Giovanni Santostasi - The Bitcoin Power Law Theory

[fillippone]

Everything you wanted to know about The Bitcoin Power Law Theory, but were afraid to ask!
OP post on Bitcointalk.org: The BTC Scaling Law

During the last few weeks, I have been increasingly involved in studying a new model by an astrophysics professor turned neuroscientist, which describes bitcoin according to Power Laws.

Giovanni Santostasi, aka  BTCdragosfera described a model where he explains why Power Laws governing price and other Bitcoin metrics (such as Active addresses and hash rate) are not a random fact but actually the symptoms of something else, namely Bitcoin being "not a common asset but more similar to natural phenomena ruled by universal Power Laws due to recursive, infinite feedback loops fundamental to the system".
Bitcoin is more similar to a city and an organism than a financial asset.

Santostasi first posted his mumblings on Reddit more than 5 years ago:



This post went almost unnoticed: Giovanni set it aside a little bit, focusing on other things, namely his new venture on Neurosciences, but kept working on the idea and finally published the following paper:



The Bitcoin Power Law Theory

If you prefer the video format, hear a video Summary of the Theory:



The material is not very well organized, so I will try to explain the ideas better in this thread.

The Power Law is only the first part of his full BTC model, where it also models a range for bitcoin price and a bubble indicator to detect excessive price movements:



Yes, of course, you have already seen that Rainbow Graph, and actually Trolololo chart is a Power Law chart.

The innovation of Santostasi's article is that Bitcoin is considered a financial system that behaves like a natural system according to well-defined laws. These laws are Power Laws. In this sense, the article is not a "model" about Bitcoin but a coherent "Bitcoin theory."

According to Santostasi:

In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific knowledge,[1] in contrast to more common uses of the word "theory" that imply that something is unproven or speculative (which in formal terms is better characterized by the word hypothesis).[2]
(This is from Wikipedia - Ed.)

<...>
It is a full theory because it explains the entire behaviour of Bitcoin. It has several points and explains the interaction of all the on-chain parameters,

it even explains why the bubble exists and why we have a bottom. He makes predictions that make the theory falsifiable.

In science, a model is a representation of an idea, an object or even a process or a system that is used to describe and explain phenomena that cannot be experienced directly. Models are central to what scientists do, both in their research as well as when communicating their explanations.

A model is very similar to a hypothesis, so it is an initial mathematical formula or algorithm to try to replicate some of the behaviour of the subject studied.

A theory is the ultimate way to understand a phenomenon: it is complete in the sense that it tries to explain all the observed behaviour.
In this case, how the on-chain parameters work, how the adoption is growing (via a virus-like mechanism), and how the adoption affects the price (via Metcalfe law).


How the price brings in more miners, how the hash rate is related to price, how the Difficulty Adjustment kicks in and creates an inhibitory loop that creates stability for the system, and so on and on

People do not comprehend it yet: it tells us everything we need to know about Bitcoin, and there is a corollary that even explains the bubbles and their relevance. It can be improved and made better, but it is coherent and complete: it is really a big deal.

(I made some little readjustments to make the sentences more readable)

Introduction: What is a Power Law?

According to Wikipedia:

In statistics, a Power Law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial size of those quantities: one quantity varies as a power of another.

Power Laws can be written in the following form:

Y=10^B*(x+S)^A

or:

log(y)=A*log(x+S)+B

A lot of natural, sociological, mathematical, physical, and psychological phenomena follow Power Laws.

The Power Law has a few important features.

• Scale invariance: Power Laws remain valid when the involved variables change the order of magnitude.
• Lack of well-defined average value: Power Laws have a median but lack a mean value.
• Universality: Power Laws with the same exponent produce similar dynamics.

The first property is that a Power Law drawn in a log-log chart, or a chart where both axes are on a logarithmic scale, is a straight line with slope A, B intercept, and S as a shift parameter.

Please note that a straight line in a log-log plot is necessary, but there is insufficient evidence for Power Laws. Determining a Power Law existence only because there is a straight line fitted in a log-log chart is an unsatisfactory approach to the statistical method.

	bitcoin price plotted against time	A graph you might have already seen Log bitcoin price, plotted against time
	Now both axis are Log, and a linear relationship appears	The previous graph slightly reworked

Please note that those 4 graphs represent the exact same data. The blue line is the same as the red one.
The only difference is visual, and this is best captured by the red line in the log-log chart, which appears to describe the Bitcoin prices.
In reality, the explanatory power is the same in all the graphs, but the linear scale "undervalues" the errors in the first steps of the graph and "overvalues" the errors in the last steps, as the prices have increased four orders of magnitude.

The log-log chart evenly "decompresses" the chart's price and time dimension, and the best-fit function appears to be a straight line.

I made those graphs myself to check the reality of the claimed properties of the log-log chart.

If you want to understand better what Power laws are and why they are so ubiquitous in science, please have a look at the following links:

	Geoffrey West: The surprising math of cities and corporations	Why do Power Laws Work so Widely? | Episode 2207 | Closer To Truth

Giovanni Santostasi already published an article answering a few questions and correcting misconceptions about PLT (Power Law Theory):

Common Misconceptions and Fallacies Regarding the Bitcoin Theory of Bitcoin

This is a rendition of the "bitcoin clock" using the Power Laws: the beautiful spiral well represents the soundness of the theory.





Bitcoin Price is not the only variable that has a governing Power Law; addresses and hash rate are also governed by similar laws.



This adds beauty to the model, as we can find a "cross" relationship.
 
There is a beautiful YouTube video about the relationship between these quantities:



Addresses and Prices are tied via a Power Law with something resembling the Metcalfe Law.
HashPower and Price are linked via a Power Law that strongly supports price via Mining Hardware cost.


The major point of this model is that scarcity is not considered anywhere in the model. The PLT doesn't consider S2F relevant for price determination.
Of course, the author soon entered into a disagreement with PlanB:



In this article Giovanni explain why Scarcity doesn't play a role in price determination:

Scarcity is not what Drives Bitcoin Price

<...>
Here 2 models, the power law model that has zero assumption on scarcity, just based on the observation the price is going up in a predictable manner. Scarcity it is not part of the model at all. The other, S2F where scarcity is the main driver, in fact, it assumes scarcity increases with time. The power law (with no assumption on scarcity) leads to “hurry up and get some BTC now”. As you can see S2F instead says you can get in at any time and still make the same amount of gains, no matter if you joined 10 year ago (for the same amount of 4 years HODLING time) or 10 years from now (again for the same HODLING time). Both investors will make a 10x return over this time. While you notice for the Power Law model it is important to join as soon as possible. So do you see how people use of the scarcity argument leads to illogical conclusions that are not supported by facts?

If you want to deep dive in this, there is a video here:
Why BTC stock-to-flow model based on scarcity is worse than wrong, it is complete nonsense.


Santostasi is not done yet. Firstly he's trying to organise the knowledge scattered over a few articles and X posts.
The first output will be a scientific paper, possibly peer-reviewed, and a more educational book detailing his theory.


Resources:

• Giovanni Santostasi Twitter Account
• The Bitcoin Power Law Theory
• YOUTUBE: The Bitcoin Power Law Theory
• Wikipedia: Power Law
• The Physics of Bitcoin
• Common Misconceptions and Fallacies Regarding the Bitcoin Theory of Bitcoin
• BTC Trolololo model revisited (still valid today) is really a Power Law in disguise
• Bitcoin long term power law Chart
• Bitcoin long term power law Chart - GLASSNODE
• Power-law price models of bitcoin
• Bitcoin’s power-law really debunked?
• The science behind $1,000,000 bitcoin with Giovanni Santostasi
• Episode 45 with Giovani. Power Laws

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[fillippone]

This morning PlanG (let's call him this way) posted a new update:  





Someone asked a relevant question in the comments:



Lol, I asked a further question about this. I will post an update when I have an answer.

EDIT:
It was quicker than expected:


Here a full preview of the attached image:

[davis196]

Congrats on making such a long and informative forum thread. I'm not interested in science, statistics and mathematics, but the theory of this Italian guy makes sense.
OK, so the Bitcoin price will keep growing in the future. So what? This is a Bitcoin forum and most people are convinced that the BTC price will keep growing in the future. Maybe you should post this in a forum full of crypto haters and skeptics in order to convince them about the future of Bitcoin.
Will this mathematical model work if some external factors influence the BTC market? What if Bitcoin gets mass banned globally. Does it mean that the Bitcoin price could still hit 1 million by 2033, even if Bitcoin gets banned?

[BTCdragosfera]

This is Giovanni.

It is astounding to me that people do not realize what this is all about.
It is a full theory of how Bitcoin is, how it works, and how it behaves. The predictability of the price is really one of the least interesting things besides the fact that being scale invariant it is predictable.

The Theory is consistent in almost all kinds of questions you want to ask about Bitcoin. For example, answering your question. No, it will not be banned because Bitcoin survived as a scale-invariant system for 15 years.

It is anti-fragile, it is flexible and resilient. All the qualities that people use words to describe Bitcoin are actually proven mathematically (besides being scarce) in this Theory.
And it is a Theory, not a model. A full Theory, the only one I know in existence, of what Bitcoin is.

The Theory tells Bitcoin is not an asset, it is more like a living organism, a living being, a city, a mountain.

An important missing part of the previous post is to show the universality of power laws, how they can describe natural phenomena, social phenomena, and how cities grow.

Every single Bitcoiner should know the Theory and they should try to understand it. If it is true, and so far all the evidence points to be true, then it is the most important discovery about Bitcoin ever.

Saylor can use analogies or metaphors about Bitcoin, the Theory uses science to show what Bitcoin is really about.

It is amazing and weird to me that is it not viral or well known and discussed by everybody, not because I created it, but because it tells an incredibly beautiful narrative about Bitcoin and it is not a bunch of made-up words, but it is based on scientific evidence, logic, math, and physical arguments.

I know it is early and most people do not have a scientific background but it is still amazing that the significance of this discovery is not yet understood by most.
Hopefully, it will happen soon or later.

[Briankimp1]

In statistics, a Power Law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial size of those quantities: one quantity varies as a power of another.

You my dear have come up with one of the most captivating and theoretical explanation of the Bitcoin Power Law all I can say is a big thank you, I’m no physician neither am I a mathematician nor a statistician but after reading your wonderful thread, I quoted what stood out for me which also for me the main message of this thread.
I’m glad with everything outlined here I was able to pick up some knowledge I’d always keep in mind and apply daily.

[fillippone]

I had an extensive chat with Giovanni.
I added a few materials to the OP based on this conversation, and I am going to dump even more material in the coming days.
I have been literally overwhelmed by his enthusiasm.

I understand hi has quite a unique approach to the subject, which is also quite in contrast with many things we learnt in the past years. So, a lot. to digest.

[Cryptomultiplier]

This is Giovanni.

It is astounding to me that people do not realize what this is all about.
It is a full theory of how Bitcoin is, how it works, and how it behaves. The predictability of the price is really one of the least interesting things besides the fact that being scale invariant it is predictable.

The Theory is consistent in almost all kinds of questions you want to ask about Bitcoin. For example, answering your question. No, it will not be banned because Bitcoin survived as a scale-invariant system for 15 years.

It is anti-fragile, it is flexible and resilient. All the qualities that people use words to describe Bitcoin are actually proven mathematically (besides being scarce) in this Theory.
And it is a Theory, not a model. A full Theory, the only one I know in existence, of what Bitcoin is.

The Theory tells Bitcoin is not an asset, it is more like a living organism, a living being, a city, a mountain.

An important missing part of the previous post is to show the universality of power laws, how they can describe natural phenomena, social phenomena, and how cities grow.

Every single Bitcoiner should know the Theory and they should try to understand it. If it is true, and so far all the evidence points to be true, then it is the most important discovery about Bitcoin ever.

Saylor can use analogies or metaphors about Bitcoin, the Theory uses science to show what Bitcoin is really about.

It is amazing and weird to me that is it not viral or well known and discussed by everybody, not because I created it, but because it tells an incredibly beautiful narrative about Bitcoin and it is not a bunch of made-up words, but it is based on scientific evidence, logic, math, and physical arguments.

I know it is early and most people do not have a scientific background but it is still amazing that the significance of this discovery is not yet understood by most.
Hopefully, it will happen soon or later.

Thankfully, I have a good understanding of the mathematical and scientific aspect of this theory and I must say I found this read most fascinating as it sure puts an ease to my thoughts on the future prospects of Bitcoin. When it comes to power laws, Giovanni sure took his time to make his findings and arrived at his conclusions.

From my perspective, Giovanni has done good job having presented his power law model predictions of Bitcoin and his highlight on Scale invariance which to me, also means that if any or all of the columns is rescaled or resized by dividing or multiplication, the results won't change the power law predictions of scale invariance.

This explains just what and how the halving will happen upon division and still the value of BTC remains intact and keeps growing.

[franky1]

its not a law if you have to change the numbers per market cycle

all you are doing is straightening a curve... thats just chart manipulation not anything to do with economics

yes the adjustments become less massive per cycle due to each cycle having less coins to adjust much like the natural curve becomes less wild per cycle left alone.

Giovanni has not invented or discovered some magical economic formulae that predicts the future,, he just worked out a way to straighten a curve of the past(inaccurately but close enough to then draw a line through it).. but then needs to alter the number in the future. thus not a law

if you were to use his old numbers then you will see how things change and dont fit the new numbers

but lets see him scream back how he is master of numbers coz "rocket science" and to just trust his number now are best for now cos "rocket science"

and wait 4 years for him to change them again and say "trust new numbers coz rocket science"

screw it.. lets just rip him apart now instead of waiting for him to chest beat his ego


yes he has a set of numbers to bend a standard log from curve to flat-ish of historic data.. thats not rocket science.. is just chart manipulation. even high school kids do that
but look at the purple line and the yellow diagonal-hump-diagonals he added as a overlay

the purple line starts at 20% of market peak and by 3rd cycle is crossing through 50% of peak and using his own yellow diagonal-hump-diagonal it shows the purple being above peaks

meaning the purple line is not centering all the markets at a 50% mid point. nor is the yellow humps (ath) going to be above his purples. which means it is inaccurate and shows no pattern of staying within range of anything he created.

all he has managed to do is manipulate a curve of normal log into a near but inaccurate straight-ish line.. but will need to change the numbers so its not even going to stay straight forever if he just stuck with the same numbers forever

[Don Pedro Dinero]

Very interesting. What happens is that without having knowledge of so much depth on the subject I wonder if it will not have flaws also as the S2F, which for years was the paradigm of bitcoiners.

Will this mathematical model work if some external factors influence the BTC market? What if Bitcoin gets mass banned globally. Does it mean that the Bitcoin price could still hit 1 million by 2033, even if Bitcoin gets banned?

I think it is very unlikely that this will happen but what you say is a flaw that many models have, that then there are things in the real world that happen and were not foreseen in the model.

[Sg4j1n3ll0]

the work done by the professor is truly impressive, I would have the pleasure of talking to him about the topic, (Giovanni, if you're there, give it a shot ) it's always nice to see a mathematical formula in action

[franky1]

I think it is very unlikely that this will happen but what you say is a flaw that many models have, that then there are things in the real world that happen and were not foreseen in the model.

its not a law or a model

its a manipulation of historic data to appear in a different shaped chart.. and thats it..
its not mathematical genius.. its basic math..
its not predictive its retroactive.. the number only works on old data, and the number has to change in future market cycles
he has already changed his numbers a few times in just 1-2 cycles
yes because there is not much coin left and so the natural log curve doesnt angle as much. so his straightening of the curve doesnt need to adjust much each time. but its not a formulae that will still work with the same number in the future. and as shown even using his image his purple line does not even go through the centre equally of each market cycle so even his purple line is already inaccurate already

he spent too much time promoting the one number for the last year that he didnt stay uptodate with adjusting his number to stay uptodate.. thus he already lost control and debunked himself by promoting a certain number for too long pretending its a law/power number..
yep time itself broke his own number and he doesnt want to admit it, instead he has shown in this last year an egotist arrogance that his number is strong even when time itself proves otherwise

i doubt he is a rocket scientist or neuro scientist. he just thinks he can manipulate data and idiots so called himself a scientist, he is more of a sociology gamer not a scientist

[BTCdragosfera]

franky1,
I am not sure about the reporting harassment policies here.
If you continue to do ad hominem, attacking my professional background, my integrity, or other personal attacks I will report you. it is obvious to anybody that you are a troll and have zero understanding or knowledge about these subjects. It is not even worth answering you or addressing any of the things you are saying besides telling you that I would not tolerate personal attacks so if this forum allows me to report this behavior I will.
You even follow me from post to post just to harass me. If you want to have a scientific discussion or you want to ask questions I will answer them but again stop the personal attacks. This is the last time I ask nicely. Thank you.

[fillippone]

I am not a scientist, a physicist  or a statician, but it would have some value computing the following?

Using different subsets of data, progressively adding days, see how some quantities evolve:

• The variation of the parameters
• Hurst exponent
• Size of the state space

I mean: put the hypothesis of Bitcoin is a Power Law at a more serious test than graphically fitting a straight line in a log-log chat.

[MusaMohamed]

I can not answer it in math because the model is complicated for me but I believe Hashrate and what contributes to Bitcoin Network Hashrate, ASICs and Power, are important for Bitcoin network and its price.

The Power Law Model is not perfect, as no model is perfect, but I think the author goes with a good idea to build it.

I think it is simple to see Bitcoin future with Lindy effects. Like gold, it has been exsiting long time enough to die as an asset and Bitcoin is growing similarly.

The bullish case for Bitcoin
Bitcoin's Lindy model
Is Bitcoin Antifragile?

[Don Pedro Dinero]

its not a law or a model

its a manipulation of historic data to appear in a different shaped chart.. and thats it..
its not mathematical genius.. its basic math..
its not predictive its retroactive.. the number only works on old data, and the number has to change in future market cycles
he has already changed his numbers a few times in just 1-2 cycles

You mean he is something like PlanB, who, when the data did not match what he had predicted, reformulated the theory to fit the data over and over again?

franky1,
I am not sure about the reporting harassment policies here.
If you continue to do ad hominem, attacking my professional background, my integrity, or other personal attacks I will report you.

The reasons why franky1's posts could be deleted or measures taken against him are summarized here:
   
Unofficial list of (official) Bitcointalk.org rules, guidelines, FAQ

I don't particularly get into whether you or he is right, as I lack sufficient knowledge, but I doubt very much that if you report his posts in this thread you will get anything.

[franky1]

its not harrassment if i am talking about the numbers and showing the guys chart and how his numbers do not match his statements

the chart in my post(which is the guys own chart) shows his purple line does not sit as a median of the chart results even after manipulating the chart. thus the numbers are off(meandering outside of the price data) even after manipulation.. as can be validated by the yellow line which also shows the purple line shifts out of phase

meaning the guy has to change his numbers periodically to try to get things to fit.. thus its not a power law.
his numbers are already out of date

the guy is just upset that he got debunked and takes it as a personal attack rather then realise he has been trying to push his own false narrative which is the failure of the topic

debunking false narratives is not harrassment.. if a spammer keeps spamming a false narrative its the spammer causing more harm to other readers. by him continually trying to push how his number is a power law. is the error, and he cannot just take the revelation and start afresh on a different formulae that could work.. but instead keeps pushing how he feels his numbers are a law, even when they change and thus cannot be used to produce models of future results because the future results will be out of phase

[hatshepsut93]

So this theory tries to tell us that Bitcoin's price is a result of some sophisticated adoption curve, but from my point of view adoption is largely irrelevant for Bitcoin - most of those who own Bitcoin are speculators, some are short-term speculators, some are long-term speculators, but everyone is planning to at some point sell. So instead Bitcoin should be analyzed as a zero-sum investment game. If more money comes in than comes out, the price grows. This growth incentivizes money to stay and wait, basically a positive feedback loop. But this loop can break if too little money will be coming in and those who were waiting will become disappointed and start quitting.

[MusaMohamed]

So this theory tries to tell us that Bitcoin's price is a result of some sophisticated adoption curve, but from my point of view adoption is largely irrelevant for Bitcoin - most of those who own Bitcoin are speculators, some are short-term speculators, some are long-term speculators, but everyone is planning to at some point sell.

Adoption is important and speculators are not all in Bitcoin market. They are only one component in Bitcoin market and they have their roles, contributions, capital in the market but they are not all.

Adoption is important because it brings new people and new capital in the market. With time, bigger adoption, the market will have more people, from investors to speculators and traders, they all contribute to bigger trading volume in the market. With bigger trading volume, big investors have one more reason to join it because they will have less trouble to enter and exit the market with big capital.

Adoption is important for value of Bitcoin and because you said about speculators, they are contributing to price on the market in short term. Value is for long term and more sustainable grows with time.

So instead Bitcoin should be analyzed as a zero-sum investment game. If more money comes in than comes out, the price grows.

I agree about zero-sum game. It is true for traditional markets like stock market too.

[Dump3er]

So this theory tries to tell us that Bitcoin's price is a result of some sophisticated adoption curve, but from my point of view adoption is largely irrelevant for Bitcoin - most of those who own Bitcoin are speculators, some are short-term speculators, some are long-term speculators, but everyone is planning to at some point sell. So instead Bitcoin should be analyzed as a zero-sum investment game. If more money comes in than comes out, the price grows. This growth incentivizes money to stay and wait, basically a positive feedback loop. But this loop can break if too little money will be coming in and those who were waiting will become disappointed and start quitting.

This is quite a controversial comment, but frankly, going back and forth here would end up in a game of definition, semantics and misunderstandings or lack of knowledge on all fronts.

I think one of the most important things that fillippone pointed out is

Bitcoin is more similar to a city and an organism than a financial asset.

I have been trying to wrap my head around the Power Law Theory here, but it is tough to develop a clear understanding of the matter. franky1 has got some valid points and he is pinning it down when he refers clearly to the term "law". Arbitrarily tweaking numbers such that resulting graphs seem as they were adhering to a law isn't a particularly good way that there is a law at work.

But at the same time I get what is trying to be conveyed here in the thread as a whole and there is some agreement on my part although I have difficulties to put it into very good wording, let alone mathematical formulas.

franky1 made the point of retroactive vs. predictive and this fundamentally interferes with laws. While at first retroactively detecting a law can make sense, arbitrarily tweaking formulas to adhere putatively to a law is problematic or plainly false.

I think the term "theory" would be more appropriate here and it wouldn't really undermine Santostasi's points. His remarks could still be very relevant, it is just that the term "law" may go too far. The reason for my stance here goes back to

Bitcoin is more similar to a city and an organism than a financial asset.

While there are more and more mathematical models trying to depict "the emergence of cities and urban patterning...", none of these models will ever result in a law as there is a plethora of externalities that could fully undermine mathematical assumptions. The Power of Law would have to hold universally true despite potential externalities. Bitcoin is subject to countless of influencing factors and if it seems to be following a certain pattern retrospectively for a specified period of time, it would be highly hypothetical to derive a law from that.

That's why this remark

In this sense the content of the article is not a "model" about Bitcoin, but a coherent "Bitcoin theory".

should be carefully considered in the context of whether there are laws at work here. Whether it represents a law might rather be a "coherent theory". I somwhere read the sentence that laws usually nail something down in a very concise manner, and if we are dealing with infinitely complex matters like the development of ecosystems, puring these complex matters into laws is probably doomed to fail. Maybe it could make sense for partial aspects of an ecosystem, but it kind of undermines the whole idea when partial aspects need to be considered in isolation only to make sure they could then be following a law while in reality an isolated consideration makes no sense.


I find this type of discussion very uselful and I wasn't aware of the topic until now. fillippone shared a good one here! In my opinion this will remain a point of contention as there are lots of ways to attack the "law" hypothesis. I don't have a final opinion on this, but I do believe that there is something at work that is at least very approximative of laws (or Power Laws for that matter). I think one of the problems might be that the term "law" raises the bar for universal validity to an undisputable maximum and that's where peope trying to put very complex things into a law will always run into differing opinions. I think there is nothing wrong with someone trying to discern patterns and modelling those into formulas. In a world with ever-growing complexity, the term "law" itself may deserve a less confined interpretation in some contexts. If a pattern were to repeat infinitely, does it make that pattern a law?

[fillippone]

Giovanni, PlanG, said it was going to organize all the material in a scientific paper, meant to be peer-reviewed.

Apparently, he has been working on this:



I guess having a peer reviewed scientific paper on Bitcoin, is a considerable step forward when compared to medium post.