# FCT Issuance Formula

This section provides a detailed explanation of the formula that governs the issuance of FCT, intended for technical readers who want to understand issuance on a block-by-block basis.

To see the current mint rate, issuance progress, and other real-time FCT metrics, visit [fct.fyi](https://fct.fyi/).

## Overview

FCT issuance is designed to provide:

* **Predictable ownership** through a deterministic total supply cap
* **Stable issuance** via dynamic rate adjustments every 500 blocks
* **Protection from gas spikes** by minting based on ETH burned, not gas units

## Basic minting formula

FCT is minted proportionally to the ETH burned for transaction calldata:

$$
\text{FCT minted} = \text{ETH burned for data} \times \text{mint rate}
$$

Where:

* **ETH burned for data** = Data Gas × Block Base Fee (Data Gas is defined in the [Calldata gas calculation](#calldata-gas-calculation) section)
* **Mint rate** = Dynamically adjusted rate (FCT-wei per ETH-wei)

The *mint rate* is denominated in **FCT-wei per ETH-wei burned**.

**Important**: Data Gas only includes the gas for the transaction's calldata/event data - not the total gas used by the transaction.

## Total supply cap

The total supply of FCT is:

* **1,646,951,661 FCT** (human-readable)
* **1,646,951,661,163,841,381,479,607,357** (in FCT-wei, with 18 decimals)

The protocol enforces this cap through an issuance-based halving schedule.

### Halving schedule

Halvings are intended to occur every 5,256,000 blocks. However, the actual halvings are triggered by issuance thresholds, not time:

* **1st Halving**: 50% of total supply minted
* **2nd Halving**: 75% of total supply minted (50% + 25%)
* **Subsequent**: Each adds half of remaining supply

Each halving reduces the per-period issuance target by 50%.

**Example**: If the current per-period target is 100,000 FCT, after the next halving it becomes 50,000 FCT. This ensures issuance slows down over time as the total supply approaches its cap.

## Dynamic rate adjustment

### What is a period?

A **period** is a span of time during which the FCT mint rate remains constant. When a period ends, the protocol recalculates the rate based on how much FCT was actually minted versus the target.

Periods can end *during* a transaction. If a transaction's minting would exceed the period's target, the period ends mid-transaction:

* The portion of ETH burned before hitting the target mints at the current period's rate
* The remaining portion mints at the new period's rate

The same applies to halvings - they can occur within a single transaction.

This creates a self-balancing system: if too much FCT is minted, rates go down; if too little is minted, rates go up.

### Adjustment periods

A period ends when **either**:

1. 500 L2 blocks elapse, or
2. The period's FCT target is hit

This dual-threshold system ensures rapid response to demand changes while maintaining predictable issuance.

### Rate calculation

The rate adjusts based on which threshold triggered the period end.

**Variable glossary:**

* `old_rate`, `new_rate`: FCT-wei per ETH-wei burned
* `target`: per-period FCT target (e.g., 100,000 FCT)
* `minted`: actual FCT minted in period
* `blocks_elapsed`: blocks in period when target hit

#### Under-issuance (500 blocks reached first)

When the period times out before hitting the target:

```
if 500-block timeout:
    if minted == 0:
        new_rate = min(old_rate * 4, MAX_MINT_RATE)
    else:
        new_rate = old_rate × min(target / minted, 4)
    new_rate = clamp(new_rate, MIN_MINT_RATE, MAX_MINT_RATE)
```

Capped at 4× the old rate to prevent extreme spikes.

#### Over-issuance (Target reached first)

When the target is minted in fewer than 500 blocks:

```
if target hit first:
    new_rate = old_rate × max(blocks_elapsed / 500, 0.25)
    new_rate = clamp(new_rate, MIN_MINT_RATE, MAX_MINT_RATE)
```

Capped at 0.25× the old rate to prevent extreme drops.

### Examples

Assuming a target of 100,000 FCT per period and old\_rate = 1,000,000,000,000,000 (FCT-wei/ETH-wei):

1. **Moderate under-issuance**: 80,000 FCT minted in 500 blocks
   * new\_rate = old\_rate × 1.25
2. **Severe under-issuance**: 25,000 FCT minted in 500 blocks
   * new\_rate = old\_rate × 4.0 (capped)
3. **Moderate over-issuance**: Target hit in 450 blocks
   * new\_rate = old\_rate × 0.9
4. **Severe over-issuance**: Target hit in 50 blocks
   * new\_rate = old\_rate × 0.25 (capped)

## Calldata gas calculation

Following Ethereum's EIP-7623 gas pricing:

$$
\text{Data Gas} = (\text{Zero Bytes} \times 10) + (\text{Non-Zero Bytes} \times 40)
$$

## L1 contract-initiated transactions

Facet transactions created by L1 smart contracts use event data instead of calldata:

$$
\text{Event Data Gas} = \text{Data Bytes} \times 8
$$

This gas is multiplied by the block's base fee to get ETH burned, then by the mint rate to get FCT minted (for contract-initiated Facet tx only).

## Protocol constants

| Constant                          | Value                     | Description           |
| --------------------------------- | ------------------------- | --------------------- |
| `ADJUSTMENT_PERIOD_TARGET_LENGTH` | 500 blocks                | Period length target  |
| `MAX_RATE_ADJUSTMENT_UP_FACTOR`   | 4×                        | Maximum rate increase |
| `MAX_RATE_ADJUSTMENT_DOWN_FACTOR` | 0.25×                     | Maximum rate decrease |
| `MAX_MINT_RATE`                   | 2\*\*128 - 1 ≈ 3.4 × 10³⁸ | Global maximum rate   |
| `MIN_MINT_RATE`                   | 1                         | Global minimum rate   |

## State variables

The protocol tracks:

* `fct_mint_rate`: Current issuance rate (FCT-wei/ETH-wei)
* `current_period_start_block`: L2 block when period began
* `current_period_fct_minted`: FCT minted so far this period
* `total_fct_minted`: Cumulative supply

These values update with each L1 block in `setL1BlockValuesEcotone()`.

## Fixed-point arithmetic

All fractional calculations use 18-decimal fixed-point arithmetic and truncate toward zero. This ensures deterministic results across all implementations.

## Appendix: Halving schedule

Assuming the protocol reaches each halving on schedule (yearly):

| Year | Halving | Supply Minted (% of Total) | Cumulative Supply (% of Total) |
| ---- | ------- | -------------------------- | ------------------------------ |
| 1    | -       | 50%                        | 50%                            |
| 2    | 1st     | 25%                        | 75%                            |
| 3    | 2nd     | 12.5%                      | 87.5%                          |
| 4    | 3rd     | 6.25%                      | 93.75%                         |
| 5    | 4th     | 3.125%                     | 96.875%                        |
| 6    | 5th     | 1.5625%                    | 98.4375%                       |

The total supply asymptotically approaches but never exceeds the cap.