The Case for XOR
Makoto Takemiya
SORAMITSU Co., Ltd.
t@soramitsu.co.jp

Abstract. XOR is a supranational currency that has its supply and primary market managed by a computer program that runs on a blockchain.
XOR is not controlled by any country, company, or individual, and is thus
a global economic system designed for the common good of humanity.
To facilitate economic growth, money must be deployed in an economy
to create new goods and services. Unlike other cryptocurrencies, such as
Bitcoin, countries can make proposals to fund productive investments via
XOR allocated from a fund, or from minting TBCD, which is convertible
to XOR on the open market, all via an open governance process. Thismeans that XOR does not act as a foreign currency that is outside thecontrol of democratic governments, but rather can be integrated into thedomestic economy wherever it is used, to fund nominal GDP growth.
Furthermore, XOR is not a debt-based currency, so more egalitariansocial outcomes can be realized, compared to contemporary economic
systems, as economic growth is not inhibited to service an ever-growing
debt. Thus using XOR as legal tender in countries for discharging debts,
purchasing goods and services, and paying taxes, can lead to increased
economic growth, because increased productive output can be funded.

1

Introduction

Money allows the ﬁnite resources in our world to be allocated eﬃciently, without
requiring central planning that would be impossible to solve optimally due tothe combinatorial complexity involved in such a calculation. Money provides
a satisﬁcing (i.e., good enough, cf. [9]) solution to resource allocation, and assuch, economics has the potential to uplift societies and shape our world for the
better, but only if economic systems are rationally constructed to create socially
beneﬁcial outcomes.
Money has three deﬁning properties: it is a unit of account (i.e., a measureof value), a store of value, and a unit of exchange. These properties allow money
to solve the problem of lack of trust in exchange relations and allocation ofﬁnite resources. Currently, in most markets, ﬁat currencies issued by central
banks best realize these properties. However, this has not always been the case:historical examples of both successful privately-issued money and unsuccessful
central bank-issued money abound.
The rapid technological maturation of cryptocurrencies has led to intense
debate on the role of non-central bank-issued digital money in 21st century

2

Makoto Takemiya

economies and societies [8]. Cryptocurrencies are digital assets secured and controlled via cryptographic proofs, issued and transacted on distributed ledger
technologies (DLTs) such as blockchain. As the diversity and sophistication of
cryptocurrencies have increased, a consensus has formed that the monetary utility of a given cryptocurrency will depend upon how well it can act as a measureof value, a store of value, and a unit of exchange [4].
Cryptocurrencies could oﬀer a range of advantages over contemporary, debtbased ﬁat systems, especially for cross-border interoperability, speed, eﬃciency,
security, resilience, programmability, political independence, decentralization,and transparency. The natively digital nature of cryptocurrencies suits them tothe complex 21st century ﬁnancial landscape, which will include not just peerto-peer transactions, but also automated and machine-to-machine transactions.
This paper will explore how a cryptocurrency called XOR can be used bycountries to facilitate reliable and predictable economic growth. First, we explain
what economic growth is and how it can be achieved. Next, we discuss how XOR
can promote economic growth in countries that accept it as legal tender. We thencompare a XOR-driven economy versus use of Bitcoin as legal tender in countries
like El Salvador. Finally, we explain the steps for a country to accept XOR as
legal tender and integrate it into their economy.

2

Creating Economic Growth

Economic growth typically is deﬁned as an increase in transactions contributing
to the gross domestic product (GDP) [2] of a country. GDP transactions are, inturn, typically increased by either increasing the quantity or the eﬃciency of utilization of factor inputs, in order to create new goods and services. Factor inputs
are typically taken in macroeconomics to be land, labor, capital, and technology. Fully utilizing these inputs optimally to create goods and services (output)
can lead to the full realization of potential output, Y ∗ . It is important to notethat transferring existing assets from one owner to another (asset transactions)do not contribute to the accounting used to calculate the GDP for a country,
because no new output is created.
The potential output for a country can be conceptualized as a function of thequantity of factor inputs (QFI) and their use (total factor productivity; TFP):Y ∗ = f (QF I ∗ ; T F P ∗ ),(1)

where QF I ∗ and T F P ∗ are the potential quantity of factor inputs and potential total factor productivity, respectively. Put in simple terms, to reach thepotential output of a country, resources (factor inputs) should be utilized optimally to create the highest total value of goods or services.
The equation of exchange shows, intuitively, that the amount of money usedin transactions (M × V ; M := quantity of money, V := velocity, or, number oftimes the same money is used in transactions in a year) has to equal the valueof the transactions (P × Q; P := price of goods/services, Q := number of goods
services sold):

The Case for XOR

M × V = P × Q.

3

(2)

However, in economies where cash is used or electronic payment providers
do not provide all statistics, the value of all transactions in an economy is notknown directly and is instead proxied via nominal GDP (P × Y ; Y := output ofgoods/services in an economy):
M × V = P × Y.

(3)

As Werner [12] points out, using the equation of exchange without diﬀerentiating the use of the money1 in it has many known problems, including thefamous “velocity decline” problems observed in economies with speculative asset
bubbles. So, it is important to disaggregate the types of money used in the equation of exchange, depending on money used for purchases of goods or services
that contribute to GDP (i.e., money used for real economic transactions, MR )and money used for asset purchases, which are not included in GDP accounting(i.e., ﬁnancial or speculative use of money, MF ).
∆MR × VR = ∆(PR × QR ) = ∆(PR × YR )(4)

∆MF × VF = ∆(PF × QF ).

(5)

While simple, these equations have profound implications, which are backed
up by empirical evidence in [12]. Namely, how money is created and allocated inan economy directly determines the: 1) amount of economic growth (or contraction), 2) stability of prices, and 3) the formation of asset bubbles [13]. Because
VR is typically stable in a large economy (people have common needs that do
not change, like daily food, water, and shelter), and PR also resists change dueto the reluctance of ﬁrms to adjust prices [1], changing MR is the primary way
to attenuate real GDP, YR , by enabling the creation of new goods and services.
Important to note here is that interest rates are not used in these equations.
That is because interest rates are the price of borrowing money and not a causal
factor related to the quantity of money. In fact, higher interest rates are positively correlated with nominal GDP growth in many economies, and Granger
causality analysis has shown that higher nominal GDP growth causes higher
interest rates [12] (pp. 110, etc.). So there is no empirical support showing thatlowering interest rates leads to economic growth, meaning that this is not a
relationship that exists in reality.
Another common misconception is that foreign direct investment (FDI) canlead to economic growth. Insofar as a country is not using a foreign currency
that is neither issued nor controlled by their local banking sector, it has been
demonstrated that FDI does not have a statistically signiﬁcant relationship with
1

Note: in this paper we just treat all credit and money aggregates as money forsimplicity.

4

Makoto Takemiya

economic growth [3]. Intuitively, this is because foreign investors who are competent always extract more value than they create, as they seek capital gains andnot a socially beneﬁcial outcome for the countries they invest in. Therefore, FDI
cannot be relied on to facilitate economic growth in a country, and competentmonetary policy should try to eliminate FDI to the furthest extent possible.
In summary, to have economic growth, money should be created and allocatedto facilitate the creation of new goods and services, based on a real economic
need to utilize more factor inputs, more eﬃciently.

3

XOR as a Catalyst for Economic Growth

XOR is a cryptocurrency designed to mitigate the volatility risks, governance lacunae, and ineﬃciency of ﬁrst-generation cryptocurrencies like Bitcoin. It is thenative token of SORA, a decentralized economic system based on a blockchain
network and founded to enable cryptocurrencies to advance humanity by funding new productive output of goods and services. The SORA economic model,
technical implementation, and governance mechanisms all suit it for use as a
medium of exchange, as well as both a measure and store of value.
SORA’s economic model is based on the empirical research of Fisher [5, 7],
Werner [11], Shimomura [15], Kurihara [6], and Yamaguchi and Yamaguchi [14],as well as of SORAMITSU2 founder Takemiya [10].
As explained in Section 2, to enable economic growth, money must: 1) beable to be issued in response to genuine economic demand, while 2) resisting
arbitrary issuance (e.g., in response to political pressure), but rather issued only
for the creation of new goods or services. It should also: 3) be issued in a way thatenables forward guidance (i.e., that sends signals to the market) about liquidity
and price.
XOR fulﬁlls these requirements through the use of a token bonding curve—
an algorithm (or, smart contract in the blockchain parlance) that automaticallymanages the token supply elastically in response to demand. As shown in Figure 1, the token bonding curve is comprised of two pricing functions, which deﬁne
the primary market prices for XOR: 1) a buy-price function, and 2) a sell-pricefunction. The buy-price function is a line, starting at 634 USD per XOR andincreasing by 1 USD for each 1,337 XOR issued. The buy-price function mints
XOR when people buy from it, putting the currency used to buy the XOR into
reserves, which are used by the sell-price function. The sell-price function, inturn, is set to buy back XOR at 20% less than the buy-price function and it sells
the reserves held by the token bonding curve in exchange for XOR. Whereas
the buy-price function mints XOR, the sell-price function burns XOR, reducing
the XOR supply. In the event of inadequate reserves held by the token bonding
curve, the sell-price function sells tokens along a continuous curve, starting at
20% less than the buy-price function’s current price for XOR. The mathematics
behind the token bonding curve are known to all participants in the XOR mar2

https://soramitsu.co.jp

The Case for XOR

5

ket and are transparent, meaning that forward guidance on XOR liquidity andprices are possible using the buy-price and sell-price market data.

Pr iceBu y -Fu n cell-Price
Ideal Stion

Functi

n
Margi

20%

on

ce
-Pr i
l Sell
Actua

ctio
Fun

n

Token Bonding Curve Reserves

The area of this surface is the difference between ideal andactual reserves

Fig. 1: The SORA token bonding curve as the primary market maker to buy andsell XOR.

Because the buy-price and sell-price functions of the token bonding curve
mint and burn XOR, respectively, the XOR supply is elastic and able to scale either up or down to any sized economy, making it suited for adoption by countriesof any size as legal tender as a money with stable and predictable purchasing
power.
On a technical level, the XOR token bonding curve and the blockchain technology (Parity Substrate) used to validate transactions are much more computationally eﬃcient than ﬁrst-generation cryptocurrencies: transactions take anaverage of 3 seconds to complete and cost only a few cents, whereas transactions on Bitcoin can take upwards of 15 minutes to complete and cost several
dollars. SORA has no mining and uses very little electricity, while Bitcoin uses
more electricity than many countries to power their unnecessary and wastefulmining competition. The SORA network has been benchmarked with 100 million accounts transacting at a sustained throughput of 6,000 transactions per
second, proving transactional capacity suitable for most countries. The decentralized cryptocurrency exchange, Polkaswap, launched on the SORA network in
April 2021, has validated the eﬃciency and scalability of XOR under real mar-6

Makoto Takemiya

ket conditions, with millions of successful transactions and no security issues todate.
The XOR economy is rationally governed by decentralized token voting on
the SORA blockchain. Referendums among token holders to perform actions suchas upgrading the network, distributing XOR from the treasury, or even minting
and allocating TBCD (Token Bonding Curve Dollar), a token that is convertible
to XOR and is used for funding productive initiatives, allowing the economy toadapt to the needs of XOR users, including governments that use XOR as a legal
tender currency. Because governments can make proposals to fund productive
initiatives, such as basic research or the creation of new goods or services, XOR
acts as a domestic ﬁat currency would, but without costly interest payments or
moral hazards involved in overly diluting their domestic currency. By not giving
bureaucrats other peoples’ money to spend, they are more likely to take careand work hard to prevent misallocation. With the XOR model, all expenditures
result in the possible inﬂation of the XOR money supply, because TBCD can beused to mint XOR via the token bonding curve smart contract, which directly
aﬀects all XOR holders, including the bureaucrats, so it is no longer other peoples’ money. This solves a signiﬁcant structural moral hazard in contemporarymonetary systems, where the decision makers do not have signiﬁcant, personal“skin in the game,” and often create and allocate money for buying votes via
ineﬃcient public works projects or other unproductive uses.
Using a XOR-based economy also precludes the need for taxation, as governments can be funded without taking money from their producers. This helps
to reduce corruption, as governments that do this would not have sources of income other than from democratically allocated XOR tokens, as well as to provide
a better incentive structure for producers. Governments traditionally tax only
those who are productive, not taxing those who are burdens on society, whichis the opposite of what should be done from a system dynamics perspective. By
not taxing the productive classes, at least the incentive structure in society is
not actively mis-aligned, as it is in most contemporary ﬁat currency systems.
Taken together, all these properties of XOR and the SORA economic systemprovide signiﬁcant advantages to governments and their citizens, compared tocontemporary economic systems. To further understand the beneﬁts of using
XOR as legal tender, next we will compare use of XOR to the legal tenderstatus of Bitcoin in El Salvador.

4Comparison to Bitcoin Legal Tender Status in El
Salvador

Excitement over various advantages of using cryptocurrencies has led to widespread
speculation and private adoption of cryptocurrencies, primarily as a store ofvalue, but also as a unit of exchange: the total market capitalization of the twomost popular cryptocurrencies, Bitcoin (BTC) and Ethereum (ETH), is over$450 Billion USD; thousands of merchants accept them as payment; and ATMs

The Case for XOR

7exist at which they can be bought using payment cards or cash3 , or sold forcash. In many jurisdictions, cryptocurrencies are recognized as valid a meansof payment.4 It is even possible to purchase Bitcoin from Swiss Federal Railway ticket machines using cash and a valid Swiss phone number as KYC, andcertain localities accept tax payments in selected cryptocurrencies, giving them
quasi-legal tender status, such as the Cantons of Zug5 and Lugano.6
El Salvador recently pushed the debate on the monetary function of cryptocurrencies forward by recognizing Bitcoin as a legal tender: as of September
7th, 2021, Bitcoin may be used to discharge debts, accepted as payment forgoods and services, and used to pay taxes. The main objectives behind the El
Salvadoran Bitcoin Law are to lower the cost of international remittances, provide access to the ﬁnancial system for the unbanked, and reduce reliance on the
USD, which El Salvador adopted as legal tender in 2001.7
On a technical level, the main mode of Bitcoin distribution in El Salvador
is via a mobile application, Chivo Wallet, designed in cooperation between thegovernment and one or more technology providers. Chivo wallet utilizes anotherblockchain called Algorand8 to enable faster transactions than would be possible on the Bitcoin blockchain, which is notoriously slow and expensive to use.
Users are also free to use other Bitcoin wallets as well. Cash-in/cash-out can be
performed at government exchange agents or presumably at banks, as well as ata still-small, but growing, number of Bitcoin ATMs.
Some remarkable early successes have been announced by the chief proponentof the Bitcoin Law, President Nayib Bukele, primarily regarding popular uptake:– As of the 3rd October 2021, three million El Salvadorans have used Chivo
Wallet—nearly 50% of the population—in part driven by a sign-up bonus of$30 USD in Bitcoin9– More money has ﬂowed into, than out of, Bitcoin ATMs10– A partnership has been struck with multinational ﬁrms Puma Energy and
Uno Terra to incentive Bitcoin uptake through discounts on fuel bought withthe currency113

https://coinatmradar.com
https://www.oecd.org/tax/tax-policy/taxing-virtual-currencies-an-overv
iew-of-tax-treatments-and-emerging-tax-policy-issues.htm
5https://www.zg.ch/behoerden/finanzdirektion/steuerverwaltung/tax-payme
nt-with-cryptocourrencies
6
https://www.nasdaq.com/articles/lugano-switzerland-will-make-bitcoin-legal-tender7
https://www.pwc.com/gx/en/financial-services/pdf/el-salvadors-law-a-me
aningful-test-for-bitcoin.pdf
8
https://coingeek.com/shocker-bitcoin-in-el-salvador-is-fake/9
https://twitter.com/nayibbukele/status/1444775650292899840](https://twitter.com/nayibbukele/status/1444775650292899840
10
https://twitter.com/nayibbukele/status/1445923488083107845
11https://twitter.com/nayibbukele/status/1443410462129983490
4

8

Makoto Takemiya– Bitcoin wallet apps appear to have garnered better user reviews than many
El Salvadoran banking apps12– The governmental Bitcoin Trust, authorized in August 2021 with a balanceof $150 million USD, has accumulated a “surplus” of $5 million, some ofwhich will be used to build a veterinary hospital13
However, international organizations and economists based in the global
North, such as the IMF and World Bank, have mostly voiced disapproval of the El
Salvadoran Bitcoin Law14 . These organizations are well known to have politicalaﬃliations that could conﬂict with any move away from dollarization, regardless of the eﬃcacy of using cryptocurrencies to promote economic growth. Thus
other Central and South American countries, are withholding judgment for thetime being, and the Central American Bank for Economic Integration (CABEI)
has committed to providing El Salvador with technical assistance. Dante Mossi,
executive president of CABEI, indicates that while El Salvador’s move is experimental, it could instigate a snowball eﬀect within the region if successful 15 .
Unfortunately, using Bitcoin as a legal tender in El Salvador severely limits
the ability of their economy to grow. As shown in Section 2, to increase the goods
and services at the same price level, more money should be put into circulation,
to facilitate the creation of those goods and services. Bitcoin is a foreign currency
to El Salvador because new Bitcoins cannot be minted to fund the productionof goods and services, thus the government is at the mercy of foreign investors
to inject Bitcoin into the El Salvadoran economy, in the same way that the
USD also is a foreign currency that must originate from abroad. Thus instead ofusing newly created money to fund economic growth, the government has been
buying Bitcoin as a speculative investment, or even worse, using limited energy
resources to mine Bitcoin, which uses money and resources that could instead
have gone into productive output for the economy.
Additionally, Bitcoin has limited long-term viability. The supply is supposedly limited to 21 million tokens, but with that limit, future miners will not
be able to sustain suﬃcient mining activity to properly secure the Bitcoin network16 . This will lead to either changing the Bitcoin protocol to have more than
21 million Bitcoins, changing the consensus away from Proof-of-Work, or the
Bitcoin network will be easily exploited and not safe to use. Any of these options is going to severely damage the reputation and viability of Bitcoin and12https://www.kevinrooke.blog/el-salvador-and-bitcoin-two-weeks-in/
https://www.reuters.com/business/finance/el-salvador-use-bitcoin-gains-fund-veterinary-hospital-president-says-2021-10-10/
14
https://blogs.imf.org/2021/07/26/cryptoassets-as-national-currency-a-s
tep-too-far/
15
https://www.reuters.com/business/finance/remittance-costs-key-take-upsalvadoran-bitcoin-plan-development-bank-2021-08-24/
16
For reference, on December 29, 2022, $340,000 were paid to miners in transaction
fees, while $14 million were paid to miners in newly minted Bitcoins. This shows thedaily amount of value that miners need to secure the network, which must be paid
for from the Bitcoin economy, in exchange for no productive output (no new goods
or services that users can spend Bitcoins on).
13

The Case for XOR

9thus Bitcoin cannot be considered safe or reliable in the long term and should
not be the basis for any national economy.
XOR, on the other hand, does not have these downsides. XOR does not act
as a foreign currency to a country, because a country such as El Salvador, could
make proposals for injecting XOR into their economy to create new productive
output. Instead of spending public funds to buy XOR, like El Salvador doeswith Bitcoin, the XOR ecosystem can give money to the government or to the
producers of goods or services directly. This can unlock the full potential output
of a country, because all factor inputs can be fully utilized, to the extent possible
given the total factor productivity of the country. In simple terms, using XOR
allows a country to utilize its factor inputs for production of new goods andservices to their full potential, because the need for money is satisﬁed. Moneyis an artiﬁcial construct and can be created as needed, so long as it is createdto facilitate production. Because XOR creation is done with the democratic
oversight of token holders, with the aim to allocate XOR only for the creationof new goods and services, devaluation of XOR will not occur as the price levelwithin the economy can stay stable.
Also, XOR exists on the SORA network which uses environmentally friendly
and safe technology to gain consensus about transactions in the network, andthere is no mining. Because of the lack of Proof-of-Work mining, SORA does
not need to pay miners or waste the energy resources of a country. Instead,the SORA technology can quickly, cheaply, and eﬃciently process hundreds ofmillions of transactions per day.

5

Steps to Implement the SORA Economic System in a
Country

The ﬁrst step to take advantage of the beneﬁts that use of XOR can oﬀer a country is to pass legislation allowing XOR to be used as legal tender, meaning thatis should be allowed for: 1) payment of debts, 2) payment for goods or services,and 3) payment for taxes and government services. Drafting the legislation issomething we can help with, but there are two main options for the use of XOR:
1) to use XOR as the only currency allowed for transactions in the country, or2) allow XOR to be used in parallel with other currencies, such as those alreadyin use in the country. Whereas 1) can most quickly facilitate use of XOR in acountry and could potentially reap the most economic beneﬁts, the fastest, 2)
allows multiple currencies (such as a domestic ﬁat currency along with XOR)
to coexist and thus the market can choose the best currency for their needs.
Option 2) is the model that El Salvador adopted when they passed their Bitcoin
legislation.
Once the proper legislation in place that allows XOR to be used to pay debts,
pay for goods or services, and pay for taxes and government services, then rollingout localized wallet software for the populace is the next step. This can be done
at low cost by using the open source SORA wallet, shown in Figure 2, andcustomizing it with the brand of the country, as well as any other idiosyncratic

10

Makoto Takemiya:

Fig. 2: The open source SORA mobile wallet.

needs that the country or its populace might have. This work can be fundedthrough grants from the SORA ecosystem via the SORA Builders Programme17 ,which provides ﬁnancing for the development of software and apps in the SORA
ecosystem.
With the legislation and wallet software in place, the next step is for thegovernment of a country adopting XOR to designate a person in charge of liasoning with the SORA community. This person should be able to write proposals
in English and communicate with the SORA ecosystem to make the proposals
needed by the country to allocate XOR. Additionally, if the country has theresources, it is highly recommended to appoint a committee in charge of analyzing the economy, the quantity and quality of factor inputs for production, anddetermine where to deploy XOR to best increase the production of goods andservices. This is something the SORA ecosystem can also help with setting up
and building a process around with the government.
The key point is that very quickly and with no cost, any government in theworld can adopt XOR as legal tender and start receiving the beneﬁts of being apart of the SORA economy. If XOR is accepted as legal tender in parallel withother currencies, there is very little systemic risk to the economy as well, because
market forces will be able to choose the most useful currencies to use.
17

https://medium.com/sora-xor/sora-builders-programme-979bea8831ed

The Case for XOR

6

11

Conclusions

Creating money that is used to create new goods and services leads to economic
growth without consumer price inﬂation. Money creation and allocation is themost important tool for providing for a prosperous society, able to fund thecreation of new goods and services to push humanity forward.
Cryptocurrencies are a new form of money that holds the potential to makeinternational trade more eﬃcient, but legacy cryptocurrencies, like Bitcoin, have
many disadvantages that limit their eﬃcacy for facilitating economic growth. In
particular, Bitcoin acts as a foreign currency to economies that use it, which
limits the potential for economic growth because new money cannot be created
for the production of new goods and services.
XOR is a new type of cryptocurrency without the technical or economic
limitations of its predecessors. It can easily handle the transactional needs ofhundreds of millions of users. By adopting XOR as a legal tender in a country,
the country can take advantage of more eﬃcient international trade, while also
being able to receive and allocate XOR for the productive creation of goods andservices, which leads to economic growth and a more prosperous lifestyle for
their citizens. A XOR-based economy in a country that has a government which
actively makes proposals to allocate XOR for productive uses, is not limited
by capital to create output using their factor inputs. Such a country can reachits full potential, while joining a supranational economic system, which allows
more open and uninhibited trade, without the need for selling national assets toforeigners via foreign direct investment.

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