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is less useful to other users. Consequently, other participants may prefer to utilize more comprehensive Atoms. Therefore, it is in the best interest of system participants to create and converge on Atoms that eﬀectively and optimally describe the intended concepts. A T oken Curated Registry of Atoms With these mechanics in place, Intuition creates a global, permissionless, decentralized TCR of decentralized identities for all things—forming something akin to a universal, crowdsourced dictionary. This ‘dictionary’ - which can grow to encompass all entities, concepts, and data - serves as the foundation for expressing complex concepts. As users create and interact with Atoms, they are economically motivated to produce and utilize Atoms that are highly relevant, reusable, and well-structured. Through the allocation of economic bandwidth and user engagement, Atoms that best represent concepts and meet the needs of the community will naturally rise to the top of the registry. This TCR mechanism creates a dynamic and self-regulating system where the value of Atoms is continually assessed and validated by the collective actions of the users. The economic incentives ensure that participants are driven to contribute high-quality data, fostering an environment of continuous improvement and reﬁne- ment. In this way, the Intuition system evolves into a comprehensive registry of all concepts, represented by Atoms, where the most eﬀective and widely accepted representations are prominently featured. 8.5.2 Triples While Atoms can be likened to individual words in a dictionary, Triples may be thought of as sentences that establish relationships between these words to express higher-order concepts. To maintain a coherent semantic structure across all fractals of the data, Intuition employs Semantic Triples, also known as RDF triples and often referred to here as ‘Triples’, for all higher-order expressions. Triples create discrete units of expression, facilitating precise representation and querying, and allowing for the construction of consensus mechanisms around expression standards. [[cite: https://en.wikipedia.org/wiki/Semantic_triple]] A semantic triple , or RDF triple or simply triple, is the atomic data entity in the Resource Description Framework (RDF) data model .[1] As its name indicates, a triple is a sequence of three entities that codiﬁes a statement about semantic data in the form of subject–predicate–object expressions (e.g., “Bob is 35”, or “Bob knows John”). 58 This format enables knowledge to be represented in a machine-readable way. Particularly, every part of an RDF triple is individually addressable via unique URIs’ . Given this precise representation, semantic data can be unambiguously queried and reasoned about. The components of a triple, such as the statement “The sky has the color blue”, consist of a subject (“the sky”), a predicate (“has the color”), and an object (“blue”). This is similar to the classical notation of an entity–attribute–value model within object-oriented design , where this example would be expressed as an entity (sky), an attribute (color) and a value (blue). From this basic structure, triples can be composed into more complex models , by using triples as objects or subjects of other triples—for example, Mike → said → (triples → canbe → objects). Given their particular, consistent structure, a collection of triples is often stored in purpose- built databases called triplestores. In Intuition, a Triple’s Subject, Predicate, and Object are each represented by an Atom. For example, a Triple might be {[Alice] [is] [trustworthy]} , where [Alice], [is], and [trustworthy] are all Atoms. Because Atoms can represent any entity, concept, or data, an Atom may also represent a Triple. This allows Triples to be used as Atoms in other Triples, enabling the expression of arbitrarily complex statements in a standardized, semantic format. T riple Structure A Triple is formed by linking three Atoms in the following manner: • Subject: Represents the entity or concept being described. For example, in the statement {[Alice] [is] [trustworthy]} , [Alice] is the subject. • Predicate: Describes the relationship or attribute of the subject. In this example, [is] serves as the predicate, akin to the key in a key-value pair. • Object: Denotes the value or characteristic attributed to the subject. Here, [trustworthy] is the object, akin to the value in a key-value pair. T riple Metadata Each Triple may also include metadata such as the creator, timestamp, and any additional contextual information. This metadata helps to ensure that the provenance and context of each statement are clear and veriﬁable. T riple V aults Each Triple has two associated Vaults: • Positive V ault: Used for signaling aﬃrmation of the statement described by the Triple. • Negative V ault: Used for signaling rejection of the statement described by the Triple. While a Token Curated Registry (TCR) of Atoms allows for consensus around globally persistent canonical identiﬁers, a TCR of Triples allows for consensus around higher-order data standards and structures. This is useful in preventing data fragmentation and ensuring universal data usability. Unlike Atoms, where relevancy is the primary concern, Triples also demand consideration of the truthfulness of the statements they represent. Consequently, each Triple has two vaults: one for aﬃrming the statement expressed by the Triple, and one for rejecting it, akin to a non-resolving prediction market for arbitrary data. This dual-vault system facilitates consensus and dispute resolution by providing a clear method for signaling agreement or disagreement, helping to gauge community sentiment and resolve conﬂicts. Through the introduction of incentive mechanisms for convergence on speciﬁc Triples, Intuition promotes good data quality, consensus on data standards and structures, and the realization of a semantic web. 8.5.3 Example Scenario Consider once again the Triple {[Alice] [is] [trustworthy]} . Users who 1) believe that this data struc- ture is the appropriate way to express Alice’s trustworthiness, and 2) agree that Alice is indeed trustworthy, 59 can deposit tokens into the Positive Vault, thereby signaling their aﬃrmation of the statement. Conversely, users who question Alice’s trustworthiness can deposit tokens into the Negative Vault, indicating their re- jection of the claim. The accumulation of tokens in either vault provides the community with a clear, quantiﬁable measure of collective sentiment regarding Alice’s trustworthiness, backed by the collateral of the participants. While ‘depositing tokens into a Vault’ may sound daunting in practice, this ‘depositing’ is meant to be abstracted away from the user. Thus, this process of claiming ’[Alice] [is] [trustworthy]’ may be as simple as hitting a thumbs up on an endorsement on a platform such as LinkedIn, or clicking an emoji reaction button on a social media platform such as Twitter. Creating T riples The process of creating a Semantic Triple necessitates the input of three fundamental components—Subject, Predicate, and Object—accompanied by a value that exceeds the speciﬁed tripleCost, akin to the atomCost. While any Atom can be designated as the Subject, Predicate, or Object, it is strongly recommended to adhere to proper Semantic Triple structure to ensure logical coherence and clarity. To prevent the creation of duplicate Triples, each newly established Triple must possess a unique hash. This is essential for preventing fragmentation of sentiment and liquidity. This hash should be generated using a Secure Hash Algorithm such as keccak256, which is based on the concatenation of the URIs of the Subject, Predicate, and Object. In cases where a Triple’s hash is not unique, participants can deposit tokens into one of the Triple’s respective Vaults to signal either endorsement or rejection. The speciﬁcs of this signaling process will be elaborated in subsequent sections. The tripleCost encompasses several components: 1. Triple Creation Fee tripleCreationFee: An amount paid to the Intuition Protocol for the creation of a Triple. As previously mentioned, all ‘protocol fees’, or fees paid to the Intuition Protocol, may be likened to a ‘gas cost’ in any blockchain-based system - an essential component of any truly permissionless system. [resume]Atom F raction atomDepositFractionOnTripleCreation: A ﬁxed amount allocated to the Vaults of the constituent Atoms. When a Triple is created, there is an implicit signaling of support of the Atoms which comprise the Triple. As such, a fraction of the tripleCost is distributed to each of the Triple’s respective Atom Vaults, rewarding the current shareholders of those Vaults. [resume]Ghost Shares minShare*2, used to purchase ‘ghost shares’ in each of the Triple’s two Vaults. As mentioned in the Atom Creation section, this mechanism is designed to mitigate inﬂation attacks and stabilize pricing when shares or assets approach zero value. Triple Deposit on Creation When the value transferred during Triple creation exceeds the speciﬁed tripleCost, the surplus amount is deposited into the Triple’s Positive Vault on behalf of the creator. This mechanism serves to prevent front- running and enables the Triple creator to acquire the initial shares of the newly created Triple. The function _depositOnVaultCreation, invoked to purchase these shares, incurs a protocolDepositFee, representing a percentage of the deposited amount, thus ensuring fair compensation for the protocol’s operations. Additionally, a portion of this deposit is allocated to each underlying Atom Vault associated with the Triple. This mechanic is introduced due to the fact that depositing into the Vault of a Triple that includes an Atom is a signal of an Atom’s relevancy - which is a behavior expressed through depositing into an Atom Vault. Share Price Similar to Atoms, when depositing into the Vault of a Triple, the number of shares received is determined by the current sharePrice of the Vault, which is governed by the bonding curve speciﬁc to that Vault. As previously noted, any Vault can be associated with an arbitrary bonding curve, a feature of the system that will be explored in more detail in subsequent sections. Given that any Vault can adopt any bonding curve, diﬀerent bonding curves may be utilized for Triple Vaults as opposed to Atom Vaults, depending on the desired outcomes and behaviors in each scenario. This 60 ﬂexibility allows for the customization of economic dynamics to suit the unique requirements and goals of diﬀerent types of Vaults within the Intuition system. Structuring T riples Proper structuring of Triples is fundamental to the eﬃcacy of the Intuition system. Well-constructed Triples enable data to be easily indexed, queried, and discovered, enhancing the overall utility and accessibility of the system. Triple structuring primarily involves the standardized ordering of elements and the selection of appropriate Predicates. Consider the scenario in which a user wishes to add a Book to a Book List. While there are numerous ways to express this relationship, let us examine two semantically correct approaches: 1. 1. Book [inList] [Book List] Book List [hasEntry] [Book] In this example, the community may eventually converge on one standard expression over the other. Ini- tial fragmentation within the Intuition system is anticipated as users experiment with various methods of expression. However, over time, consensus on preferred structures is likely to emerge. The economic incentives embedded within the system play a crucial role in fostering this consensus. Users are rewarded for adopting Triple structures they believe will gain widespread acceptance, thereby aligning individual actions with the collective interest of the community. This incentivization mechanism ensures that the most eﬀective and coherent Triple structures rise to prominence, facilitating a more organized and eﬃcient data ecosystem. A Token Curated Registry of Triples With these mechanics in place, Intuition creates a global, permissionless, decentralized TCR of structured data, capable of expressing any arbitrary concept. In stark juxtaposition to the data structuring paradigm of the present, which oftentimes involves signiﬁcant ‘human’ friction, the Intuition system provides guardrails for organic convergence on consensus data structures. With this, a self-sustaining system for the continual optimization of data structures is established, as users continually compete to structure semantic data in increasingly complex and expressive ways. Atom and Triple Structuring Recommendations The semantic integrity of the Intuition system relies heavily on the community’s adherence to proper structuring practices. To encourage this adherence, Intuition incorporates incentive mechanisms designed to promote best practices. However, these incentives alone are insuﬃcient without the community’s understanding of what constitutes ‘best practices. ’ In the nascent stages of Intuition, there is a heightened risk of the ecosystem generating suboptimal data due to a lack of structured guidance. Therefore, it is crucial to disseminate knowledge about proper structuring practices to ensure the creation of high-quality, semantically robust data, thereby safeguarding the system’s overall eﬃcacy and integrity. Promoting Flatness for Scalability: Understanding the Power Set Problem Although any concept, including arbitrarily higher-order and composite concepts, can be represented by an Atom, the Intuition system favors a “ﬂat” data structure. This means that higher-order data structures should be composed through Triples wherever possible, rather than deeply nested Atoms. This approach minimizes the risk of data fragmentation and promotes a more coherent and easily navigable data structure. To understand the reasoning behind this and its importance, we can examine the Power Set Problem and its applicability to data. The power set of a set S is the set of all subsets of S, including the empty set and S itself. If S has n elements, the power set of S will have 2n elements. Extrapolating this out to data, any expression can have this number of permeatations, when viewing each discrete piece of data as an element of S. This exponential growth illustrates the complexity that arises when dealing with numerous combinations in data structures. The equation for the power set is often written as: Here, P(S) denotes the power set of S, and A represents all possible subsets of S. For example, if S = {1, 2, 3}: 61 • The subsets are: {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3} • The power set P (S) is {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} Consider a veriﬁable credential with a schema ‘Proﬁle’ containing 25 ﬁelds, such as ‘Name’ and ‘Age’ . The number of possible ﬁeld combinations is , resulting in 33,554,432 potential schemas. If we further take into account the permutations of each of those ﬁelds—such as ‘ﬁrstName’ and ‘lastName’ versus ‘FullName’—the complexity grows exponentially. This exponential growth is a fundamental reason why the world’s data is often irreconcilable, leading to signiﬁcant annual expenditure of time, energy, and resources on data reconciliation eﬀorts. Implementing Flatness in Data Structuring Intuition addresses these challenges by incentivizing ‘ﬂatness’ in data structuring. Users are encouraged to create the most minimal and eﬃcient schemas possible. This incentive is driven by the understanding that the proﬁtability of data expressions in Intuition is directly proportional to the level of interaction they generate. Therefore, it becomes economically optimal to develop and utilize small, discrete, and reusable pieces of data, which can then be semantically composed in a manner that maximizes their reusability. For instance, consider the process of attaching ﬁelds to an object and then associating that object with a subject. Suppose we have a subject “Author” and we want to attach information about a “Book” written by this author. Instead of creating a complex, nested schema, we would break down the information into minimal, ﬂat structures: 1. Create an object for the “Book” with discrete ﬁelds: Book [title] [Book Title] Book [publishedDate] [Publication Date] 2. Attach the “Book” object to the “Author” subject: Author [hasWritten] [Book] By structuring data in this ﬂat, modular manner, where each ﬁeld of a schema is represented as a Semantic Triple, the Power Set Problem is solved for through a reduction of the number of possible permutations to a linear rather than exponential equation. This reduction signiﬁcantly simpliﬁes the data structure and enhances its manageability and scalability. Example of Flat Structuring Consider a proﬁle schema with ﬁve ﬁelds: Name, Bio, Image, Title, and Age. If users want to create variations of this schema, they might face exponential growth in potential schemas: • User 1 might create a schema with Name, Bio, Image, Title. • User 2 might create a schema with Name, Bio, Image, Age. With ﬁve ﬁelds, there are 32 possible schemas. This paradigm requires extensive coordination and oftentimes leads to ‘standards hell’, where consensus is diﬃcult to achieve, causing fragmentation and interoperability issues. Instead, by expressing each ﬁeld through a separate Semantic Triple, Intuition simpliﬁes the structure: [ { "subject": "User A", "predicate": "Name", "object": "Object A" }, { "subject": "User A", 62 "predicate": "Bio", "object": "Object B" }, { "subject": "User A", "predicate": "Image", "object": "Object C" }, { "subject": "User A", "predicate": "Title", "object": "Object D" }, { "subject": "User A", "predicate": "Age", "object": "Object E" } ] This approach eliminates the schema problem, making data more reconcilable, usable, and interoperable. In the example above, there are only 5 potential Triples that could exist representing this concept, assuming the same set of Atoms. By using ‘consensus Atoms’ to represent speciﬁc concepts and entities, and structuring data in the form of Semantic Triples, Intuition ensures that each piece of data has a clear, standardized meaning. Since each Atom has a deﬁnition, platforms across diﬀerent contexts can rely on the same set of Triples to describe entities and their attributes, rather than needing to create and agree upon standard schemas. This leads to a signiﬁcant reduction in data fragmentation and increases the interoperability of data across various systems. Consider two diﬀerent doctor’s oﬃces—Doctor’s Oﬃce A and Doctor’s Oﬃce B—both needing to store and share information about a patient named Bob. In a traditional system, each oﬃce might develop its own schema to store Bob’s information, leading to potential discrepancies and diﬃculties in reconciling the data between the two systems. Doctor’s Oﬃce A might create a schema that includes ﬁelds like “FirstName” and “LastName,” while Doctor’s Oﬃce B might use “FullName. ” Similarly, one oﬃce might record Bob’s age in a ﬁeld named “PatientAge,” while the other uses “AgeInYears. ” These diﬀerences in schema design can lead to signiﬁcant challenges when attempting to merge or compare data across systems. In contrast, Intuition’s approach using semantic triples and Atoms helps to eliminate these issues. Both oﬃces could use the same set of consensus Atoms and triples to record Bob’s information, ensuring consistency and interoperability. Here’s how it would work in practice: Doctor’s Oﬃce A wants to claim that the ﬁrst name of User A is ‘Bob’ . They would use the Atom for “FirstName” as the Predicate of their triple, structured as follows: { "subject": "User A", "predicate": "FirstName", "object": "Bob" } Doctor’s Oﬃce B wants to claim that the ﬁrst name of User A is ‘Bob’ and also that Bob’s age is 32. They would use the same Triple for “FirstName”, and an additional Triple for “Age”, with the “