> For the complete documentation index, see [llms.txt](https://docs.pots.money/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.pots.money/how-ibs-works/algorithm-supplying.md).

# Algorithm Supplying

#### Supply Without Discretion

Every monetary system faces the same fundamental challenge: how much currency should exist? Too little, and the economy stagnates. Too much, and inflation erodes value.

Central banks answer this question with committees, models, and political judgment. IBS answers it with <mark style="color:$primary;">**on-chain mathematics**</mark>.

<figure><img src="/files/trcOeEfNME7IzADLR97M" alt=""><figcaption></figcaption></figure>

#### The Premium Index

The core signal governing IBS supply is the Premium Index $$\Pi$$:

$$\Pi = \frac{P\_{market}}{B\_{IBS}}$$

Where:

* $$P\_{market}$$ = current IBS market price (derived from the USDT/IBS ratio in the LP pool)
* $$B\_{IBS}$$ = USDT backing per IBS
* $$B\_{IBS} = \frac{V\_{LP} + V\_{RBS} + V\_{ST}}{\mathbf{S\_{circ}}}$$

Where:

* $$V\_{LP}$$  = USDT value in the liquidity pool
* $$V\_{RBS}$$ = USDT reserves in the Range Bounded Stability module
* $$V\_{ST}$$  = USDT in the Safety Treasury、
* $$S\_{circ} = IBS circulating supply$$ = IBS circulated supply (MCL-bounded)

{% hint style="success" %}
Example: If $$P\_{market}= $40$$  and $$B\_{IBS} = $10$$ , then $$\Pi = 400%%$$ %. The protocol interprets this as strong demand and authorizes new bond issuance at elevated APRs.
{% endhint %}

#### The Emission Function

The bond APR offered to new participants is a function of the Premium Index:

$$r\_{bond}(\Pi) = r\_{base} \cdot (\Pi - 1) \cdot \beta$$

Where:

* $$r\_{base}$$ = base interest rate (initial value: 5% APR)
* $$\Pi - 1$$ = excess premium above parity
* $$\beta$$ = emission sensitivity coefficient (initial value: 0.8)

This ensures that bond APR scales proportionally with demand pressure.&#x20;

When

&#x20;$$ \Pi = 1$ $$ (market price equals backing),  $$r\_{bond} = 0$$ — no new bonds are issued.&#x20;

When

&#x20;$$ \Pi = 4$ $$,  $$r\_{bond} = 12%$$% APR

#### The Max Circulation Limit (MCL)

The MCL acts as the hard ceiling on IBS supply, enforcing the $1 USDT redemption guarantee:

$$text{MCL condition:} \quad \frac{V\_{total}}{S\_{circ}} > 1 + \epsilon$$

Where $$\epsilon$$ is the safety buffer (initial value: 0.15, i.e., 15%). When the treasury-to-supply ratio approaches $$1 + \epsilon$$, the AEM applies a progressive throttle:

$$\dot{S}(t) = \dot{S}*{max} \cdot \max\left(0,\ \frac{R(t) - (1 + \epsilon)}{R*{target} - (1 + \epsilon)}\right)$$

Where:

* $$\dot{S}(t)$$ = instantaneous emission rate at time $$t$$
* $$R(t) = V\_{total}(t) / S\_{circ}(t)$$ = current backing ratio
* $$R\_{target}$$ = target backing ratio (initial value: 2.0, i.e., 200% backed)
* $$\dot{S}{max}$$ = maximum emission rate (initial value: <mark style="color:$primary;">**1% of**</mark> $$S{max}$$ <mark style="color:$primary;">**per epoch**</mark>)

As $$R(t) \to 1 + \epsilon$$, emission approaches zero continuously — preventing abrupt halts and allowing orderly wind-down.

#### Game Theory: The Bonding Equilibrium

The bond system creates a Stackelberg game between the protocol and participants:

* The protocol (leader) sets bond APR as a function of $$\Pi$$
* Participants (followers) decide whether to bond based on expected yield vs. opportunity cost

The Nash Equilibrium of this game occurs when the marginal bond participant is indifferent between bonding and not bonding:

$$r\_{bond}(\Pi^\*) = r\_{market}$$

Where $$r\_{market}$$ is the prevailing risk-free rate in DeFi. At this equilibrium, $$\Pi^\*$$ stabilizes — new demand exactly offsets new supply, and the Premium Index mean-reverts to its equilibrium value.

This is the algorithmic equivalent of the Federal Reserve's Taylor Rule: a systematic, rule-based response to economic conditions that eliminates the need for discretionary intervention.

{% hint style="success" %}
⚙️ The Key Insight

Because the emission function is public and deterministic, rational participants can forecast future supply with precision. This eliminates the uncertainty premium that plagues discretionary monetary systems — and makes IBS a more credible store of value.
{% endhint %}

#### Initial Parameters

| Parameter              | Symbol             | Initial Value      | Governance     |
| ---------------------- | ------------------ | ------------------ | -------------- |
| Base interest rate     | $$r\_{base}$$      | 5% APR             | DAO-adjustable |
| Emission sensitivity   | $$\beta$$          | 0.8                | DAO-adjustable |
| Safety buffer          | $$\epsilon$$       | 0.15 (15%)         | DAO-adjustable |
| Target backing ratio   | $$R\_{target}$$    | 2.0 (200%)         | DAO-adjustable |
| Max emission per epoch | $$\dot{S}\_{max}$$ | 1% of $$S\_{max}$$ | DAO-adjustable |
| Epoch duration         | $$\tau$$           | 8 hours            | DAO-adjustable |

> All parameters are subject to DAO governance. See the Parameter Reference Table.