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Calculations on A Perspective of Golden Ratio

A study of Golden Ratio Perception

By Parker Emmerson

Through History, there have been many ways of portraying the Golden Ratio.

In this paper, I am going to outline how the Golden Ratio plays into our everyday perception of reality.

We are also going to go on a journey through Mathematics and Geometry to discover if there is any relation of our perception of reality on a daily basis. Please consult the Attached diagrams for a more in depth understanding of the symbology.

The Science of this paper is in the power of Observation and the art of sacred geometry. The observation is philosophically spoken by saying that sacred geometry is a perspectival emanation of our reality. There is a point at which, when one observes two equal line segments, they appear to be in golden ratio with each other.

Some Background Information:




Let us also note that:



Our first Postulate:

There is a point at which, when one views two equal line segments at perspective, they appear to be in Golden Ratio with each other, and L is in golden ratio with the larger of the two lengths that are viewed at perspective.


this creates an analogous relationship of y and ϕ That is like this:

y: ϕy:: ϕy:(ϕ (ϕy))

The trigonometric relations which follow our diagram of golden ratio perception of two equal line segments for the angle θk are:

tan(θk)= h/(L+x) = ϕy/(r2-r1)= ϕy/√(L^2-(ϕy)^2)

sin(θk)= h/r2 = ϕy/L

cos(θk)= L+x)/r2 = (r2-r1)/ ϕy = (√(L^2-(ϕy)^2))/ϕy)

These trig relations show us that:

R2-R1= √(L^2-(ϕy)^2)

From this, we can definitively show that Theta K is constant and that it is equal to 38.17… degrees so long as our relation of L= ϕ (ϕy) stays the same.

θk=38.17314 that is to say that:


(sin(θk)*L)/y=ϕ;  (sin(θk)*ϕ(ϕ y))/y=ϕ

ϕy= sin(θk)*ø(øy)

1/ϕ= sin(θk)

ϕ=1/ sin(θk)

Now let us examine the other thetas, B, and T.

tan(θb)= h/x

sin(θb)= h/√(((2L+x)^2)+h^2)

cos(θb)= x/√(h^2+x^2)

tan(θT)= h/(2L+x)=y/√(L^2-(y^2)=y/(R3-R2)



A quick Case Study of the Theories:


if x=L, what is h?

and L=2


What is y?

Y = .763

What is Theta t?

Theta T=22.45

What is Theta B?

Theta B=51.002

That Concludes the Extent of the study for the mean time. It looks as though we have shown the correct way of calculating our distance and height from the two equal line segments if we want to perceive them in Golden Ratio.

Man is Dog’s Best Friend. Dog is man’s best friend. They all have a nice time and play together in a field of wild roses and honeysuckle It will be a sad day when dog parts man, and man parts dog, but there are many men and many dogs and many days.

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Blogband, and Bitcoin: Digital Media Wallet Patents

Greetings! and Welcome to Blogband!

Blogband is A patented social network for musicians to collaborate online in a band that they start or join. It is a global workspace for bands and musicians to distribute their music and by proof of work, record contributions to their finalized songs. Musicians and bands will be able to seamlessly sell their music online. However, music distribution is only beginning. Blockchain based licensing using cryptographic signatures to assign ownership of digital media over our patented platform is the future.

I hope you are doing well today. Thank you for your interest in I have always believed that the virtual world was vastly underutilized as a way to distribute and market independent music, videos, and virtual reality significant objects and seeks to radically change the status quo into an environment where crypto-currencies emerge as a major tool for e-commerce in the virtual realms. We provide the perfect framework to develop technology relevant to this end, and we have a proven track record of establishing IP assets that have serious value in today’s technology battles.

Myblogband LLC has been around since 2007 and was re-branded as Blogband LLC once the patent was awarded two US Patents, with a third and fourth issuance on the way. We have a strong IP asset package marketed by the top IP asset attorney and entrepreneur – JiNan Glasgo, and we are still young and growing in our scope of business activities. Our vision for establishing IP and solid business growth involves media licensing and integrating Bitcoin, Litecoin, and Ethereum on our platform for digital media licensing. In addition, we are seeking interested parties who would like to invest in making Blogband a real challenge to current music distribution platforms and the establishment music industry.

The heart of’s patent is a distinct function that enables collaboration within a band/group framework, though monetization using cryptocurrency has been the focus of our most recent patents and patent applications. From my original invention, users can create a band (group) and invite other members of the site to join the band. Then, any member in the band can then create a song file, download tracks already uploaded within the file, rework them on their remote computers/tablets and re-upload them to the website, selecting the most recent version as, “for sale,” independently of any music dealer. Any member of the band can also choose which track is to be displayed as the official song version on the band page’s music player. It is on this combined functionality and the social network that hinges upon it that we obtained a patent with an early filing date of 2009.

Like Bitcoin, proof of work is established and contributors to the project are credited accordingly throughout the creative process when uploading their tracks, and the distribution of profits obtained through sales of their work is completed seemlessly using the blockchain for payments. Bitcoin fits perfectly in this paradigm as songs sold through get tagged with separate Bitcoin addresses for payouts to the creators. Current continuation in part (CIP) patent applications include the exclusive use of Bitcoin payments within this system.
With our patent, CIP filing and patented software functions, we hope you will find Blogband LLC can be a perfect startup company to join forces with the Bitcoin protocol and network to revolutionize independent music licensing and distribution of profits fairly to contributors to content.

1) Artists have a hard time quickly and efficiently distributing their content and receiving adequate payment. Too much money is given to middlemen, and only a few artists dominate the heard music. We need to rectify the situation so independent music scenes can thrive.

2) Time-stamping and proof of authorship.

3) Fast and easy distribution of payments for content.

The independent music talent pool is richer than ever, but its pockets are empty. Corporate middle-men and streaming, ad-based platforms have monopolized the marketplace by enabling steals of songs,  and in the process depriving talented independent artists as well as superstars major earning potential. We think the contemporary music economy needs to change in order for music cultures and subcultures to flourish. It needs to adopt innovative ways of bringing revenue directly to musicians to empower and incentivize them to produce better, faster, stronger, keeping our music industry alive and thriving. The patented innovation we propose is the integration of our media-oriented cryptocurrency, SonIQ, into our patented online social network for musicians, MyBlogBand (US20100326256 A1, US8487173 B2, US8962964 B2), to allow for seamless licensing, payment, distribution, and collaboration of independent music, media and even artificial intelligence.

Independent music has gained enormous steam since the advent of the internet. In recent years, listeners have grown jaded with radio’s limited, formulaic offerings and turned to the web for free or cheap access to raw, talented musicians all over the map. But whether this buffet of independent music can outlast listeners’ appetites depends on indie artists actually making a good living from their popularity, which internet platforms haven’t engendered so far. Lacking profits, artists have been resorting to grueling tours, like troubadours of olden days.

An argument for cheapening the music industry is that consumers are accustomed to not pay, and consumers are the boss. But because the state of things is not sustainable, whoever provides a viable alternative first will become a disruptive pioneer and a champion of democracy.  We live in a time in which the importance of sustainability is more apparent and appealing than ever. We think cryptocurrency can be seamlessly integrated into the user experience and eventually prove its own value as consumers see music quality and availability improve through the use of this payment system. 

MyBlogBand will be a patented, custom-tailored cryptocurrency social network for multimedia artists that will let them prove their contributions to media as well as license media access and return ownership of content as access to a library of data. This feature is distinct from iTunes, Spotify, Pandora and other streaming music services: iTunes only allows limited access to purchased media by authorized devices with non-transferable license. The others don’t grant ownership of content, limit accessible content types to music and limit themselves to popular, syndicated artists, making it harder to discover new artists and indie musicians.

2. A Digital Media Wallet on MyBlogBand will allow licensing via SonIQ, a custom-tailored cryptocurrency for the social media framework. The idea here is to use the cryptocurrency styled mining network to facilitate the licensing of media, be it video, audio or visual. Licenses to access media would be generated using the Bitcoin network in the SonIQ embodiment over a social media framework of MyBlogBand, an idea currently addressed in my patent-pending CIP application. It could also license content through the cryptocurrency network node with individual licenses to media stored on a Cloud server.

What is a Bitcoin network node? A Bitcoin network node is a record of all Bitcoin transactions that have taken place that is current and up-to-date with the current issuance of all Bitcoins and transactions of all Bitcoins. The same is true for a node of any current cryptocurrency. This idea of a node is essential to the concept of a crypto currency or cryptographic ledger technology. People who operate computers that are used to solve the encryption algorithm that issues crypto-currencies (Bitcoin, Litecoin, etc.) are referred to as miners, and it is their job to see to it that Bitcoins are issued within the constraints of the open source software project. Bitcoins are entries into the distributed, cryptographically protected ledger that indicate a positive balance located at a cryptographically protected address. Bitcoin addresses are generated by operating a Bitcoin node and indicating that one would be able to accept Bitcoins when they are sent to a particular string of numbers that was generated within the constraints of the Bitcoin software protocol.

What is a Bitcoin wallet? A Bitcoin wallet is a positive balance located at a Bitcoin address. Bitcoin wallets are either Cloud based or stored on a hard drive. Access is granted to a Bitcoin wallet/address when a Bitcoin node has the correct private, cryptographic key (set of numbers) to send Bitcoins from that respective address.

How are licenses to media contained and protected in this embodiment? Given an individual piece of media, for example a song, entitled “Song 1,” authorization to play the song, copy the song, transfer the song or sell the song would be granted

using a cryptographic key issued by a mining network such as the Bitcoin network/protocol. A user’s online account would be credited with access to the media

over a suite of different hardware/software platforms that have access to this data stored on “the Cloud.” Cryptographic keys that grant access to the media would be stored on the Cloud and all the user would have to do is log into their account. Users could transfer those cryptographic keys to be stored locally on hardware. A “wallet” software is used to organize the cryptographic keys that grant access to data, therefore turning it to consumable media. The wallet organizes the data+cryptographic keys as a cryptocurrency node on the cryptocurrency network in a Graphic User Interface such that it is easily accessible through a browser. In this embodiment, the keys are still held on the Cloud, so the media is accessible wherever the data is available so long as the user is logged into his Cloud account. The cryptocurrency, distributed ledger technology is simply used to maintain the licenses to transform data into media.

How are media licenses transferred from one person to another? By means of access to the Cloud account, the user may transfer these licenses using a website or by having his local Media Wallet transfer the licenses from the Cloud server to another wallet or Cloud account. Any format of media may be transferred.

How do licenses operate in conjunction with data to grant access to content? A cryptocurrency, or distributed ledger technology (synonymous), works with a public

address and a private key. A decentralized encrypting network (like the Bitcoin network) maintains the history of all transfers/transactions that take place. Data is downloaded from many different distributors and platforms, with the downloading/receiving of data, licenses to access the content are also conferred to a public address, the private keys to which are held on a Cloud server or local disk. All of this is made available to the user through their Media Wallet.

How is content finally delivered to the end user? Once the user has the data, the private key that grants access to the data or balance, which is enshrined by the Bitcoin or other cryptocurrency network at a particular address also grants access to the data, thereby turning it into media, because a centralized or distributed database of media files verifies the presence of the correct keys at the cryptocurrency node through either proof of stake (proof that there is the presence of the key) or transfer of the key one time per media usage to the owner’s own wallet.

3. Licensing media as granted access to a host of media stored on a Cloud server.

The owner of a private key that corresponds to the correct respective value on a cryptocurrency network is also granted access to a subscription style service of media.

4. Licensing media content through a Bitcoin network node with individual licenses to

particular pieces of media stored on a local server/computer/hard-drive/wallet.

Data is downloaded and locally stored licenses (private keys) grant access. The private

keys can be transferred from one address to another address on a cryptocurrency

network or the balance located at an address that signifies access to the data can be

sent to another address, and thus access to the media is conferred that way.

5. Licensing media content through a Bitcoin network node with individual licenses to a host of media stored locally.

6. A custom-tailored cryptocurrency — SonIQ — for the express purpose of granting media licensing on the basis of distributed, cryptographic ledger technology. A wallet that can organize and categorize different kinds of licenses to different kinds of media using a multitude of cryptocurrency platforms including the cryptocurrency platform that has been custom-tailored to make media licensing easier. Cryptographic network- mining network (present, existing, or novel and tailored). . Further, we hope to allow for the tokenization of media content through a digital media crypto-wallet, so that virtual items in games can be included in the ownable content transferable over a blockchain. Virtual weapons, clothing, items, cars, or any acquirable object in a video or computer game can be tokenized, held, synced, and transferred between games, users and players for different devices, terminals, consoles or games for different purposes.

7. We want to be adaptable to future technologies, so our eye is also on integrating AI structures. Artificial intelligence robots can integrate different robot features, buy and trade different parts of themselves as assets.

Basic terms:

License node – An up-to-date record of the presence of all licenses.

Direct send – The transfer of both the data for media and the cryptographic token by which the data is allowed to be media.

License authorization key – Generated by the network of the custom cryptographic,

distributed ledger/currency when a content owner/provider/generator receives payment via Bitcoin, the aforementioned custom currency or other currency.

Media Wallet – a cryptocurrency wallet that contains access keys to different kinds of data.

License for different purposes: right to perform the song, right to play the song in a venue, right to copy the song, right to sell the song, right to distribute the song.

We started the Bitcoin Dispensary in 2015 as a joint venture, and formed it into a corporation in 2016. We grew the business from one ATM into Six ATMs in that time as well as netted a nice and tidy profit. The Bitcoin ATM business was a learning experience, because it required a skill set, the basics of which I had, but I also had to learn  about how to install software via a command line interface as well as secure the coins. While these technical difficulties were relatively easily overcome, the work involved in actually servicing the cash from the ATMs proved to be significantly too much, so we are partnering with a new company to service the ATMs, and they are also doing their own ICO, which is called CREAM, a spin-off of the Wu Tang Clan’s Cash Rules Everything Around Me theme,

One of the main issues with starting a Bitcoin-dealing company was regulation. That is supposedly a big word in the cryptocurrency start-up field, but as far as buying and selling bitcoin, it is really just illustrative of the stringent police state bullying-bureaucracy that we live in today combined with mass acquiescence to compliance with government edicts not backed by laws. The issue of regulation in the bitcoin buying and selling arena revolves around this idea of being a Money Service Business. Before the existence of bitcoin, in order to send money to someone, one would few options, and they all involved some form of intermediary or escrow agent. One would have to use Western Union, or a bank, or send it by the mail. All of those involved an intermediary whom you had to trust with your money. So, the law was designed to address these kinds of entities and activities. However, with bitcoin, and bitcoin ATMs, there is no third party intermediary. Ideally, clients receive their bitcoins immediately, as in with a bitcoin Vending machine, so custodial control of funds is never an issue for more than 5 seconds as individuals are inserting cash, just as when individuals purchase something over the counter. It is analogous to that way more so than a money transmitter relationship. Then, people can send bitcoin to whichever address they autonomously and independently decide to of their own volition, no third party involved.

The actual law says nothing about bitcoin, and it clearly defines money transmitter activity very specifically to refer to custodial funds. Entities are required to register as money service businesses only if they perform one of these particularly noted activities. Money transmission by definition in the law requires that custodial funds be involved, and with a bitcoin ATM or over the counter sales, custodial funds are not involved. Individuals are volitionally agreeing to buy or sell bitcoin over the counter with immediate receipt of the good intended for sale or purchase. It’s a very different relationship than money transmission. However, the problem arose when FinCEN came out and stated it was their opinion that bitcoin sellers were money transmission, and when they said that, everyone just kind of tucked their tail in and agreed to, “comply.” Nobody would sell bitcoin to you in large volumes through the above-board exchanges anymore unless you agreed to register as one of these money service businesses and admit that yourself to be a witch, I mean a money transmitter, and plead for mercy as you had done something wrong. Nobody with money fought back against the FinCEN’s totalitarian edict that was not backed by the wording of the law. Even with all of these ICOs today, nobody has stood up against them to get an injunction against their interpretation of the law, which is totally wrong and has nothing to do with what it actually says.

If you buy or sell a gold or silver coin, you are not a money transmitter. Well, if you sell a bitcoin, guess what, you are according to FinCEN.

Anyway, this all lead to a lot of people recording a lot of data about their clients and customers in preparation for ratting them out for doing something, “suspicious,” to the higher ups on the food chain if the time came. It created a nasty taste in the mouths of many individuals who were initially liberty minded folks trying to escape the system, and it made a lot of people in the industry hated by the true believers. Why were you arrested? Suspiscion.

Bitcoin NCCOB We received a letter from them.

I have been arrested seven times in my life, and not one of the times I was arrested had I ever done anything wrong, and to this day, I have no convictions on my record – it is entirely clean. However, I have seen how the system loves to make up reasons for why you should be suspected of wrong doing, when really, the government system is the one that has doing all the dirty deeds for so long. Then, when we find a loop-hole like bitcoin, they want to say, “oh no, you can’t do that, because we said so,”   ——- not because or an actual law, but because of some government appointed bureaucrat’s opinion on the matter. If you knew about how justice department employees went on to work for Goldman Sachs for seven figure per year salaries after having cleared Goldman Sachs of all wrongdoing during the financial crisis, then you wouldn’t have any doubt this kind of resistance was coming from the financial stake holders who basically pay government to do their bidding. Rather than have a debate to change the law, which would require alerting the constituents, who might actually have a voice, they like to use bureaucratic edict and opinion to issue veiled threats against business owners who want to transact in cryptocurrency. By the way, people really do risk their lives to present ideas like this.

Where are the most talented, brightest people putting their efforts? Cryptocurrency. Why did the NFL have a deal with the US Government to display certain military ceremonies at their games? Because they need people to work for the military. Well, most of the true patriots are working on cryptocurrency, because they don’t want to blindly follow orders, and they know our whole monetary system has been corrupted and co-opted by the super powerful, elites whose intent is to tax Americans into oblivion, robbing them blind with inflation. Their system worked for so many years. Lend money, that money gets invested (or doesn’t), hopefully it increases tax revenues to justify more money to lend. However, there are always fewer dollars in existence than dollar lent when you account for the interest, so it just sucks at the life blood of the American worker. They get away with this, because they are the only game in town after they confiscated all Americans gold in the 30’s, and people have surprisingly short memories and are basically taught to let bygones be bygones. However, the banking cartel has lost their monopoly to an invention that was given away for basically free by Satoshi Nakamoto. Why would you want to participate in a system that continually devalues your money and hurts your economic interests?

So, enter blockchain and bitcoin – It is extremely useful, and it is so powerful as an idea that there is nothing that they can do to control it. You cannot un-invent something so long as ideas survive in people’s minds. It has taken longer than anticipated to take root in society. Still, the average merchant on the street does not accept it. Now that I have stopped doing the daily runs in my bitcoin ATM business, however, I plan to approach merchants to ask them to accept bitcoin. Accepting bitcoin is so easy. Merchants will get on board with this for the simple reason that they should be sick of VISA charging them 2.25% on every single transaction all the time. If you realize that the 2.25% of a credit card charge is actually more like 7% of that merchant’s profit, it is a no-brainer to switch, because we can offer you 1% premium on the bitcoin. That bitcoin is going back into our machines at a 7.5% markup for the time being.

The idea of cryptocurrency is so powerful, that it should be the focus of everyone in the country, because it offers the opportunity for us to ask ourselves, “why are we paying these taxes?” The government is going to get itself into a situation where it is negotiating with bitcoin and other cryptocurrencies to get money, because it cannot obtain valuable money from the Federal Reserve, which is really going to put them in a predicament. Dollars are not desirable money, because participating with them in any way is in some way harming yourself or other people. That is an inevitable conclusion that even most bitcoin traders seem to not understand. However, some do.

The word smart contract might be a misnomer. The contract is not necessarily smart. To be smart, one must have both a high IQ and have a conscience, know the difference between what is beneficial to sentience and is not beneficial to sentience, and be capable of determining what rights ought exist and what privileges ought not exist. Today’s, quote un quote smart contracts have nothing to do with that. They are rudimentary mechanistic devices that can be exploited arbitrarily by parties of different means and agendas. There are interesting smart contract platforms, but they are completely non-intelligent, meaning the ethics of usage is completely based on the individual. However, I believe this system may more closely mimic the nature of reality rather than having any concrete form of government. Therefore, it simply will put individuals more closely on guard of their own individual safety and security at the same time.

If you have  a hard time keeping track of all of these cryptocurrencies, well there is good news, there are two cryptocurrencies for that problem.

Trying to understand the balance of the alt coins and bitcoin dollar prices can be tricky. All the alt coins generally provide a boost to the demand for bitcoin, and bitcoin and alt coins have a kind of parent-child relationship in the market. The bitcoins, for a time, subsidized the children until they could walk on their own and succeed.

Ways in which bitcoin acts as a living being; though probably not sentient right now.

Many cryptocurrencies that use the model of creating their own blockchain instead of piggy backing off of someone else’s platform have their main concern of maintaining their network and making sure they can’t get destroyed by attackers. Their main concern is making sure that nobody else can make them go away.

With the rise of Bitcoin’s price recently, what we’ve really seen is an alt coin route where alt coins have lost price in terms of bitcoin, even though alt coins may have seen substantial gains in terms of dollars.

The whole name of the game is all about accumulating bitcoin and other cryptocurrencies that one believes are going to succeed, not about logging profits in dollars. You must move fast like bitcoin in order to make dollar profits flow like water.

I saw an advertisement – “invest in the most promising cryptocurrency.” I said, “wow, that must be a lot of promises they are making!” Because it seems they are all making so many promises. It will be interesting to see which ones deliver, and to bet on which ones will actually deliver on the promises they are making will be the ticket to making the most returns on cryptocurrency investments.

People with the big, big money like things they can control, and things that fit in with their social, political or industrial agenda, so while the libertarian elements of the cryptocurrency scene might not like it that microsoft, dell, ibm, etc. are getting into things like ethereum, those could be good plays. Why ethereum? it acts like a spore, and allows lots of different things to be built on top of it, creating demand for it, which was the genius idea behind ethereum, although i’m not a particular fan of the mechanics of it.

With our social network patent, CIP filing and patented software functions, Blogband LLC is a perfect startup company to join forces with the Bitcoin protocol and network to revolutionize independent music licensing and distribution of profits. The synthesis of the collaborative cryptocurrency social network and the BlogBand Bots’ agency to cryptically edit one another and trade elements of themselves as assets anticipates a future of independent media and the evolution of artificial intelligence with creativity, autonomy and soul.

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Golden Ratio Perception: Perceiving two equal lines in golden ratio with each other; zooming, looming, and relativity of focus

A question arose to me the other day in contemplating the meaning of perception: at what angle, or angles, do we perceive two equal line segments in golden ratio with each other? How far away would we be when we perceive this phenomenon? Is it possible that we can perceive this ratio from equality at perspective at all? And, how is it that we should decide where to begin and where to end a discussion on the topic? Is it possible that there are multiple places at which we could perceive the transformation of Golden Ratio from equal ratio?

Obviously, taking 3D space perception into account would totally transform the question and make it much more complicated. That is why we shall begin discussing this in terms of only perception with one eye in a situation where one’s eye is perpendicular to the plane of the two equally lengthed line segments being perceived.

In mathematical and geometrical terms, we begin by bisecting a line segment, let’s call the total line segment AC, and when we bisect it, it because AB; BC.

Even the subjective experience is based on objective relations. For instance, when I perceive the two equal line segments, what is it that allows my eye to see the angle? Certainly I am looking at something. But what? Am I looking into the tiniest derivative of space for each part of the line segment, and thus an infinite number of arc lengths? Am I looking at each entire line segment separately? Am I looking at both line segments together? It would be clear that with one eye, all I am perceiving is within the angle measure. How, though, may I know what this angle measure is without first comprehending the meaning of angle measures through an expression which give meaning to the word “angle.”

An angle gets described in terms of a radius and arc length or the sine of other lengths available to describe it. Which arc length, then, am I perceiving that relates to an angle? How can I determine which angle it is if I am given no grounds by which I can begin to measure the angle? What expression could be determined other than an assumption of angle ratio? It seems that in our perception of Euclidian space, the rules governing the system break down in some ways, or are less clear and determinable. I believe however, that there may be three ways of looking at this that were outlined in the above set of questioning regarding the “subject” matter. Each of these ways may in deed be valid. It may be that there are multiple ways of regarding the phenomenon, thus producing different phenomena. How does one phenomenon transform into three phenomena anyway? Obviously, we would love to be able to come to an understanding of the ultimate unity of the phenomena, and this happens through the constant factor present in each of the diagrams, and could be discussed mathematically if necessary.

In the first way suggested, the line segments take on the clarity of perspective. That is the point at the origin, point A.

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The Disguising of 3 out of 5 keys as 2 out of 3 keys and implications for bitcoin security standards

The Disguising of 3 out of 5 keys as 2 out of 3 keys and implications for bitcoin security standards

Abstract: For those who are familiar in the technique and art of bitcoin encryption, we are aware of the 2 out of 3 private key system used by custodial wallet providers. There also exists a 3 out 5 private key solution for custodial wallets. This paper submits with minimal technical detail that a 3 out of 5 private key solution can be disguised as a 2 out of 3 custodial key solution, permitting a user to believe his bitcoins are protected through a 2 out of 3 custodial key system, when really, one of the private keys in the presented 2 out of 3 system can be used to extract two other keys that are used in a 3 of 5 private key used to sign transactions, and submits a solution to this problem of authenticating the validity of a 2 out of 3 key system, proving it is not a trojan horse for a 3 out of 5 valid signing authority.

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Auspicious Symbols in Buddhism and Their Mathematical Origin


The auspicious symbol of the umbrella in Buddhist philosophy is perhaps a hidden message, or a hint to the true nature of reality delivered down through the ages to those who might seek to perceive and inquire. However, the mathematical expression of the, “umbrellic transformation,” is one rarely discussed in Buddhist circles that I have encountered if ever, and it is certainly not vocally embodied in the vibrant message promoted and propagated by the majority of the Buddhist community.

This book delivers an algebraic-geometric analysis of the folding circle, as known as the umbrella. The circle that folds up into a cone holds within it the foundation and structure required for realization of the nature of reality and the expanding theory of consciousness that has collapsed into pure geometry.

As the originator of these mathematical vestments, I encourage you to read about them and gain inspiration from them in your galactic travels.

We are only beginning to understand what the meaning of the, “phenomenological velocity,” solution truly means and the curvatures that are present from the compiled, “compacted,” nestled and compressed mathematical solutions within the equation-expression of the height of the cone delivered from simple geometric-algebraic postulates and actual ideal perceptions.

We ask ourselves, “why do the galaxies spiral?” We ask ourselves, what is the phenomenon of, “dark matter,” and we lack answers to these basic questions, but with the Cone of Perception, our answers to explanations of the accelerating universe are clear; acceleration is built into the framework itself from the get go. Time is not a priori. Time is an illusion. It is not a real parameter, but instead, we use parameters of distance, angle, and curvature.

The physicists’ dirty secret is that they have assumed that mass exists as a real phenomenon, and have based all their calculations upon this concept. However functional the postulate of mass’s, “being,” is, it is still an assumption on its face. Does one actually perceive a mass? Or has one inferred that a concept of mass must exist as the basis of reality, and if so, “on what notion was this inference based?” The Geometric Pattern of Perception Theorems base their functionality of describing the motionof  and perceived being of, “objects,” in the world through pure algebra and geometry of the transformation of ideal shapes. Through perceiving and describing these transformations phenomenologically, we can extract a plentitude of, “qualia,” and equations of transformation and motion, which act as articulation of perceived phenomena of transformation and motion and may suffice for explaining curvature of space time, including the curvature perceived as correlating with dark matter.

People speak of Energy to describe the phenomenon of that which is neither created nor destroyed, but really, all  that is needed to describe that phenomenon is contained within the, “phenomenological velocity,” equation, also known as V-Curvature, since it’s not really even necessary to consider it velocity.