Interactions, Tasks & Contributions are natively built-in in Āut's protocol, and are divided in Global and Local, following this standard:

1. Global:

   1. Interactions: they represent "on-chain actions" - where a user-owned wallet calls a function in a smart contract deployed on any network (i.e., adding liquidity on a DEX, voting on a governance protocol, minting an NFT, etc.)

   2. Tasks: they are on-chain representations of off-chain actions (i.e., Tweeting, committing on Github, joining a Discord call, etc.)

2. Local:

   1. Contributions: Tasks or Interactions deployed inside a Hub are called Contributions, and can be assigned a custom weight between 1 and 10. This weight is called Contribution Points (CP).

Once a Member of the Hub has successfully completed and submitted a Contribution, these points are given to the Member, and the total CP gained by a Member during a Period will represent that Member's given contributions score (gCP) score for that Period.

Tasks / Interactions are "global" types that follow a specific data structure and can be added to the in a fully-decentralized way. Once added and verified, they will be immediately available for any Hub in the Ecosystem, including Hubs deployed in the past.

Each Hub can then select any of the Tasks defined in the TaskRegistry, and deploy a local instance of it by adding additional context (metadata).

Tasks deployed inside a Hub are called Contributions, and can be assigned a custom weight between 1 and 10. This weight is called Contribution Points (CP).

Once a Member of the Hub has successfully completed and submitted a Contribution, these points are allocated to the Member, and the total CP gained by a Member during a Period will represent that Member's gCP score for that Period:

$\displaystyle \sum_{CP = 1}^n CP_i = gCP_{i}$

General formalization for Contribution Points ($CP$) of Interaction ($\iota_{i}$)

In a more formal sense, for each Interaction in the Āut ecosystem:

$\iota_{\tiny i} \in \Iota_{\tiny Ā}: [\iota_{\tiny 1}, \iota_{\tiny 2}, ..., \iota_{\tiny n}]$

is structured so that a Contribution inside a Hub will follow the same pointing system, and will have a local, measurable weight such as:

$\forall \text { } \iota \in \Iota_{h \tiny \bullet}, \iota = 1 \leq CP_{h \tiny \bullet} \leq 10$, where:

• $CP_{h \tiny \bullet}$ is the range value of Contribution Points available for an interaction in a specific Hub ( $h \scriptsize \bullet$)

• $\iota_{i}$ represents any unique Interaction type

Interactions can be further assigned a semantic space (or "context") and linked and inter-linked together in internal modules such as Quests and Onboarding Strategies.

Expected Contributions (ECp) represent the expected value contributed by a participant to a Hub, based on their Commitment Level (iCL) and the tasks created and taken.

EC is necessary for:

1. Performance Measurement:

   • EC is the benchmark to meet in order for a participant to be fairly and meritocratically evaluated based on their actual contributions (against the expected ones), providing a measurable, human metric to assess their performance.

2. Accountability and Incentives:

   • By setting clear expectations, EC enhances accountability. Each period (1 month), Participants are incentivized to meet or exceed their EC in order to maintain or grow their Participation Score (PS).

3. Impact on Hub Prestige:

   • The EC-based aggregated performance across all participants, directly influences the Hub’s Prestige - reflecting the collective expected value and the Hub's overall growth and ability to deliver on its KPIs.

In order for the PS framework to tie together a unique contributor’s identity to each and all of the Hubs they contribute to, we need a standardized system of reference, that allows for data to be portable and verifiable across any communities and networks. The PS framework was specially designed for ĀutID holders as an essential component of the Āutonomy Matrix framework - but can be used out of the box with minimal adjustments.

An individual ĀutID is a Non-Transferable NFT ID, and it’s the first self-sovereign Identity that binds an Individual to the Hubs, projects or DAOs they contribute to. This allows them to use their profile as a Portable Identity to join new communities, and gain reputation while they browse the decentralized web.

It works as a Social Graph, that keeps track of all the Hubs, tasks, interactions, roles, commitments and connections of an individual in the decentralized web.

Āut's Participation Score (PS) is a measure of an individual's contributions to a specific Hub within the Āut ecosystem. It is calculated as the ratio of an individual's Given Contributions (GCP) to their Expected Contributions (ECP).

The Participation Score (PS) is designed to measure the value contributed by an individual Participant to a Hub - allowing an on-chain community to measure the Local Reputation of each of their Members/Participants in a fair, meritocratic, and mathematically-verifiable way.

More specifically, the PS framework is designed to measure the ratio between a Member’s intentions (Commitment Level, CL) and their actual Participation (Given Contribution Points, GCP) within a decentralized project or community.

The framework incorporates several key parameters, including Expected Contributions (EC), Given Contributions (GC), individual Commitment Level (iCL), and a constraining factor (c).

The PS framework is used natively in the ĀutID identity framework, and it's an essential component of the Āutonomy Matrix - but can be used and integrated out of the box with minimal adjustments.

PS is a key component of Āut's Āutonomy Matrix, the first-ever decentralized Reputation system - and it is used to calculate an individual's Peer Value (Absolute Reputation, $\upsilon$) in the decentralized web.

In addition to its role in calculating $\upsilon$, Participation Score can also be used to determine an individual's access to certain resources, rewards, permissions and privileges within a Hub - as well as their eligibility for certain tasks and roles.

It is a key factor in ensuring that individuals are held accountable for their commitments and contributions within a community, and helps to maintain the integrity and efficiency of the overall system.

EC is the most important parameter in the Āut's Participation framework.

It determines the expected contributions of a contributor of a Hub during a specific period.

It’s based on the Commitment Level chosen by the Individual Member, and it’s necessary to determine the ratio between the promise / commitment of a contributor, and their actual participation.

It’s calculated as:

$EC = fiCL \times TCP$

where:

• TCP: Total Contributions Points in a Community. Sum of all contributions points available in a community in a given period. They can be acquired by members by completing tasks and interactions. Each Task and Interaction has a custom weight (spacing between 1 and 10).

• fiCL: Fractional Commitment Level per Individual

EC’ = normalized EC accounting the time factor ΔT

We may consider a time factor ($tf$ or $\Delta{T}$) to determine EC based on the time left in a period:

where:

• $\Delta{T} \text{ is calculated as }= \frac {T_{l}} {T_{i}}$

• $T_{l} \text { is the time left in a period } T$;

• $T_{i} \text{ is the total time at the start of the period }T$;

This way it's possible to create a generalized abstraction to factor in participants who join a community after the start of the period T.

This works simply by accounting all absolute time available in a community in relation to each individual member:

$\sum (\Delta_{T}) = \frac {\sum (T_{l})} {\sum (T_{i})}$, from which we extrapolate a fractional $\Delta{T} \text{ as }\rightarrow(\frac {fT_{l}} {fT_{i}}) \times T$

This allows for a continuous calculation of EC for all members in different, arbitrarily small intervals within the same period T.

The main value of a Hub is to be able to expand the concept of DAO - from a list of 0x addresses, to a functional, coordinated group of individuals willing to create and achieve something together.

It expands the concept of a DAO directly at the contract level, building upon the original definition of a smart contract(s)-powered community.

It’s an on-chain project/organization where different abstractions, such as Onboarding Strategies, Reward Mechanisms, and Task Types, can be easily integrated and are available interoperably for the entire ecosystem.

At its core, it adds the native concepts of Member’s Role, Interaction and Reputation at contract level - so that each Participant to a decentralized Project, Organization or Hub is represented in a much more multidimensional, richer way - other than a basic 0x... address in a mapping function.

This turns any DAO/Project/Organization itself into an on-chain declarative statement, that sets the foundation for (1) its verifiability and measurement, (2) its standardization, (3) a socio-financial agreement where each participant can join the collective for free association.

You may see this on-chain structure as a sort of self-enforcing representation of the whole is greater than the sum of its parts on a digital scale.

What makes a Hub an evolution respect to a DAO

A Hub has fundamental concepts built-in at contract level:

• Each contributor/participant/member of a Hub has a Role in the community

• Roles (not Discord roles, or random "revokable NFTs" - but actual, custom Role names with custom RBAC permissions) are at contract level

• Each contributor/participant/member of a Hub has a Commitment Level representing the time or effort they dedicate to the community

• Each contributor/participant/member of a Hub has a Participation Score representing the measurable value of their contribution to the community

• Interactions are tracked for each Task and Participant

A Role is a self-sovereign label, that Members choose at the time of joining the community. Any time a new Task, Voting Round or Community Event is created - they can be assigned to a specific Role, allowing easier organization and trackability of scope - together with a purposeful, non-hierarchical cooperation.

Roles exist directly on-chain, and complement the concepts of Interaction and Commitment.

Combined, they allow the possibility for Participant’s individual Reputation to exist on a global level.

Each Participant commits a custom amount of time and/or effort to each community or project they contribute to. This amount is called Commitment Level (CL), and represents the time, work, and/or effort that an individual plans to dedicate to a decentralized project - a Hub.

Since a Participant’s Commitment level is the Real-World representation of the time or effort that they expect to put into each of their community, it needs to be finite in order to reflect real-world dynamics (where, alas, our day lasts only 24 hrs).

In traditional research, parameters tend to be subjective (e.g., Social graphs; social reviews) - with inconclusive results, generating systems with very little standardization and accuracy, while at the same time allowing very little customization. On the other hand, in practical engineering and system design, the early years of the internet (web “1.0”, web “2.0”, etc.) showed a tendency to build systems that are - yes, rigorous on one side, but forcing users to adapt to system’s rules, rather than systems adapting to users’ behavior.

Both have their merit - but, in order to move past “instant gratification,” a solid “humane” system design needs to aim for highest possible degree of abstraction and flexibility (resilience over robustness), while utilizing parameters that reflect the human value provided by the participating parties / actors involved.

In a nutshell:

• The system needs to be designed for long-term results (no instant gratification / social proof)

• Everything needs to be measurable, and follow a rigorous first principles, scientific method. Meaning that the subjectivity should come “locally” from the customization of parameters, not from the parameters themselves.

The Participation Score (PS) in the Āutonomy Matrix directly ties individual participants to the Hubs they are contributing to - introducing a novel approach that differentiates it from traditional local reputation protocols:

1. Dynamic Allocation:

   • PS dynamically adjusts based on real-time contributions and interactions, ensuring that the score accurately and fairly reflects current participation, and measures the value-add contributed by each individual participant.

2. Mathematical framework:

   • As mentioned earlier, traditional systems focus solely on either (1) social feedback or (2) ownership of financial assets - on the other hand, the PS framework incorporates a broader range of self-assigned metrics, including Commitment Level (iCL), roles, and the Interactions undertaken by the contributor. This self-sovereign, multi-layered approach provides a more holistic, human perspective on a participant's contributions.

3. Integration with ĀutID:

   • PS is directly linked to the unique ĀutID, required in order to join and contributing to a Hub. This creates a unified and portable reputation across different Hubs and platforms. Which in turns bring the continuity and provenance lacking in traditional reputation systems (decentralized and not).

Every time an ĀutID joins a new Hub, their Commitment Level amounts rebase dynamically, reducing the Commitment assigned to the previous Hubs. Based on their Commitment, members can hit different tiers and it’s up to each Hub to decide whether they want to differentiate permissions and rewards based on those tiers.

Below the process we use to make the CL allocation self-rebasing and discrete.

Parameters

• $iCL_{tot} = 100$: the Total Individual Commitment Level that a user j has available to allocate to the set of Hubs ${[\tt H \cdot]}$ in which they contribute.

• N: the number of Hubs ${[\tt h \cdot]} \in {[\tt H \cdot]}$ where j is already contributing.

• $iCL_{[\tt h \cdot]}$: the iCL allocated by j to a Hub ${[\tt h \cdot]}$

• $aiCL_{tot}$: the iCL allocated to Hubs where j is already contributing.

• $iCL_{new}$: the iCL allocated to the new Hub.

• $fiCL_{[\tt h \cdot]}$: the fractional CL allocated by j to each Hub.

• $uiCL_{[\tt H \cdot]}$: the updated CL for previous Hubs in the set ${[\tt H \cdot]}$.

• riCL: the remaining iCL, calculated as $iCL_{tot} - aiCL_{tot}$

Calculate the Proportional Decrease of each Hub's iCL

• Calculate the total iCL allocated to existing Hubs: $\displaystyle aiCL_{[j, \text{ } \tt h \cdot]} = \sum_{[\tt h \cdot] = 1}^N iCL_{N}$

• then allocate a portion of $riCL$ to a new Hub $[\tt h \cdot]_{(new)}$

• Calculate the remaining points: $riCL = iCL_{tot} - aiCL$

• Calculate the proportion of iCL for each existing Hub: $\displaystyle fiCL_{[j \text{ } \tt h \cdot]} = \frac{iCL_{[\tt h \cdot]}}{aiCL_{tot}} \text{ } \forall \text{ } [\tt h \cdot] \in [\tt H \cdot]$

• Adjust the allocation for each existing Hub: $\displaystyle uCL_{[\tt h \cdot]} = fiCL_{[\tt h \cdot]} \times riCL \text{ } \forall \text{ } [\tt h \cdot] \text{ } in \text{ } [\tt H \cdot]_{j}$

Final Formula

the new iCL is calculated as:

with $\displaystyle \sum {[\tt h \cdot]}_{[\tiny 1 + ... + N]} = [\tt H \cdot]$

Simplified as a matrix

Another way to visualize the iCL update is through a basic matrix:

Steps:

1. We extract riCL from the known values of:

   [i] allocated commitment, and

   [ii] newly-added commitment.

2. We apply the fiCL ratio to determine each $iCL_{[j, \text{ } \tt h \cdot]}$’s individual weight.

3. We multiply each individual $fiCL_{[1, \text{ }..., \text{ } N]}$ for previously extracted $riCL$ (1.)

Examples

Scenario [i.] -> step-by-step, with flat iCL values

Let's assume that:

• a user j is part of 5 Hubs → N = 5

• j has allocated 20 iCL points per Hub → $iCL_{\tiny [1, 2, 3, 4, 5]} = 20$

• j joins a 6th Hub, allocating 10 CL points to it → iCL_{\tiny new} = 10

In order to update existing Hubs’ allocation, we'll need to:

1. Calculate Remaining Points: $riCL = 100 - 10 = 90$

2. Calculate Sum iCL for existing Hubs: $\sum{aiCL_{tot}} = 20 \times 5 = 100$

3. Calculate Proportions: $fiCL_{\tt h \cdot} = \frac{20}{100} = 0.2 \text{ }\forall \text{ } {[\tt h \cdot]}$

4. Recalculate iCL for Existing Hubs: $uCL_{[\tt h \cdot]} = 0.2 \times 90 = 18$

So each of the 5 original Hubs would have their CL adjusted to 18, and the new Hub would have a CL of 10, maintaining the total at 100.

Scenario [ii.] -> direct calculations, with higher iCL variety

5 Hubs:

• $iCL_{[\tt h \cdot]_{1}} = 16$

• $iCL_{[\tt h \cdot]_{2}} = 18$

• $iCL_{[\tt h \cdot]_{3}} = 20$

• $iCL_{[\tt h \cdot]_{4}} = 22$

• $iCL_{[\tt h \cdot]_{5}} = 24$

• $aiCL_{tot} = 100$

new:

• $iCL_{[\tt h \cdot]_{new}} = 20$

• $uCL_{[\tt h \cdot]_{1}} = \frac {16} {100} \times (100 - 20) = 0.16 \times 80 = 12.8$

• $uCL_{[\tt h \cdot]_{2}} = \frac {18} {100} \times (100 - 20) = 0.18 \times 80 = 14.4$

• $uCL_{[\tt h \cdot]_{3}} = \frac {20} {100} \times (100 - 20) = 0.20 \times 80 = 16.0$

• $uCL_{[\tt h \cdot]_{4}} = \frac {22} {100} \times (100 - 20) = 0.22 \times 80 = 17.6$

• $uCL_{[\tt h \cdot]_{5}} = \frac {24} {100} \times (100 - 20) = 0.24 \times 80 = 19.2$

• $\displaystyle \sum_{[\tt h \cdot] = 1}^{5} = 80 + 20 \rightarrow 100$

Sequence Diagram

The Peer Value () is at the center of the Āutonomy Matrix - and it’s derived from:

1. of an individual across one or more decentralized Hubs

2. Each Hub’s - identifying the credibility of a decentralized project/community

3. completed by the Participant (the user-to-contract actions made on-chain)

4. The of a Participant to their Peers.

The is a “romantic” parameter - that represents the product between different independent variables that define the actions and participations of a free individual in a decentralized world. It uses mathematics to keep the highest degree of precision while leaving the maximum level of freedom and intentionality to participants, weighing in concepts such as the credibility of the community/ies they are part of to extrapolate the “human value” that an individual contributes to a localized environment.

It uses a directed graph approach considering the Prestige ( ) of a Hub/Community, together with the connections of an individual (Betweenness, or ) and the variety of their actions, so that the value of a Participant's contribution to a Hub (relative/local value) can be portable on a global scale (absolute value).

This is a "true passport to the decentralized web" and the first-ever, provider-unbiased, on-chain Global Reputation Aggregator.

The design of the PS system is based on a Subtractive model, borrowed from Game Theory.

It balances 4 main parameters:

1. responsiveness: how quick it can adapt and update

2. stability: how reliably updates a member’s PS progression in edge-cases (i.e.: sudden/steep changes in performance from a period to the other)

3. fairness: how meritocratic and “human” it is in reflecting someone’s effort and participation within a Hub.

4. flexibility: how customizable it is, based on each community’s unique internal dynamics and needs.

The introduction of c as a constraining factor adds a stabilizing effect, preventing abrupt changes in PS. The progressive transition to decentralized customization of c as a local parameter lets each community take its choice, while aligning risk with responsibility through a staking mechanism.

The Participation Score brings mutual accountability between participants and Hubs through:

1. Bidirectional Influence:

   • Participants' scores influence Hub reputation (Prestige) and vice versa. High-performing participants enhance Hub’s prestige, while in turn reputable/credible Hubs will attract higher-quality contributors.

2. Task Weight Assignment:

   • Hub operators and admins assign individual "weight" to each task (within a range of 1-to-10). This weight impacts both the Hub’s Prestige (through Total Community Points, TCP) and the participant’s Participation Score. The Expected Contributions (EC) value depends on TCP and the fractional individual Commitment Level (fiCL).

3. Role-Based Contributions:

   • PS is tied to the specific role of a Participant within a Hub, ensuring that contributions are relevant and valuable to the community's goals. This role-based approach creates a clear link between individual efforts and collective success.

4. Value-based Rewards:

   • Rewards and recognition within a Hub are directly linked to an individual’s PS, incentivizing participants to deliver their promises (their iCL) and maintain stable, high quality contributions. This creates a game-theoretical feedback loop where Hubs and participants mutually benefit from each other's success.

GCp & the Introduction of the Penalty Factory p-minus

If a Member were not to contribute in a given period of time (meaning -> their GCp in a given period T is equal to 0), the general formula wouldn’t be able to calculate their Participation Score.

To avoid that, we should extend the General Formula as follows:

$GC = 0 \rightarrow PS_{n} = PS_{(n-1)} \times p_{\tiny \ominus}$

where $p_{\tiny \ominus}$ represents a Penalty Factor.

The value of $p_{\tiny \ominus}$ should always be included between 0.1 and 0.9 (90-to-10%):

Hub Operators are able to customize the value of $p_{\tiny \ominus}$, and update it after the completion of the previous period T.

“Cannibal” member + c + PS’

This is an edge-case where we consider what happens if a Member completes all or the majority of TCP (Total Contribution Points) available in a Hub in a period T.

Meaning that for Member j -> $GC = TCP$.

This situation could be due to two factors:

Factor a.

The Member whose $GC = TCP$ is the only Member in the community in a given Period.

In this case we should include a new condition:

if j is a Member of $[\tt h \cdot]$, and $TCM_{[\tt h \cdot]} = 1$, then the Participation Score of j in that Period will be calculated as:

meaning that their PS remains constant.

Else, we can use the general formula for $PS_{\tiny n}$.

Factor b.

The Member whose $GC = TCP$ may be trying to collude, therefore, we need to limit their $PS_{\tiny n}$’s exponential growth.

We do so by introducing a constraint factor (c) that controls the growth of $PS_{\tiny n}$.

Together with c, we will introduce a step of normalization ( $PS_{ n}'$ )- that will protect the Hub in case a collusion attempt.

Another simple extension in this case:

if $PS_{ n} > c \times PS_{(n-1)}$, then -> $PS_{n}' = c \times PS_{n-1}$,

that we can render as:

This approach ensures that the growth of PS is constrained by the factor c, and any calculated PS exceeding this constraint will be normalized through the allowed maximum.

From the previous Edge Cases we can extend the general formula to cover for those cases:

$PS_{\tiny n} = \begin{cases} PS_{\tiny(n-1)} &\text{if } TCM = 1 \\ PS_{\tiny(n-1)} \cdot p_{\tiny \ominus} &\text{if } GC = 0 \\ min(PS_{\tiny(n-1)} \cdot \Delta \overrightarrow P, PS_{\tiny(n-1)} \cdot c) &\text{if } \Delta \overrightarrow P \ge 100 \\ max(PS_{\tiny(n-1)} \cdot \Delta \overrightarrow P, PS_{\tiny(n-1)} \cdot p_{\tiny \ominus}) &\text{if } \Delta \overrightarrow P < 100 \end{cases}$

Scenarios:

• Case A: Addresses a Member who's $GC = TCP$ (see Cannibal Member).

• Case B: Applies if a Member was inactive during an entire period.

• Case C: Applies if a Member is performing better than the previous period ( $\rightarrow \overrightarrow P_{\tiny n} \ge \overrightarrow P_{(\tiny n-1)}$). By using c, the constraining factor, it ensures that PS cannot spike more than 40% higher from a period to the next.

• Case D: Applies if a Member is underperforming respect to the previous period ( $\rightarrow \overrightarrow P_{\tiny n} < P_{(\tiny n-1)}$). By using $p_{\tiny \ominus}$, the penalty factor, with $p_{\tiny \ominus} = 0.4$, it ensures that PS cannot drop more than 40% lower from a period to the next.

These scenarios cover the vast majority of cases. Either way, soon after the V1 release, we’ll be adding additional coverage for edge-cases such as imprecise assignation of weights to internal community tasks.

$c$ : the constraining factor. It determines the maximum growth of PS from a period to the other. Especially useful with attack vectors such as Cannibal Members.

$iCL$ : Commitment Level. Represents the commitment level (CL) of an individual member (i), ranging from 1 to 10.

$TCP$ : Total Contributions Points in a Community. Sum of all contributions points available in a community in a given period. They can be acquired by members by completing tasks and interactions. Each Task and Interaction has a custom weight (spacing between 1 and 10).

$tiCL$ : Total Commitment Level in the Community. Sum of all participants' Individual Commitment Levels (iCL). Calculated as $\sum_{j = 1}^{n} iCL_{j}$

$fiCL$ : Fractional Commitment Level per Individual. Fraction of total commitment attributed to each member. It represents the weight that a member’s i has respect to the whole.

$ECP$ : Expected Contribution Points. Calculated as $fiCL \times TCP$.

$ECP'$ : Normalized $ECP$ that considers the Time Factor ( $T$)

$GCP$ : Given Contribution Points. Actual contributions made by a member in a given period.

$PS$ : the Participation Score of a Participant in a Hub $[\tt h \cdot]$. Each participant start with a $PS = 100$.

$p_{\tiny \ominus}$ : the penalty factor in case of inactivity during a given period. With a default value of 0.4, then customizable.

$\overrightarrow P$ : the Performance of a Participant within a Hub - given by the ratio between given and expected contribution points ( $\frac {GCP}{ECP}$) in a given period T, using ECP'.

$\Delta T$ : a time factor that helps determine the actual EC based on the time left in a period —> $EC' = EC \times \Delta(T)$

$wtf$ = Withdrawal Fee in case of a member leaving a community before the end of a period.

1. GCp & the Introduction of the Penalty Factory p-minus

2. “Cannibal” members + c + PS’

3. What to do in case of fire Member’s Withdrawal.

The basic Prestige model can be infinitely expanded, compartmentalizing the different sources in an approach such as $\displaystyle \frac {\sum \Delta K_{S}} {\sum S}$, where:

• $\Delta K$: the change in the parameters calculated from the individual sources S between an interval and the other, and

• $S$: the external Source of reference.

The purpose of expansions is incorporating external factors or metrics into the Prestige calculation - such as historical / financial data from existing DAOs or off-chain communities - from platforms such as Dune Analytics, or the community's impact / recognition within the broader ecosystem.

In this case we consider the basic Prestige as AV, the Absolute Value, in its extended formula:

where:

• AV is the Absolute Value, calculated using the extended formula for Prestige.

• $whatever$ is any external Source (S).

Being able to mathematically quantify the value of someone’s participation, and their personal Commitment Level to a Hub - we can use the blockchain to measure traditionally intangible assets such as human capital.

Moreover, these parameters are designed as scarce, finite commodities that reflect real-world dynamics (such as someone’s effort and availability over a given working day), making them Real-World Assets (RWA) that can be stated beforehand, for the entire duration of the cooperation, and can be monetized and incentivized fairly, enhancing the transparency of peer-to-peer, task/job-based agreements between a project and their contributors.

The Āutonomy Matrix is the first provably-neutral, permissionless, and verifiable framework to measure the global reputation of a peer as equal to the value that they create in their community, and the network at large.

Unlike traditional reputation models, it does not rely on subjective ratings or financial assets but mathematically measures participation, accountability, and influence.

It achieves this by integrating multiple self-adjusting, mathematically grounded parameters to extract Peer Value, which arises from the intersection of:

• Identity (verifiable uniqueness & historical contributions)

• Community (local reputation & contextual credibility)

• Interactions (on-chain activity & social graph positioning)

This is executed through four independent, modular and composable protocols:

1. – The identity layer that ensures self-sovereign reputation.

2. Hub – The on-chain community structure where participation occurs.

3. Interaction Tree – A contribution-tracking system that quantifies actions as Participation Score.

4. Peer Value – The final global reputation metric, weighted by Prestige and social graph dynamics.

How Reputation is Measured

The Āutonomy Matrix follows a local-first approach, where a peer's Participation Score (PS) is calculated as the ratio between actual contributions and expected commitments within a Hub​, where each Contribution is an on-chain event created in a Hub, to which is assigned a custom amount of points. It's also the first pointing system which exists on-chain, rather on a backend server ownable and modifiable by a private individual or corporation.

• This local reputation (PS) is then weighted using the Prestige primitive, which reflects the credibility of each Hub itself.

• Finally, the system incorporates graph-based network metrics to adjust for peer's relative position respect to their links, ensuring fair influence distribution across the ecosystem.

By combining meritocratic, commitment-based scoring with semantic, context-aware weighting, the Āutonomy Matrix provides a fully decentralized, Sybil-resistant, and adaptive reputation standard for Web3 governance, collaboration, and coordination.

General Formula to calculate Participation Score

$\displaystyle PS_{n} = PS_{n-1} \cdot \overrightarrow P_n$

where $\overrightarrow P$ is the Performance of a Member (j) in a given period, represented as the ratio between given and expected contribution points $(\frac {GCp}{ECp})$, using ECp' to include a time factor $\Delta T$

We calculate $\overrightarrow P_{\tiny j}$ as:

$\overrightarrow P_{\tiny j} = \frac {GC_{\tiny j}} {EC'_{\tiny j}}$

What to do in case of fire Member’s Withdrawal.

Since Āut's PS framework introduces a "staking-your-reputation" algorithm of sort, where PS is a measure of someone's credibility in the ecosystem, as well as a vector to attract and grow continuous, recurring income - then it'd make sense to introduce a Withdrawal fee (wtf).

A predictive coefficient that penalizes the withdrawing-Participants based on the negative impact of their premature abandonment ("ghosting") of the Hub.

In this case, we could take the Generalized Formula:

And - in case of withdrawal - trigger a new step of normalization for PS.

It would be calculated as:

where wtf is the Withdrawal Fee, calculated as:

where:

• is the Time Completed in the period

• is the Initial Time, the total time at the start of a period

A measurable, extendable model for on-chain KPIs, accountability & self-assessment for decentralized projects & DAOs.

The absolute value, or Prestige, of a decentralized project, community or DAO represents their on-chain credibility - based on their activity, tasks, balance in contributors’ skills and efforts.

It relies on a mathematical, context-agnostic system to verify and self-asses a project’s ability to complete tasks, achieve milestones and ultimately its growth and real traction. It replaces vanity-metrics and off-chain externalities with a basket of independent parameters with customizable weights.

The rationale behind it is that, as the decentralized space evolves, it’s critical for decentralized hubs - such as open-source project, DAOs, network states, etc. - to be accountable and measure its KPIs on-par with regular, real-world organizations.

In fact, if on one side the Participation Score and alternative systems aim to verify individual contributor’s credibility and value, it's crucial for a community's credibility to be both internally and externally verifiable. Prestige allows projects to prove their milestones and growth based on KPIs set by themselves internally - both as a warranty for the community itself, as well as for researchers assessing a DAO’s health, or investors considering to fund it.

This accountability extends the relationship between a member's participation within a community (their local reputation) and its value in the wider ecosystem - allowing an individual’s Global Reputation to be reliable and verifiable in the entire ecosystem.

Where:

• $\mathfrak {P}_{n}$ is the Prestige of a community in the given period.

• $\mathfrak {P}_{(n-1)}$ is the Prestige of a community in the previous period.

• c: constraint factor, just like in the PS framework, c controls the slope in $\mathfrak{P}$’s rate of change. It’s initially fixed at to 1.4 (40% growth), later customizable by the Hub itself.

• $p_{\tiny \ominus}$ is the penalty factor for Hubs inactive in a specific period. Same as in Participation Score.

• $\sum \Delta K$ is the sum of the rates of change of each individual parameter, between the current and the previous intervals.

Relationship between Prestige & Archetype parameters

General Formula for Prestige

From these assumptions, we derived a generalized formula for the Prestige of a decentralized community:

Where:

• is the Prestige of a community in the given period.

• is the Prestige of a community in the previous period.

• is the rate of change of each individual parameter, between the current and the previous intervals.

Calculating K & ΔK

ΔK is the rate of change of individual parameters - to calculate the total change across all parameters, we can simply use the sum of all , calculated as .

Where the individual parametric change is calculated as:

This change rate is determined by the difference in Key Performance Indicators (the parameters) between periods, each one individually normalized and weighted according to their importance in each Hub using Archetypes.

where:

• w: the weight assigned to each individual parameter (p)

• p: the "parameter" of reference.

Normalization of p

Normalized-p is calculated through:

It uses the highest value of a specific parameter across all Hubs measured during the given period. The weights for the different Parameters (below) can be set by the individual Hubs - and are set by our Hub for the edge limits.

In total, the sum of the weights must always be equal to 100 - in alignment with the models used for Discrete Commitment and Reputation staking in the Āutonomy Matrix.

By definition, each community, collective, nation or working group is so defined because it stands for something - whether that’s a mission or a shared purpose - that allows participants to join together for free association - disregarding whether the organization itself lives in the analog or digital world. This paper aims to expand the design of Prestige, a framework that allows to measure a Hub’s on-chain credibility.

A hub can be seen as the decentralized, smart-contract-powered equivalent of a website. In fact, on one side and with minimal adjustments decentralized communities can manage and determine their KPIs behind the hood, using a protocol-based, smart-contract-powered approach, and on the other, in fully permissionless fashion, we can let participants to those decentralized, online communities to interact with any end-user interface powering them with smart contracts and decentralized technologies behind the hood. This framework allows communities and contributors to measure valuable things such as KPIs and milestones directly on-chain, previously considered impossible, while at the same time defining and adding on-chain archetypes and indicators directly from an UI. These indicators are, de-facto, the archetype, the "soul" of a community, and the KPIs to establish its success and growth overtime.

Where we go from here

Three decades of the Internet, and almost a decade of DAOs, have shown us that it’s not only the user, the member, the participant, the contributor who needs to be accountable - rather, for a truly decentralized internet, and any truly decentralized financial system, the community needs to be accountable too. Being able to measure the credibility and KPIs of a decentralized hub, project, or community through a standardized and verifiable framework like Prestige can bring mutual accountability between participant<>community, and lead to a paradigm shift in various domains.

Use-cases

Some obvious use-cases are:

1. Informed investment decisions & project’s access to funding

2. Cross-/Multi-community cooperation, governance & shared accountability

3. Decentralized credit systems & milestone-based grants

1. Informed investment decisions & project’s access to funding

• Investors can use Prestige scores to assess the performance and potential of decentralized projects before throwing money into a DAO.

• Prestige scores can help investors identify projects with strong fundamentals, active communities, and a track record of delivering on their promises.

• By relying on a standardized and verifiable metric, investors can make more informed decisions and potentially reduce the risk of investing in fraudulent or underperforming projects.

• Funding Instruments like convertible notes and repayable loans can be negotiated on better terms from a project’s side, and with lower risk profile from investor’s.

• Prestige could offer a simple, standardized metric for decentralized project’s valuation, leaving less space to speculation and inflated/exploitative valuations.

2. Cross-/Multi-community cooperation, governance & accountability

• Prestige scores can facilitate collaboration and partnerships between decentralized communities.

• Projects and communities can easily merge, cooperate, co-invest, etc. with one another just using Prestige.

• In a multi-community environment, Prestige-based thresholds can be used as a tool for community governance and decision-making - assigning weight based on a project’s ability to deliver and its field-specific knowledge.

• Communities can set for voting rights, proposal submission, or access to certain features or rewards in a mergerlike environment - all while maintaining an individual brand, archetype and independence from one another.

3. Decentralized credit systems & milestone-based grants

• Prestige represents the credibility of a project - measuring its ability to complete tasks, grow a community, and deliver on its promises. This creates a network of verifiable hubs & nodes, that in turn helps mitigating risks and enhancing cross-ecosystem liquidity and network robustness.

• This means that Prestige can be used as a foundation for decentralized credit systems and lending protocols - for example offering Hubs with high Prestige lower collateral requirements, based on their provable previous results.

Conclusions

With this formula, we compare each Hub to the others directly - to prevent manipulation, or sudden spikes and drops. Since the weight is distributed across multiple parameters, the Project will be able to add/remove parameters in the future seamlessly.

This also sets the dynamics for each Hub to choose their "type" - that we call a Community Archetype. Through its Archetype, a Hub can track its own performance, and the achievement of their KPIs, period-by-period, as a traditional organization.

As well as easily assign a weight to each parameter starting with a default type setting, and progressively customizing each value.

It also sets the ground for covariance across multiple parameters, such as TCp (Total Community Points) and PS (Participation Score) of Members. In fact, despite a let’s say, extremely large community would score extremely high on the Size indicator, they would risk not to have enough Tasks for all community members, that would reflect in a drop in these Members’ Participation Scores, and therefore a drop in other Community’s parameters such as Performance (ratio between created and completed Tasks), and avg. Reputation of members.

A global, self-sovereign reputation (= not assigned by others but gained through one's actions and weighted through a meritocratic, math-based system) can unlock incredible things and bring human society ten steps forward.

Things such as profit-sharing, credit score, mutual credit, UBI, workers' comp (in case of injury), retirement plans, etc., would be as easy as multiplying every contributor's/participant's premium for their $\upsilon$ coefficient.

An on-chain, verifiable Reputation offers infinite social and financial applications - specifically, it’s at the foundation of a brand-new area of finance: RepFi, Reputation Finance.

We've already designed and started to build an instrument on top of it, specifically designed for and accessible exclusively from the ĀutOS: Peer Staking.

A gamified investment mechanism where individuals can stake their Reputation tokens, predicting the growth of other members' $\upsilon$. It works as a social prediction market-making instrument, where Stakers can select the extent and the risk profile of their predictions and are rewarded/slashed based on the accuracy of their predictions.

Other obvious applications include:

• Unrealized Rep as a Collateral (URRC) --> Rep-backed Loans

• Freelancers Pensions & Insurance

• Universal Credit Score & UBI

From the parameters p we can extract 5 community types:

1. Size: dominant parameter -> $\overlinesegment S$ A relative value that represents how “big” a Hub compared to others in the ecosystem. This Archetype encourages the largest projects to verify & maintain a positive influence in the overall ecosystem.

2. Participation: dominant parameter -> $\overline {PS}$ The average Participation Score of a Hub’s Contributors. This Archetype gives more insights about the shared trust between members, and their constant effort towards a common goal.

3. Conviction: dominant parameter -> $\overline {iCL}$ The avg. Commitment of the contributors of your Hub. This archetype is for the true believers – reflecting Members’ level of trust and belief in your project’s vision.

4. Performance: dominant parameter -> $\overrightarrow P$ The ratio between tasks created and tasks completed during a given period. This Archetype is for ambitious, coordinated communities set to create real impact and thrive.

5. Growth: dominant parameter -> $\check G$ Everything starts with something. This Archetype is not for the largest Hubs, it’s for the ones with a continuous, organic, slow and steady growth determined by their scale.

A Hub is defined as any digital, decentralized group of any sort - from a tech project with decentralized contributors, to an artist collective, to a DAO, to network state and a digital nation - whereas an organizational type is that Hub’s “template”, the configuration that can assume to optimize its structure for that specific group’s dynamics, while minimizing overheads such as redundant voting and third-party - often off-chain - integrations. Moreover, an organizational type allows online communities to specialize in a specific area that better reflects their goal and the internal balance and equilibrium between their participants - powering a fair, customizable, mathematically-measurable set of KPIs to evaluate results and period-by-period growth of a community both for internal and external purposes.

Organizational types derive from the concept of , the on-chain reputation of a community based on its results overtime.

$\mathring {a}$ is calculated as:

$\mathring {a} = \displaystyle \upsilon_{\tiny (j, \tt H \cdot)} = \displaystyle \sum_{p=1}^N (w_p \times p_n) \times \frac 1 N$

where:

• $w_{p}$ is the weight assigned to a parameter p.

• $p_{n}$ represents each one of the parameters.

• N is the number of parameters p.

and can be developed and implemented as:

$\mathring {a} = \displaystyle[(\alpha \times w_{\tiny \alpha}) + (\beta \times w_{\tiny \beta}) + (\gamma \times w_{\tiny \gamma})] \times \frac 1 3$

where $\alpha$, $\beta$ and $\gamma$ are the different parameters representing these archetypes, and $w$ is their user-assigned individual weight.

1. Centrality ()

The Centrality represents how needed/relevant is a Contributor to a Hub, comparing it directly to all other Contributors. In fact, if on one side, multiple Contributors can have a positive Participation Score - on the other, the Centrality parameter measures how high is someone's participation respect to all other top contributors. This both shows the true dedication / workload of a member to bootstrap the Hub, and helps Operators to understand who is making the heavy lift to bring the Hub to the next level, and can reward them accordingly.

To calculate a Contributor's Centrality ( ) within the Hub, we can use this simple formula:

where:

• is the Centrality of j’s Participation in each one of their Hubs.

• is the absolute centrality of j’s PS in all their local Hubs in the Set

• is the Set of all Hubs to which j contributes.

• is the highest PS value of any participant in Hub .

The generalized formula for the Peer Value ($\upsilon$) is given by:

$\upsilon_{\tiny (j, \tt H \cdot)} = \displaystyle \frac {PS'' + \mathfrak{P}'' + \mathring {a}}{3} \times 100$

where the absolute Peer Value of an individual $j$, in the set of all the Hubs they contribute to ( $H \cdot$ ), is represented by:

• $PS''$ = second step of normalization of Participation Score ( $PS$ )

• $\mathfrak{P}''$ = second step of normalization of Prestige ( $\mathfrak {P}$ )

• $\mathring {a}$ = the self-sovereign contributor archetype chosen by an individul ĀutID holder

Initial Parameters for $\upsilon$

Initially, we will be using three (3) main parameters for evaluating an individual’s Peer Value (Global Reputation):

• The Centrality ( $\alpha$ ) of the contribution of a Participant across their Hubs.

• The Betweenness (Interconnection) ( $\beta$ ) of a Participant respect to their peers.

• The Variety ( $\gamma$ ) in the Contributions delivered by a Participant across all their Hubs.

On a concrete level, they also identify the main "archetypes" of a value-contributor:

• The Pillar ( $\alpha$ )

• The Socialite ( $\beta$ )

• The Polymath ( $\gamma$ )

From these archetype we can extract a compound parameter, called Peer archetype ( $\mathring{a}$ ):

where:

• $\mathring{a}_{j, \tt N \cdot}$ is the Peer archetype of Participant j across all their Hubs $[\tt h \cdot]$ in the set $[\tt H \cdot]$.

• $\alpha$ is the Centrality of j's Participation Score (PS) in all their Hubs.

• $\beta$ is the Interconnection (Betweenness) of j with their peers.

• $\gamma$ is the variety of j’s contributions across their Hubs

The dominant parameter will determine the Archetype of the Contributor j.

$PS''$ is calculated as:

$PS'' = \displaystyle \sum_{h}^{H} PS' \times 10^{-2}$

from which we find:

$PS'_{\tiny h} = fiCL_{\tiny h} \times PS_{\tiny h}$

with

$fiCL = \displaystyle \frac {iCL_{\tiny h}} {tiCL_{\tiny H}}$

$\mathfrak{P}’’$ is calculated as:

$\mathfrak{P}’’ = \displaystyle \sum_{h}^{H} \mathfrak {P}' \times 10^{-2}$

from which we find:

$\mathfrak {P}'_{\tiny h} = fiCL_{\tiny h} \times \mathfrak {P}_{\tiny h}$

with

$fiCL_{\tiny h} = \displaystyle \frac {iCL_{\tiny h}} {tiCL_{\tiny H}}$

2. Betweenness (β)

In practical terms, the Betweenness of an individual in the Web3 ecosystem represents how well connected they are, and how "central" an individual is for their connections. It's based on a simple, progressive score, that quantifies this "social score" based on how close everyone is to all the others they are connected to.

It's simply calculated by using this formula:

Where:

• is the Betweenness of j, based on the amount of connections they have with their peers, weighed by the Proximity Level of those connections

• N is the number of Proximity Levels, in this case, 4:

  • are the number of connections at each Proximity Level (PL)

  • are the weights corresponding to each Proximity Level,

    • with ,

    • and a weight of:

• is the total number of connections across all levels

3. Variety ($\gamma$)

The concept of Variety is quite intuitive: it calculates how "diverse" are someone's contributions across all the different Hubs they are part of. This keeps into consideration the Role of the individual in each one of their Hubs, as well as the Market in which each Hub operates, and the different Contributions they commit to complete, and actually submit. In one sentence: someone's Variety score is based on the amount of "unique" contributions (= contributions which do not repeat) they deliver across all their Hubs, divided by the total amount of Contributions submitted (= how many of the Contributions submitted are different from the others).

It's calculated using the formula:

where $r\gamma$ is the "credible relative variety" of j’s contribution at the local Hub’s level.

Once we have $r\gamma_{j, h} \text { } \forall \text { } \tt h \cdot in \text { } \tt H \cdot_{j}$, then we can calculate $\gamma$ as:

The parametric, weight-based approach to $\upsilon$ makes the general formula for $\upsilon$ infinitely expandable - allowing the addition of more parameters after the 3 original ones (variety, betweenness and centrality), based on free market dynamics.

By calculating the Peer Value of a Participant in the context of each Hub they participate in, we can create a rich, multi-dimensional view of their overall impact within the ecosystem - and a nuanced representation of the relationships between contributors and the communities they participate in.

In this directed graph-based model:

• each Hub $\boxed {h \cdot}$ can be represented as a Node

• each contributor (j) can be represented as an Edge

• each action/task/interaction completed by j in any of their Hubs is represented as a Link

Incorporating a directed graph-based approach to Peer Value / Global Reputation within the Āutonomy Matrix offers a powerful and granular way to model and visually represent the complex relationships and inter(in)dependencies within the decentralized ecosystem.

To implement this directed graph-based approach in the Āutonomy Matrix, we create and maintain a graph that captures the relationships between contributors and Hubs, as well as the relevant metrics ( $PS \text{ and }\mathfrak P$) for each Node, Edge and Link. The $\upsilon$ scores can then easily be calculated and updated in real-time as contributors participate in different communities / contribute to different projects, while in parallel the Prestige of those Hubs evolves.

By providing a contextual, multi-dimensional view of contributor reputation, this approach can help foster greater trust, collaboration, and value creation across the ecosystem.

With or without us. Within or beyond our lifetime :)

Conclusions

A global, self-sovereign reputation (= not assigned by others, but gained through one's own actions and weighted through a meritocratic, math-based system) can unlock incredible things, and bring human society 10 steps forward.

Things such as profit-sharing, credit score, mutual credit, UBI, workers' comp (in case of injury), retirement plans etc. would be as easy as multiplying every contributor's/participant's premium for their $\upsilon$ coefficient.

Tests & Simulations - trust but verify

1. Stress factors [TCM + iCL]

• Total Community Members (TCM) spike & drop

  • The simulation includes periods with different numbers of community members, ranging from 1 to 100,000.

• iCL random fluctuations

  • Fluctuating $\overline{iCL}$: The average individual Commitment Level varies across periods to simulate changes in overall community commitment.

  • Changing $iCL$: Each member ($M_{\tiny [1, 2, 3]}$) has a different individual commitment level, that keeps changing and being updated each period.

2. Fixed Parameters

• 10 periods

• 3 individual members ( $M_{\tiny [1]}, M_{\tiny[ 2]}, M_{\tiny [3]}$ )

• a stable performance ( $\overrightarrow P = \frac {GCp}{ECp}$ ) set to a constant value of 1.05 (105%).

3. Parameters used

• TCM (Total Community Members): The number of members in the community for each period.

• $\overline{iCL}$ (Average Individual Commitment Level): The average commitment level of all members in the community for each period.

• ${iCL}$ (Individual Commitment Level): The commitment level of each member, ranging from 1 to 10.

• $fiCL$ (Fractional Commitment Level): The fraction of the total commitment level attributed to each member.

• TCP (Total Contribution Points): The total number of contribution points available in the community for each period.

• ECp (Expected Contribution Points): The expected number of contribution points for each member based on their fiCL, calculated as $ECp = fiCL \cdot TCp$.

• GCp (Given Contribution Points): The actual number of contribution points contributed by each member, calculated as $GC = \overrightarrow P \cdot EC$.

• PS (Participation Score): The cumulative participation score for each member, calculated as $PS_n = PS_{n-1} \cdot \overrightarrow P$, with $PS_{\tiny 0} = 100$.

4. Approximations for convenience

1. TCP: The total contribution points available in each period. Here we constrained using the formula $TCP \le TCM \cdot 100$ "heavy tasks” worth 10 Contribution Points.

2. PS: The participation score for each member. Calculated as $PS_n = PS_{n-1} \cdot \overrightarrow P$, where $PS_{\tiny 0} = 100$, to simulate cumulative growth based on consistent over-performance.

3. iCL: The fraction of the total commitment level attributed to each member. Here calculated as $fiCL = iCL \times \displaystyle\frac {1}{TCM \times \overline{iCL}}$ This way we’d set up one single average iCL ( $\overline {iCL}$) for the entire community, instead of generating millions of individual iCLs for each member.

5. Results

Trust, but verify: simulations of Prestige under different stress factors

Here we share a set of simulations taking into account the highest value for each parameter and normalizing them accordingly.

We also use different default archetype to determine the different weight distributions for each Hub based on their community type - the leading parameter of choice - and we analyze how this influences the evolution of $\mathfrak {P}$.

⚠️ *It’s important to notice that neither the results or the weight allocations are influenced by the parameter/type itself. Rather, the Prestige framework is designed to be infinitely expandable, and we expect hundreds of Hub Types in the near future. The only requirement - as we specified in prior docs and publications - is for each newly-added parameter to be measurable, and combine existing or mathematically provable strategies and Archetypes.*

1. Stress Factors

1. Hub A (Archetype: Size):

   • High and increasing TCM

   • Consistent high performance ($\overrightarrow{P}$)

   • Emphasis on Size ( $w_{\tiny \overlinesegment S}$) with 60% weight

2. Hub B (Archetype: Performance):

   • Fluctuating and declining TCM

   • Consistently low and declining performance ( $\overrightarrow{P}$)

   • Negative growth ( $\check{G}$)

   • Emphasis on Performance ( $w_{\tiny \overrightarrow{P}}$) with 60% weight

3. Hub C (Archetype: Conviction):

   • Moderate growth in TCM

   • Consistently high Conviction ( $\overline{iCL}$)

   • Emphasis on Conviction ( $w_{\tiny \overline{iCL}}$) with 60% weight