, which discusses these questions:

Why hasn’t he signed?

Why did someone else sign against him?

Alleged lies and inconsistencies

Treat Satoshi identity as a probabilistic matter

The fact that Wright hasn’t signed publicly so far is clearly a negative factor not a positive one in the question of his Satoshi identity. But one needs to put this in the big picture objectively.

Consider this mathematically as a probabilistic matter. His opponents treat the signature issue not as one of the probabilistic factors but as conclusive and absolutely dispositive evidence that “he is **not **Satoshi”. In other words, they believe signature alone proves with 100% certainty that Wright is not Satoshi. Or, if we put this in the above probabilistic determination model, Wright’s opponents’ do not consider the signature issue as a separate probabilistic factor, but instead used as an absolute operator that nullifies the validity of all other evidence.

Alternatively, in the above discussed Bayesian methodology, Wright’s opponents assume the probability P(E|H) is 0, that is, the probability of Wright’s not signing given that the Hypothesis is true (that Wright is Satoshi) is absolutely zero, and therefore the Posterior Probability P(H|E) of the Hypothesis given the Evidence (Wright’s not signing) is also zero.

But this is a logical fallacy. See above analysis using the Bayesian methodology.

The probability of the Evidence (Wright’s not signing) given that the Hypothesis is true (that Wright is Satoshi) is not zero. If you want give it an unfavorable (but at least marginally rational) estimate to result in a small number, you may, but as long as it is not zero, any reduction of the posterior probability of the Hypothesis can be easily compensated and overcome through multiple posterior probability updates using the numerous other evidences.

On the other hand, if more rationally and objectively estimated, the probability of Wright’s not signing if he is Satoshi isn’t that small at all, making the math even easier. See Craig Wright is Satoshi, counter arguments.

From a probabilistic viewpoint, a negative factor is not the same as a negative proof, just like a positive factor is not the same as a positive proof either. It is a probabilistic matter, and everything should be weighed probabilistically using a sound mathematical model such as Bayesian method (see above).

The fact that he hasn’t signed does reduce the posterior probability that he is Satoshi as a result of that one particular Bayesian iteration, but it (1) does not make the posterior probability zero; and (2) does not logically make other independent evidences disappear, which through Bayesian posterior probability iterations easily raise the final probability back to close to 1 (100%).

What’s important is that there can be logically independent reasons that he hasn’t signed, and these reasons do not logically contradict the other evidence listed in this article that he is Satoshi. Therefore such evidence cannot simply be thrown away just because one doesn’t like the fact that he has refused sign. See Craig Wright is Satoshi, counter arguments.

After seeing all the evidence, do you honestly still conclude the probability that Wright is Satoshi is absolutely zero just because he hasn’t signed publicly, and you can reconcile this conclusion with all the other available evidence? Even if you don’t follow the math, at least resort to your common sense. Don’t let emotion, prejudice, and ulterior motive occupy your heart and mind. Leave some room for objectivity, fairness, science, and humanity.

# Given the totality of the evidence, I’d say:

1) Those who haven’t examined the evidence should stop saying Craig Wright is not the inventor of Bitcoin, just so that you don’t find yourself embarrassed one day; and if you can’t say yes, just honestly say you don’t know, and are willing to learn about it.

2) Those who’ve examined the evidence but are still able to believe Craig Wright is not the inventor of Bitcoin, you’ve got an extremely hardened heart, capable of denying any truth or fact you don’t want to believe. It’s a detriment, not a blessing.

3) People who already know that Craig Wright is the inventor of Bitcoin yet for some reason have to deny it publicly, I’m sorry life has come so hard on you. Losing freedom due to earthly bribes is a sad thing.