---
# System prepended metadata

title: "E(\nn\n)"

---

**Introduction:**

The AO network is a Layer One foundational crypto network powered by the \$AO token. AO tokens have a capped total supply of 21 million, minted continuously following Bitcoin’s halving schedule every four years, with tokens minted every 5 minutes. Unlike Bitcoin, AO's minting decreases slightly each month, ensuring a smooth release rather than abrupt halving events.

Minting AO tokens is achieved exclusively by:

* Holding \$AR tokens (Arweave), with approximately 33,3% of AO tokens allocated over time to AR holders. This began retroactively on February 27, 2024, distributing AO tokens based on AR holdings. As of June 13, 2024, about 0.016 AO tokens per AR have been minted.
* Depositing selected tokens such as stETH (staked Ethereum) and DAI into the AO ecosystem, representing around 66,6% of future AO minting. Deposited tokens generate yield within specialized vaults, with yields directed to ecosystem growth and development.

Investors receive \$AO tokens in return, which are tradable on public exchanges. Typically, the market value of \$AO tokens surpasses the base yield from holding the original assets, providing a strong economic incentive for participation.

Initially, AO tokens remain locked until roughly 15% (approximately 3.15 million AO) of the total supply has been minted, expected around February 8, 2025.

Example AO token accrual for AR holders:

* 1 AR: 0.016 AO
* 100 AR: 1.6 AO
* 1000 AR: 16 AO

Example AO token accrual for yield providers (stETH) based on asset pool percentage over 12 months:

* 0.1% of pool: \~2,105 AO
* 1% of pool: \~21,049 AO
* 5% of pool: \~105,243 AO

```
               ┌──────────── Every 5 minutes ────────────┐
               │            New $AO emitted              │
               └──────────────────┬──────────────────────┘
                                  │
                ┌─────────────────┴─────────────────┐
                │   Phase BEFORE 18-Jun-2024        │
                │   (Test-net → Pre-bridge)         │
                └────┬───────────────┬──────────────┘
                     │100%           │0%
                     ▼               ▼
              AR-Holder Pool    Bridge-Yield Pool
                     │               │
                     ▼               ▼
                Claimable AO     (none yet)

                ┌─────────────────┐─────────────────┐
                │   Phase AFTER   │   (today)       │
                │   18-Jun-2024   │                 │
                └────┬────────────┴─────────┬───────┘
                     │33.3 %         66.6 %│
                     ▼                     ▼
              AR-Holder Pool     Bridge-Yield Pool
                     │                     │
              ┌──────┴───────┐   ┌────────▼────────┐
              ▼              ▼   ▼                 ▼
        Wallet claim   Implicit → PI        Investors deposit
        (self custody) Delegation (CEX)      stETH / DAI … → AO
```

Capital Flow 
```
Investor
  │  (e.g. stETH)
  ▼
Pre-Bridge Contract (Ethereum)     ← assets stay here, withdrawable 24/7
  │
  │ Native yield
  ▼
Ecosystem Dev Wallets        ← yield funds Ao core infra / grants
  │
Mint engine notes TVL        ← triggers 66.6 % of each AO drip
  │
  ▼
Investor wallet on Arweave   ← daily AO reward proportional to share
```

---

**Delegation, FairLaunches, and the PI Index:**

A core incentive within the AO network is the implementation of the FairLaunch model. FairLaunch enables teams to create tokens and secure project funding through a transparent and community-driven process. Tokens generated through FairLaunch are distributed to investors, encapsulating the project's value.

Structure of a FairLaunch:

* Projects set specific parameters, including:

  * Percentage of their total token supply to auction.
  * Auction start date.
  * Duration of the auction.
  * Decay factor for token emission.
  * Date when tokens become liquid.

The decay curve follows the formula:

E(n) = E₀ × r^(n−1)

* E₀ is the initial tokens minted on day one.
* r is the daily decay factor.
* n is the number of days.

Funding occurs exclusively through \$AO tokens. Every 24 hours, a fixed amount of the project token is exchanged based on the amount of \$AO tokens delegated to the project. Higher delegation of \$AO tokens results in higher mint or auction prices, fostering competitive and dynamic participation.

```
           AO balance      (auto-generated every 24 hours)
                 │
      ╔══════════╧══════════╗  Delegation choice (5 % steps)
      ║                    ║
      ▼                    ▼
 Keep AO            ┌───────────────┐
 (liquid)           │  Delegation   │
                    │   Router      │
                    └─┬─────┬───┬───┘
                      │     │   │
                      │     │   └──► Claim AR instead
                      │     │
                      │     └──────► Individual Project N
                      │
                      └────────────► PI Index (gets AO, mints PI)
```

To prevent a "down only" scenario for low liquidity, low float tokens, projects have the option to initiate auctions without making tokens immediately liquid. Tokens can be made liquid at a later predetermined date, ensuring adequate float and liquidity, thus supporting healthy trading conditions. This is currently a work-in-progress design.

FairLaunches are funded exclusively through yield delegation in \$AO tokens. Investors receiving \$AO tokens through asset deposits or holding \$AR tokens can delegate their earned \$AO yield fully or partially across various investment options (baskets).

Delegation baskets include:

* PI Index (an on-chain index fund, detailed further below)
* Specific individual projects
* Opting to retain \$AO without delegation
* Delegating yield to receive additional \$AR tokens

Delegation is structured in increments of 5%.

```
t = 0 (auction start) ───┐
                         │ Decay curve E(n) = E₀ · r^(n-1)
Every 24 h───────────────┤───────────────────────────────────► t = n
                         │
                         │  Delegation snapshot (Σ AO today)
                         ▼
                ┌───────────────────────────┐
                │ Mint X project-tokens     │  X ↓ as n ↑
                │ Swap X ↔ $AO              │  Price ↑ with ΣAO
                └──────────┬────────────────┘
                           │
   ┌───────────────────────┴───────────────────────┐
   │ Project multisig receives AO (growth runway)  │
   │ Investors receive project-token (vested)      │
   └───────────────────────────────────────────────┘
                ↑
                │ (optional delay)
                └── Tokens become liquid on “T-Liq” date
```

---

**PI Index:**

The PI Index is an on-chain derivative token structured as follows:

* 1/3 \$AO token
* 1/3 \$AR token
* 1/3 Ecosystem Tokens

There are two key considerations regarding the PI Index:

1. **Ecosystem Token Selection and Allocation:**

   Ecosystem tokens included in the PI Index are selected based on delegation activity. Any project receiving a minimum delegation of 1 \$AO is eligible for PI Index inclusion. PI Index allocation to a specific project matches investor delegation proportionally.

   *Example:*

   If Project A receives a total delegation of 10,000 \$AO, Project B receives 5,000 \$AO, and Project C receives 1,000 \$AO, the PI Index allocation would reflect this distribution proportionally:

   * Project A: 10,000 \$AO delegation → receives 62.5% of PI Ecosystem Token allocation
   * Project B: 5,000 \$AO delegation → receives 31.25%
   * Project C: 1,000 \$AO delegation → receives 6.25%

   Thus, PI Index ensures that community preferences directly influence its composition and allocations.

   The PI allocation algorithm aims to be unbiased, though it remains open to community suggestions. PI Index has two types of deposits:

   * **Explicit Delegation**: Investors explicitly delegate their \$AO to PI and receive PI tokens in return.
   * **Implicit Delegation**: Occurs by default for centralized entities like exchanges that hold AR tokens but do not distribute earned AO tokens to individual users unless explicitly opted out. Without opting out, the earned AO tokens are delegated to PI automatically.

```
         ┌────────────────── PI Token ──────────────────┐
         │ 33.3 % AO │ 33.3 % AR │ 33.3 % Ecosystem bag │
         └───────────┬───────────┴───────────┬──────────┘
                     │                       │
Explicit AO → PI  Implicit AO → PI (CEX)   Rebalance ×
                     │                       │
                     │                       ▼
                     └────── Delegates PI (not AO) ──────►
                                   to Projects
                        (weight ∝ community AO delegation)
```

**Capital Flow Illustration (ASCII Diagram):**

```
Investor → Deposits Assets or Holds AR
↓
Receives AO Yield
↓
Option to Delegate AO:
├─→ Retain AO
├─→ Delegate to Individual Projects (direct AO delegation)
├─→ Delegate to PI Index (receives PI tokens)
└─→ Delegate to AR (receives AR tokens)

PI Index → Delegates PI Tokens (equivalent AO value) → Selected Projects

```

**Note:** Projects receiving delegation from PI Index get PI tokens, aligning their incentives with the broader ecosystem rather than receiving direct AO tokens. THe $PI Token pricing is determined in $AO inside the PI index. 

**Summary of Invariants:**

- Users can delegate to Projects, PI Index, AR, or retain AO.
- Delegation to PI Index provides PI tokens.
- When the PI Index delegates to projects, it provides PI tokens (priced equivalently to AO) rather than direct AO tokens, aligning incentives across the ecosystem.
- Delegation occurs once every 24 hours.
- PI tokens are not liquid (transferable) at this point in time.



**Key Questions for Future Development:**

What are the most catastrophic risk scenarios for the PI token, such as significant value loss in its backing? Can we simulate these scenarios and determine preventive strategies (e.g., allocation adjustments, risk management, and mitigation measures)?

What portfolio allocation strategies can be implemented, particularly for investable assets that remain illiquid for certain periods? Should the PI Index continue to allocate funds to such illiquid tokens, or should they be excluded entirely? What risk implications does this carry?

What rebalancing strategies are viable for low-liquidity assets? Simulate scenarios, such as a 10-20-50-100% volatility in an asset's value, and analyze implications of various rebalancing timings and strategies, such as auctions, given the current constraints of liquidity and available on-chain financial instruments.