# Introduction
Pastopia is the first-ever open-world game that will help players learn to code in Python and other Blockchain languages powered by an underlying regenerative finance economy designed with the intention of upskilling youths in at-risk communities to meet the global demands of a digitally-skilled workforce.

Our value-centric and player-driven circular economy that not only rewards and educates players but also provide a veritable means for players to apply their learnings in-game to assist fellow players within the game community in exchange for token rewards.

With a strong emphasis on User Generated Content (UGC), Pastopia generously rewards participants who contribute to the enhancement of the game through the creation of novel content and assets. These contributions are facilitated via our cutting-edge open development tools and peer-to-peer (P2P) community.

Developed by Quurk - we were incepted based on a shared conviction that education should be made more universally accessible, equalising access for anyone to want to learn. The conception and subsequent design of Pastopia, its key gameplay mechanics, and tokenised unit economy are devised to mitigate the shortcomings present in traditional classroom-centric educational routes:
1. **Addressing the looming digital skills gap:** Present and future generations of students face a growing digital skills deficit, resulting in a scenario where fresh graduates may lack the necessary competencies to tackle future job roles.
1. **Mitigating learning opportunity disparities:** The stark inequality in access to similar learning opportunities means students from impoverished or high-risk communities often struggle to escape the cycle of generational poverty, thereby exacerbating the wealth gap.
1. **Adapting to the changing landscape of education:** As the internet becomes increasingly accessible and decentralised, presenting free access to information, and as workforce demands evolve to prioritise specialised skills over degree qualifications, it's essential to reshape the role of education.
1. **Revolutionising pedagogy through financial incentives:** The realms of learning and education often struggle with providing immediate positive feedback and maintaining effective engagement loops to retain learners' interest. By integrating financial incentives, we can inject a newfound dynamism and motivation into the learning process, thereby fostering sustained engagement and progress.

With these concerns in mind, we embarked on the journey to create Pastopia, an open-world game designed to foster a self-perpetuating ecosystem that offers a gratifying self-guided learning experience. Players gain tangible skills in computational thinking and coding while immersing themselves in an enjoyable open-world gameplay. This then evolves into a P2P learning environment where more proficient players can assist or undertake tasks for other community members.

In terms of game design, we incorporate the principles of positive psychology and Gagne’s Conditions of Learning Theory to abstract educational content into gameplay and narrative design. This approach ensures our games serve a dual purpose - they entertain while simultaneously educating.

Our mission is supported by a robust Regenerative Finance (ReFi) token economy that directs profits towards furthering educational initiatives and content within Pastopia ultimately aimed at enhancing human capital. The value generated additionally accrues into a social impact score for core stakeholders, determined by our unique proprietary metrics and linked to our native $Pastopia & $BeMella tokens. Through this, we strive to uplift individuals while facilitating their upskilling journey, thereby making a substantial societal impact.

# Business Models
>Engage-to-learn & earn

In this document, we delve into our strategic thought process and the proposed realization of incentivized business models, firmly grounded in the bedrock of blockchain technology. We examine and propose solutions for the progressive journey towards decentralization (as a means of maximising our social-return-on-investment), while highlighting the unique challenges and opportunities that arise from incorporation open economies into game-based-platforms and modern day business design.

#### Foundation
Inspired by proven revenue models in Web2 and Web3 economies - we attempt to design an multi-layered open economy that transcends the limitations of traditional equity-only / token-only based economic incentivisation mechanisms to create a hyper-structure capable of transforming the future of pedagogy and equitable access to education.

As such Pastopia is powered by a continuous and dynamically evolving business model crossing the threshold of centralised and decentralised economic engagement. Our objective is to build a circular, sustainable and forward thinking business model that has the potential to maximally and positively impact the core stake- and shareholders of the Pastopia economy to ensure the long-term success and realisation of our vision and mission.

To achieve these goals we are implementing blockchain technology and plan to decentralise access to and ownership of Pastopia Game IP across multiple strategies optimally engaging all stakeholders and growing our social impact with our proprietary Social-Return-on-Investment (SROI) quantification methods.

>ⓘ Our SROI quantification processes are derived from taking into account critical capital and labor contributions to the platform and rewarding these with a tokenised representation of value ($Bemella).

At the heart of Pastopia is our dedication to deliver the best-in-class educational content and game-based-learning environment possible - the foundation that will transform the future of pedagogy. Combining multi-disciplinary technologies to empower the creation of digital wealth & wellbeing and effectively applying these to cross the chasm of digital and real-world economies to create sound hybrid economies based and aligned communities.

The realisation of such a vision present us with a compelling mission for the future of education and social impact and greatly enhancing our likelihood of seeding a self-propagating economy.

To achieve our goals we are leveraging cutting edge technological advances for content abstraction into core gameplay loops, expansive centralised and decentralised value accrual strategies and quantitative methodologies for substantiating a SROI for the overarching economy.

In understanding the differentiation between our unique IPs we may proceed to outline our proposed business model and highlight stakeholders critical to the success of Pastopia. As the ecosystem matures and we consolidate our regenerative finance economy a economic equilibrium is prioritised.

## Key Stakeholders
#### Equity Shareholders
1. **Quurk Labs:** Quurk Labs continuously designs and implements new educational content into the open world of Pastopia and other Quurk Labs ventures. The commercialisation of our proprietary content abstraction framework is empowered by our go-to-market, sales strategy and economic engagement with educational institutions and 3rd party IP builders. Quurk Labs also has a direct stake in various tokenised Pastopia IP.
1. **Investors** are exposed to future revenue derived from the commercialisation of our consolidated game-based-learning platform and value appreciation of Pastopia IP. Favoured by an early GTM and commercialisation strategy, their investment is quickly de-risked and manifold returned. Thus setting the stage for a beneficial transition to a tokenised and sustainable economic equilibrium with late stage IP stakeholders.

>ⓘ Phase 1 of our commercial product, go-to-market and sales strategy prioritises returns and de-risks the initial investment for early equity holders.

#### Game IP Stakeholders
1. **Pastopia Foundation:** The Pastopia Foundation is the strategic Shepard and IP stakeholder of our open-world game. The genesis of the Pastopia foundation will coincide with the $Pastopia token genesis event ($Pastopia TGE) and features a council of key stakeholders across the depth and breadth of the organisation. In collaboration with these stakeholders, the Foundation manages and actively coordinates funds secured in the on-chain treasury, reserves and guides the process of effectively distributing game IP.

Over time actions of the Foundation will be informed and guided by $Pastopia token holders as we decentralise IP ownership.
1. **Pastopia IP Token Holders:** Pastopia will feature a rich IP token economy, spanning fungible and non-fungible tokens across the entire value chain of decentralised finance and community building. Unique to our economy is the substantiation of social-return-on-investment in the form of $BEMELLA tokens, that attempts to quantify the at times intangible value of contribution towards supporting a healthy and self-propagating economy aimed at upskilling and uplifting of human capital.

> ⓘ Pastopia will feature a rich crafting and user-generated-content system maintained and coordinated by $Quurk token holders.

#### Game Based Stakeholders
1. **Students:** The Pastopia game is not-only custom built to enable equitable access to the highest quality educational content and enhanced pedagogy that allows us to realise our mission of uniquely upskilling and uplifting human capital, serving underprivileged communities and financing the transformation of education.

It is also designed with the intended progression from Student to Creator & Contributor in mind, which will serve as the catalyst to a healthy knowledge sharing P2P community. The mastery of this progression loop is accompanied by increasingly profitable engagement with the game IP.

Students are provided with the coding know-how to uniquely contribute to Pastopia's game-based learning platform, by solving and verifying bounties for other players, creating unique blueprints, crafting assets and eventually engaging in competitive environments, diverse player and student engagement will be enabled by our unique player progression system.

1. **Contributors:** User-generated-content will be empowered by the licensing of our unique content abstraction framework and asset / content IP creation toolkit. Content contributions will be varied in form, ranging from asset and coding blueprints that enable novel gameplay mechanisms and utilities as well as the inclusion and proliferation of STEM and Coding knowledge through our in-game quest builders.

Effectively this creates space to 2 major in-game contributors:
1. 3rd Party Educational Content Providers; leveraging Pastopia's unique content abstraction framework to supplement and add to the content produced by Quurk Labs. The tokenisation of IP rights relating to the 3rd Party commercialisation of our game-based-learning platform will be financially composable within the greater Pastopia economy.
2. User-Generated-Content for additional gameplay features, mechanisms and assets collectively referred to as blueprints. Pastopias UCG mechanisms will prove superior to traditional game economies, as Players and Users are gradually equipped with the know-how and means to create and custody their own sub-IP.

By creating a framework where users are familiarised and educated on the application of coding and computational thinking they will be empowered to contribute and creatively engage with our in-game economy. Presenting an strong opportunity and utility to sustain the foundation and excitement of accessing Pastopia.

#### Capital Stakeholders & Mechanisms
1. **Stakers:** The mechanism and implementation of staking value & reserve assets to the Pastopia economy and precisely the Pastopia Bonding Surface is dependent on the policy framework currently empowering Pastopia. The initial policy framework, prioritises growing on-chain platform owned liquidity, granting access to certain governance features and reducing in-game fees and transaction costs. In general all staking mechanisms are designed to enhance the economic stability and sustainability of Pastopia's decentralised finance economy and as such generate an SROI in the form of $BeMella tokens.
1. **Liquidity Providers:** Liquidity providers subsidise on-chain liquidity by providing capital and extract capital by diluting on-chain transaction fees earned by Pastopia. Quintessentially on-chain LP's may be effectively engaged to spur the growth of the economy. Depending on risk and return profile, financing liquidity providers with native token incentives is a costly venture. Pastopia aims to reduce dependencies on 3rd party liquidity providers by accumulating significant platform owned liquidity.
1. **Bonders / Bonding:** Bonding liquidity refers to the permanent addition of various reserve currencies to the underlying platform reserves - this action interacts with the various Bonding Surfaces and platform reserves which are goverend by $Pastopia holders. Incentivising bonding is favourable to incentivising LP's and such carries a higher weighted impact on the composite metric determining SROI within Pastopia's economy.
1. **Patrons:** Patrons are similar to bonders except in that they donate capital to Pastopia. Becoming a Patron of Pastopia is the most generous of capital contributions and is incentivised with unique governance access and further broad recognition within the Pastopia ecosystem.

## Game Design Optimisation Trilemma
#### The Challenges of Game Design
In general game development today optimizes for a trilemma spanning challenge, gratification, and economic engagement.
By incorporating blockchain technology and integration of decentralised finance we greatly enhance the avenues for economic engagement for Pastopia IP.

Pastopia unique advantage is found in the fact that it features hybrid institutional and open economic monetisation models. It is worth highlighting again that the revenue generation of going to market as a subscription based game with institutional clients, eliminates most economic friction for players. It also provides a strategic opportunity to gradually decentralise Pastopia IP and introduce players to the core aspects of our tokenised creator economy in addition to providing additional educational content as Quurk Labs to the platform.

Previous implementations of tokenised & partially tokenised in-game economies ultimately failed to address the core challenges and economic opportunities in enhancing game-design. Since the inception of the first Play-to-Earn and digital metaverses - blockchain based business models, platforms and revenue potential have continued to mature and are now capable of effectively enabling new capital controls securing revenue potential, smart business models and value added features to both the macro economic and micro economic commercial strategies.

The on-chain economy strategy and smart contract / token designs are architected to be flexibly implemented and effectively governed to address the evolving core needs of game design and growth initiatives of the platform and core IP stakeholders.

Pastopia's open economy is envisioned to feature both fungible and non-fungible assets over time.

By introducing fungible IP tokens and establishing ownership over core economic infrastructure of Pastopia, we introduce a highly investable and liquid asset classes and are able to further distance our reliance on core game-play production loops and player monetisation.

We believe that in order for a game based economy to be capable of sustaining itself, the core content, creative tools and access to liquidity must first mature.

## Education Edition
The Education Edition of Pastopia serves as a specialized product catering to the needs of educational institutions and private third-party entities. It provides a unique blend of core coding and computational game-based content, enriched by in-depth insights into player engagement, proficiency, and progression within Pastopia, as meticulously detailed in the [Content Abstraction Framework Concept Paper](https://docs.google.com/document/d/1tXk8lJzeAS6rqUKejzBzbbP-0ZBCdVIk/edit?usp=sharing&ouid=116483808514975323744&rtpof=true&sd=true).

The monetization of the Education Edition relies on three major pillars:

1. **Software-as-a-Service Model:** A dynamic pricing model charges institutions based on Monthly Active Users and grants access to specialized content tailored for student usage.
1. **Subsidization:** The subsidization of this edition comes from various sources such as governments, charities, and on-chain revenue. These funds are strategically distributed to support underprivileged communities, ensuring equitable access.
1. **Open API Access:** Our proprietary data becomes a valuable resource for educational institutions, government bodies, research organizations, and content creators. They can access user and content data through our open API, enabling them to derive meaningful insights and further refine their strategies.

In essence, the Education Edition of Pastopia presents a comprehensive platform for learning and growth, backed by commercial strategies that aim to promote equal opportunities and access for all communities.

## Open Economy Model
We believe that by empowering a investor & creator & player lead high-velocity economy we can simultaneously create both novel economic engagement and enhance the gratification inherent to our game-based-learning and pedagogical incentive design powering the core value production loop within the Pastopia economy.

Yet a significant hurdle in creating enduring Web3 games is the process of tokenizing all game assets and related game IP while simultaneously maintaining control over the game's economy. This becomes particularly challenging in the early life stages of a game, when swift user growth and the subsequent issuance of in-game digital assets surpass the game's capacity to equilibrate supply and demand.

Historically, stable game economies have demonstrated characteristics of the [Lindy Effect](https://en.wikipedia.org/wiki/Lindy_effect), where longevity serves as a reliable indicator of future sustainability. In such cases, games with an established history are more likely to maintain their in-game economies over the long term. An exemplary case is Runescape, a game with a 20-year tenure, still maintains a robust economy that has remained relatively steady throughout its existence. This stability is evident from the consistent mid 4-figure real-world value of a Runescape party hat, a rare in-game item, throughout the game's extensive lifespan.

Hence, our task is to navigate these early growth stages with a well-structured economic design, leaning on lessons from both long-standing game economies and the novel approaches possible with blockchain technology, to ensure a healthy and balanced token economy from the outset.

The application of components of blockchain and smart-contract technology greatly enhance our ability to provide the optimal strategies to create lasting and sustainable game economies with equitable stakeholder alignement.

The success of empowering a self-propagating community and having a hand in shaping the future of educational content and pedagogy eventually falls to every stakeholder of the Pastopia ecosystem yet is initally guided by equity shareholders and The Foundation.

### Tokenomics
#### The 4 Pillars of Tokenised Pastopia IP
Quurk will initially feature 4-Tiers of tokenised IP and IP rights:
1. **$Pastopia:** ERC-20 token denominating ownership over fungible on-chain revenue streams, capital reserves and specific governance rights relating to the propagation and commercial decentralisation of Pastopia IP & content within and without our game-based-learning platform.

Holders of $Pastopia will greatly benefit from the growth and utility of game IP, production loops and quality content entering the game-based-learning platform.

Early models of the $Pastopia token distribution:

https://docs.google.com/spreadsheets/d/1I9AhFZy0unLes-5iuV6pA1d_z3B_G6ta7M_dAFukW0Y/edit?usp=sharing

2. **$Bemella:** Every vital stakeholder interaction within Pastopia's broader stakeholder ecosystem is rewarded with the substantiation and creation of a social return on investment (SROI) in the form of $Bemella.
The creation, distribution and burning of $Bemella is facilitated by the $Bemella bonding curve which in turn is governed by $Pastopia & $Bemella stakers. $Bemella and its governance will effectively represent the consolidated and weighted index of positive contributions and engagement with the platform and thus consequently the societal impact derived from positively and impact-fully transforming the educational system and introducing new and enhanced pedagogical concepts.
$Bemella is the energy that powers Pastopia and game-based utilities.

3. **2 Tiered NFT Game Asset Economy:**
1. Commercial Rights Holders: Commercial rights holders take ownership of foundational and licensable game assets in the form of NFTs, such as character designs and weapon blueprints, personal worlds and other on-chain yield-bearing components that are unique to Pastopia and contribute to the vital production and game loops within Pastopia.
1. Non-Commercial Rights Holders: License IP from commercial rights holders and benefit from enhanced gameplay and equitable access to quality learning opportunities. Non-commercial rights users have the ability to become commercial rights holders.

> ⓘ $Bemella is one of the core tools and mechanisms in creating a sustainable, optimally-incentive aligned economy facilitating equitable access to education, digital wealth and social impact. Where positive societal impact sets the foundation for an expansive and sustainable digital economy.

Collectively game IP refers to all game designs rights, trademarks, Pastopia's digital universe and in-game items. The process of gradually decentralising ownership of game IP is the foundation that will enable equitable access for all stakeholders, while creating clear frameworks for the commercial value accrual of populating and contributing to the content and growth of Pastopia.

### Creator Economy
The Creative Economy within Pastopia thrives on the ability to generate non-fungible tokens (NFTs) representing in-game assets and Intellectual Property (IP) blueprints. This unlocks avenues for commercialization, empowering individuals to monetize their engagement, contribution, and invested capital within the gaming sphere. The value of such contributions is quantified, appraised, and compensated based on the volume of these tokenized IPs or their derivatives.

In the early days, blockchain games utilized NFTs primarily as an exclusive pass or VIP access to gaming experiences. In a bid to validate these high-value access costs, an amalgamation of 'play-to-earn' and 'pay-to-play' concepts was introduced. However, this approach was plagued with numerous drawbacks, including a lack of focus on iterative quality enhancement in game development and user experience, a business orientation heavily skewed towards NFT buyers rather than the actual gaming community, and unstable economies driven by new participants without genuine stakeholder involvement from the gaming community.

We aim to pioneer the Gradual Decentralisation of Game IP (GGIP) mechanism, promoting a Play to Own and Earn (P2O) methodology. At the same time, we tap into the success of the Free to Play (F2P) model and microtransaction-based revenue generation. This system paves the way for broader IP extension across sectors beyond gaming.

To actualize this vision, it is crucial to discern the interests of utility / aesthetics buyers and those wishing to commercialize the underlying IP assets from gamers' desires to engage with the product. This differentiation should be reflected not only in the corporate strategy but also in the legal and contractual rights distribution within the NFT collections.

We propose a dual-layer NFT system, consisting of Commercial-Right IP NFTs and In-Game NFTs. The former allows shared IP rights over specific assets, asset classes, and educational content, whereas the latter symbolizes in-game assets owned by players. In simpler terms, Commercial-Right IP NFTs are designed for those seeking to acquire and monetize Pastopia IP ("Asset Owners"), while In-Game NFTs cater to end-users or gamers ("Gamers").

The GGIP mechanism permits the decentralized usage of in-game assets. F2P players can acquire these resources through gameplay or microtransactions, with the pricier commercial ownership rights distinctly separated from the gameplay loop. The GGIP system will be augmented with an in-game currency system, serving as a medium of exchange for players and bolstering liquidity in the game's primary market. This in-game currency can be purchased using fiat money or earned as rewards and incentives for stakeholders.

The GGIP is pivotal for extending gaming IP across diverse platforms and franchises. Commercial-Rights NFT holders, possessing fractionalized IP and royalty rights, are incentivized to commercialize their IP and earn royalties.

The combination of Pastopia's user-generated content (UGC) and decentralized IP ownership via GGIP transforms the platform from being just a game to an encompassing IP ecosystem. Here, all stakeholders - Asset Owners, Creators, and Gamers - have unique roles generating mutual value in a scalable manner.

Asset Owners are driven to negotiate and secure licensing deals enhancing the Pastopia brand IP, yielding a share of licensing revenue commensurate with their individual efforts. Creators are afforded the opportunity to enrich content, rendering the game self-sustainable and capable of self-expansion. This fosters improved gamer retention, with GGIP licensing terms ensuring Creators build what gamers desire. Gamers, as the final consumers of the Pastopia game, serve as the ecosystem's growth engine, facilitating sustainable rewards for all involved parties.

As a result, the incentives of all participants align, with each motivated to contribute towards a thriving and robust IP ecosystem.

#### User Generated Content
**Issues with Current Web2 UGC Games:**
1. **Content restriction:** User-Generated Content (UGC) in existing games is limited by the rules, technology, copyright, and legal constraints of the game. If a game shuts down, all the user-created content disappears, providing no ownership, recognition, or revenue for creators.
1. **IP conflicts:** While UGC has been integrated into game industry business models, legal and regulatory aspects have not received adequate attention. Questions about intellectual property rights and the legal status of UGC remain unanswered. Legal actions by IP owners, such as Nintendo in the case of a Pokemon mod for Minecraft, further complicate the issue.
1. **Lack of transparency:** Current projects lack clear guidelines for user interactions, content moderation, and fair compensation for creators. Equitable treatment, fair application of rules, and consistent moderation practices are essential for fostering a supportive and engaging environment.
1. **Unequal revenue distribution:** Revenue generated in Web2 games is heavily centralized around game publishers or platform owners, leading to significant imbalances in income distribution among players and users who contribute value to the games. This disparity fails to recognize the substantial contributions of the community.
1. **Lack of incentives:** User-generated content often arises from individuals' passion and desire for self-expression. However, traditional games do not provide a truly open economy that rewards users who create and contribute value. In Web2, UGC models can become exploitative, with creators receiving little beyond recognition while studios benefit financially.

**How we incentivise UGC and IP composability in Pastopia:**
1. **Extensive content freedom:** Pastopia allows players to create diverse and expansive UGC ranging from educational content to the creation of in game IP assets, breaking away from content restrictions imposed by previous games. The game, toolkits and economic framework provided ensure that user-created content persists even if the game undergoes changes or discontinuation.
1. **Robust IP framework:** Pastopia addresses legal and regulatory dimensions of UGC by implementing a comprehensive IP tokenisation framework empowered by Acxyn that empowers and secures players', creators' and investor' rights.
1. **Transparent environment:** Governance over Pastopia and the coordination of game progression, asset inclusion and IP proliferation is managed and guided by the Foundation and decentralised through the distribution of $Pastopia & $Bemella
1. **Equitable revenue distribution:** Unique revenue sharing capabilities of NFT's, such as the customisable distribution of licensing and utility fees to minters, holders and users of in-game assets and content.
1. **Incentivized ecosystem:** $Bemella is granted to Contributors in return for their capital and labor intensive investments to Pastopia. Creators receive tangible rewards, such as tokens or in-game assets, based on the success of their creations, empowering them to participate actively and benefit economically from their efforts.

By addressing these key issues, Pastopia revolutionizes the UGC gaming landscape, empowering players as creators, protecting and empowering their rights, and fostering a sustainable and rewarding gaming experience for all participants.

### Investor Economy
> ⓘ This section describes the strategy and implementation of Fungible Cryptocurrencies representing Pastopia IP

The tokenization of Pastopia's intellectual property (IP) and the associated Social Return on Investment (SROI) are actualized through the fungible tokens $PASTOPIA and $BEMELLA. These tokens are intricately interconnected through their integration into the Pastopia bonding surface, as explained in the concept of multi-dimensional bonding curves. Their significance within the Pastopia economy is further enhanced through staking and bonding mechanisms.

###### Staking Features and Value Accrual in Pastopia
######

**Staking**
Holders of $Pastopia and $BeMella tokens have the opportunity to stake their liquidity tokens within the ecosystem. By doing so, they qualify for accessing IP revenue and allow the platform to establish and extend control over broader market dynamics by endorsing official staking pools. Staking plays a crucial role in various fee mechanisms, informing the protocol of the fees that users or investors are required to pay when engaging in transactions within the token economy.

Staking also serves as a means to align the interests of token holders with the success and growth of the Pastopia ecosystem. By staking their tokens, holders contribute to the liquidity and stability of the platform, while also gaining potential rewards or benefits tied to the IP revenue generated. This incentivizes active participation and engagement within the ecosystem, fostering a symbiotic relationship between stakeholders and the broader token economy.

The integration of staking with fee mechanisms ensures that the costs associated with transacting within the token economy are appropriately captured. These fees contribute to the sustainability of the platform, providing ongoing resources for development, maintenance, and further enhancements. Additionally, the ability to define and endorse official staking pools allows the platform to maintain control over market dynamics, ensuring a robust and well-governed ecosystem.

By integrating staking, bonding, and fee mechanisms, Pastopia establishes a framework that aligns incentives, drives economic participation, and supports the overall growth and success of its token economy.

Acxyn Ecosystem Fees and rebates are determined and discounted in relation to the total volume generated by its on-chain activities as well as the overall value of staked reserve assets.

**Bonding**
Leveraging on key insights derived from Acxyn's novel Proof-of-Fun valuation algorithm, and our own in-house proprietary SROI oracle, we may determine optimal strike prices for the issuance of Bonds and reserve assets from the protocol reserves and bonding surface to facilitate automated market operations aimed at enhancing the platform-owned-liqudity and economic stablity to supercharge our growth potential.

#### Social-Return-On-Investment
**Why Pastopia Applies SROI To Its Token Economy**
Social Return on Investment (SROI) can be effectively applied to evaluate the impact of Pastopia. While SROI is commonly used in traditional corporate settings to enhance program management, improve planning and evaluation, and communicate the value of their work, it also holds significance for philanthropists, venture capitalists, foundations, and non-profit organizations. These entities can utilize SROI to quantify their social impact in financial terms.

It should be noted that assigning a dollar value to social impact can be challenging, and various methodologies have been developed to aid in quantifying results. For instance, the Analytical Hierarchy Process (AHP) is a method that converts qualitative information into quantitative values, helping to provide a clearer picture of social impact.

When measuring SROI for Pastopia, several key elements are essential:

1. **Inputs:** These include the resources invested in the activity, such as the costs associated with running, maintaining and growing Pastopia, development expenses, on-chain liquidity, token incentives and revenue.
1. **Outputs:** This refers to the tangible and direct products resulting from the activity, such as the number of users trained, creators engaging and providing content or and general engagement with the Pastopia game. It further takes into account the growth of the reserves within the Pastopia Trust.
1. **Outcomes:** These represent the changes that occur in individuals as a result of the activity, such as increased education production function compared to demographic averages, the number of token rewards per user, users referred to employment opportunities, and reduced reliance on charitable support due to economic optimization within Pastopia's education production function.
1. **Impact:** This signifies the measurable difference between the actual outcome and an estimate of what would have occurred in the absence of the program. For Quurk, it could be determined by assessing the disparity between Quurk's education production function score and the traditional education function score.

By evaluating these elements and calculating the SROI, Quurk can effectively measure its social impact and demonstrate its value in terms of educational outcomes and economic optimization. This approach enables stakeholders to understand the true value generated by Quurk and make informed decisions regarding resource allocation and future development and reserve ratios.

**Defining Social Return on Investment (SROI)**:
Social Return on Investment is an innovative approach that aims to quantify the value of social outcomes in initiatives within the human services sector. It draws inspiration from concepts in business and economics, utilizing elements of cost-benefit analysis, social accounting, and social auditing. The purpose of SROI is to measure and communicate the value of program outcomes, encompassing both monetary and non-monetary aspects. The development of SROI was spearheaded by REDF (formerly the Roberts Enterprise Development Fund), and it has gained traction among practitioners in Scotland, the United Kingdom, and increasingly, the United States.

SROI serves as a framework to address key questions and provide insights into the effectiveness of social initiatives. According to Carla Javits of REDF, it helps to answer the following questions:

1. How can we effectively measure the success of our efforts?
1. How do we determine whether we are achieving the desired outcomes we set out to accomplish?
1. How can we make informed decisions regarding the optimal allocation of our resources?

At its core, SROI calculates the return on investment by comparing the total monetary benefits derived from social investments to the total monetary costs incurred. However, SROI goes beyond financial metrics alone and incorporates broader social and environmental impacts, recognizing that not all outcomes can be accurately quantified in monetary terms.

By employing the SROI methodology, organizations such as Quurk and Pastopia gain a deeper understanding of the social value created by their initiatives. It enables stakeholders to assess the effectiveness of their efforts, make informed decisions based on data-driven insights, and allocate resources more efficiently. Ultimately, SROI helps to foster a culture of accountability and transparency in the human services sector, leading to more impactful and sustainable social outcomes.


**How Pastopia Quantifies SROI**
Underlying the Pastopia token economy is the recognition that we actively contribute to the betterment of humankind, with equitable access to a state-of-the-art game based learning platform and a highly engaging pedagogy.

Quantifying that value, enables us to intuitively propagate the value across our core stakeholders.

Using a specially customised weighted The Cobb-Douglas production function allows us to a standard framework for valuing contributions to the platfor . It can be expressed as follows:

Y = A * L^α * K^β

In this equation:
* Y represents the total production, which measures the combined value of all SROI generated by stakeholders of Pastopia across x blocks
* L refers to the labor input, quantified by the number and efficiency of creators, students and users immersing themselves in Pastopia.
* K denotes the capital input, which encompasses providing liquidity, bonding, producing content and in-game items (quantified by the tax and royalty fees genrated) The value of the capital input is divided by the price of capital for normalization purposes.
* A represents the multi-factor productivity, which encapsulates the influence of technological advancements and other factors that affect overall productivity.
* α and β are the output elasticities of capital and labor, respectively. These values are hyperparamenters governed by core stakeholders of Pastopia.

The Cobb-Douglas production function considers capital and labor as the two fundamental "factors of production." It provides a mathematical representation of how these factors interact and contribute to overall production output.

Fortunately the Cobb-Douglas function may be intuitively overlapped on the genesis bonding surface where isoquant variants determine exchange rate and collateralisation ratio.

###### Wire-grid Cobb–Douglas production surface with [isoquants](https://en.wikipedia.org/wiki/Isoquant)

---

**Quantifying SROI on Students & Creators Labor**
The functioning of this system can be understood through the following components:

A = a(s,Q,C,H,I)

1. A (Skills Learned): A represents the skills acquired or achievements earned by players in the Pastopia game. It reflects the level of proficiency attained by individuals during their learning journey within the game.
1. s (Time of Learning): s corresponds to the duration of learning or the amount of time players spend engaging with Pastopia. It captures the temporal aspect of the learning process and indicates the investment of time made by individuals.
1. Q (Quality of Creators and Contribution): Q is a vector that encompasses the quality of the creators involved in Pastopia and their contributions to the game. It considers the quality and revenue generated by the creative input of individuals involved in developing Pastopia, as well as their impact on the overall production and improvement of the game and content.
1. C (User Characteristics): C represents a vector of user characteristics, specifically their innate abilities and traits that contribute to their specific playstyle within the game. These characteristics could include cognitive abilities, problem-solving skills, or other relevant attributes that influence individual performance.
1. H (In-House Characteristics): H is another vector that captures the in-house characteristics related to the improvement of the game. These characteristics encompass factors within the game development process, such as updates, enhancements, and refinements made by the game's creators to improve the overall user experience and educational impact.
1. I (Non-Profit Inputs): I represents the last vector, which comprises inputs provided by non-profit organizations. These inputs include measured data related to geographic areas and relevant metrics that help assess the educational impact of Quurk. These metrics can be used to generate a score reflecting Quurk's impact on education.

By compiling and analyzing these vectors, a comprehensive composite score is generated, which quantifies the educational and social impact of Pastopia. This score can be compared to the standard education score of specific areas as well as historic baselines generated by Pastopia, enabling a measurement of the difference and the overall impact generated.

By aligning the educational impact with financial incentives, Pastopia aims to create a sustainable model that rewards and encourages meaningful educational outcomes within its gaming ecosystem.

**How Quurk can multiply ROI on SROI**
To calculate the impact of Quurk and its initiatives, it is crucial for the community leaders to conduct a comprehensive assessment of the relevant costs and monetized benefits. This process leads to the development of an impact map, which quantifies and maps the total unit value received by each stakeholder. The following steps outline the process for calculating the impact:

1. **Determine Total Unit Value:** Multiply the financial value by the quantity of outcomes achieved for each stakeholder. This calculation yields the total unit value, representing the combined value of the outcomes for that specific stakeholder.
1. **Calculate Total Unit Value/Impact:** Repeat the previous step for each outcome, calculating the total unit value or impact for each set of outcomes. This provides a comprehensive understanding of the total value generated for each stakeholder group.
1. **Calculate Net Present Value (NPV) of Benefits:** To determine the Social Return on Investment (SROI), Quurk automates the calculation the net present value of the benefits. NPV considers the value of the benefits over time by adjusting the periodic cash flows to their present-day value, using an appropriate discount rate (r) and benefit period (t). The net present value of the benefits serves as the numerator within the SROI equation.


By calculating the impact and incorporating the concept of net present value, Quurk gains insights into the long-term value and sustainability of its initiatives. This allows Quurk and its stakeholders to understand the financial implications of their efforts and make informed decisions based on a comprehensive evaluation of their social impact. The SROI calculation provides a meaningful metric that measures the effectiveness of Quurk's programs in generating value for stakeholders and the broader community.
Effectively ROI on SROI will be capitalised through the precise issuance of $BeMella underwriting our SROI.

#### Bonding Curves

> MDBC's are the heart of our intricate token economy.

**One Dimensional Bonding Curves**
Bonding curves provide a mechanism for creating and redeeming tokens by exchanging them for a reserve asset, based on a predefined mathematical formula or curve. This curve establishes a relationship between the total supply of the issued token and the amount of reserve asset held as collateral. The entire process, including token issuance, redemption, and reserve management, is typically facilitated by an Autonomous Agent, which operates similarly to a smart contract on Ethereum or other blockchain platforms.

###### One-Dimensional Bonding Curve and Collateral Reserve

A common and straightforward example of a bonding curve is the one-dimensional case, where a single reserve asset is linked to the token being issued. In this scenario, the curve is represented by a mathematical function that takes one variable as an argument. For instance:

r = s^2

where:
r is the total reserve deposited
s is the total supply of the token issued

The price per token in units of the reserve asset is the derivative of the above formula:

p = dr/ds 2s

Please note that in this example, the price of tokens increases as their supply grows, resulting in earlier investors obtaining a more favorable (lower) price. Similarly, early sellers can benefit from a better (higher) price, while subsequent sellers may need to sell their tokens at a lower price. Consequently, in the absence of additional incentives, the token supply becomes inherently unstable as holders rush to sell their tokens rapidly, ultimately driving the supply to zero.

**Multi-dimensional bonding Curves**
Multi-dimensional bonding curves expand upon the concept of one-dimensional bonding curves discussed earlier. One notable pioneer in this area is Balancer, which introduced the concept of "bonding surfaces" by enabling multiple reserve currencies to back the issuance of a token.

To illustrate this, let's consider the simplest example of a two-dimensional curve or surface. This curve allows the issuance of two tokens, for example $Pastopia & $Bemella, against a shared reserve.

where:
r is the amount of the reserve asset deposited on the bonding curve;



parts in this system compared with one-dimensional bonding curves, and this opens new possibilities for financial engineering, in particular for tangibly substantiating a social return on investment, that creates a positive-sum contribution environment.

In practical terms, the multi-dimensional bonding curve allows us to choose whether to issue token $Pastopia, or $BeMella, or both simultaneously in return for stakeholdes providing reserve assets to the dynamic bonding curve reserve.

By allowing for the issuance of different tokens against a shared reserve, the multi-dimensional bonding curve provides flexibility and enables the creation of diverse token ecosystems.

**Dynamic Reserve Ratios in Multi Dimensional Bonding Curves**
Multi-dimensional bonding curves can be further customised by establishing a dynamically pegged reserve value, weighted correspondingly to the supply of all assets closely associated to the genesis bonding surface.

At Pastopia we quantify the Social-Return-On-Investment through proprietary valuation metrics, the result of which is a composite function establishing a baseline for the positive value contribution to the Platform and by extension greater society. Establishing this baseline we collateralise the issuance of $Bemella as the tokenised substantiation of multi-factor-productivity and social impact of our game-based-learning platform.


Furthermore, through integration within the Acxyn ecosystem, we continuously render the net-present-value of $Pastopia IP and derive actionable insights into adjusting the economic levers of the bonding curve maximising revenue, growth potential and exercising capital controls to create the foundation of our regenerative finance economy.


**How Pastopia uses Multi-dimensional dynamic bonding surfaces**
In the immersive world of Pastopia, the concept of bonding surfaces is intricately linked to the vast oceans symbolize by the game's lore. By harnessing this technology, we are able to seamlessly integrate the entire fungible economy and yield-bearing reserve trust of Pastopia onto the blockchain. This integration is made possible through the manipulation of hyper-parameters that govern the bonding curve, including asset issuance, reserve ratio, transaction fees, and interest rates.

Stakers of $Pastopia and $BeMella tokens gain access to a powerful economic primitive that drives the decentralized finance (DeFi) integration of Pastopia's intellectual property. By staking these tokens, participants are granted maturity-adjusted governance access and rights within the ecosystem.

Many existing token economies are fortunate to have two sources of liquidity available to potential investors. Projects that have reached a certain level of maturity or have gained significant investor attention often list their tokens on centralized exchanges like Binance, Kraken, and Coinbase. On the other hand, decentralized finance projects typically list their tokens on decentralized exchanges such as Balancer and Uniswap, while striving to establish deep liquidity. These projects often incur ongoing expenses in the form of liquidity fees paid to liquidity providers (LPs).

With the introduction of bonding surfaces and tokenized indexes, Pastopia sets itself apart by creating three distinct avenues for economic engagement within its token economy. The interaction of external stakeholders with the Pastopia bonding curve is referred to as "bonding" within the context of these documents. These bonding interactions serve as a revenue-generating core feature of our on-chain fungible economy.

By expanding the possibilities for economic participation and introducing innovative mechanisms like the bonding curve, Pastopia establishes a robust and dynamic ecosystem that enhances liquidity, fosters engagement, and drives the sustainable growth of its token economy.