> For the complete documentation index, see [llms.txt](https://change-chain-1.gitbook.io/change-chain/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://change-chain-1.gitbook.io/change-chain/mining/tokenomics.md).

# Tokenomics

### Introduction

Change Chain introduces a unique tokenomics model designed to balance network security, incentivize miners, and ensure a fair distribution of tokens over time. This document provides a detailed explanation of the token issuance schedule, including equations and tables to illustrate the mining rewards and token supply dynamics

***

### Total Token Supply

* **Total Supply (** $$S$$ **)**: 210,000,000,000,000 tokens (210 trillion)
* **Token Allocation**: All tokens are allocated for mining (Proof-of-Work). There is no pre-mine or token reserves allocated for other purposes.

***

## Mining and Token Issuance Schedule

### Key Parameters

**Initial Mining Period**: 60 days per cycle

**Initial Issuance (** $$M0$$ **​)**: Tokens mined in the first 60-day cycle

**Issuance Reduction Rate**: Decreases by 15% every 60 days 

**Block Time (** $$Tb$$ **​)**: 800ms

### **Blocks per Cycle (** $$Bc$$ **​)**

$$
B\_c = \frac{60 \times 24 \times 60 \times 60}{T\_b}
$$

### **Blocks per Cycle Calculation**

$$
B\_c = \frac{60 \times 24 \times 60 \times 60}{0.8} = 6,480,000 \text{ blocks}
$$

#### Determining Initial Issuance

Given that the total issuance in the first 60 days is more than 2% of the total supply and the issuance decreases by 15% every 60 days, we need to calculate $$M0$$ such that the cumulative tokens mined over infinite time do not exceed the total supply.

## **Total Tokens Mined Over Time (** $$TminedT$$ **)**

The total tokens mined over all cycles is the sum of a decreasing geometric series:

$$
T\_{\text{mined}} = \sum\_{n=1}^{\infty} M\_n = M\_0 \sum\_{n=1}^{\infty} r^{n-1} = \frac{M\_0}{1 - r}
\
$$

**Setting Total Mined Tokens Equal to Total Supply**

To ensure that the total mined tokens do not exceed the total supply (S):

$$
T\_{\text{mined}} = \frac{M\_0}{1 - r} = S
\
M\_0 = (1 - r) \times S
\
$$

#### Final Token Allocation

* **Mining Allocation**: 28,000,000,000,000 tokens (13.33% of total supply)
* **Other Allocations**: 182,00,000,000,000 tokens (86.67% of total supply)

***

#### Blocks per Cycle ( $$Bc$$ ​)

$$
B
c
​

# ​

​

60×24×60×60
​
/T
b
$$

#### Block Reward per Cycle (RnR\_nRn​)

$$
R
n
​
\=R
0
​
×r
n−1
$$

* $$R0$$​: Initial block reward
* $$r$$: Reduction factor per cycle (r=0.85)
* $$n$$: Cycle number (starting from 1)

#### Tokens Mined per Cycle ( $$Mn$$ ​)$$M\_n = R\_n \times B\_c = R\_0 \times r^{n-1} \times B\_c$$

$$
M\_n = R\_n \times B\_c = R\_0 \times r^{n-1} \times B\_c
$$

#### Total Tokens Mined Over Time ( $$Tmined$$)

$$
T\_{\text{mined}} = \sum\_{n=1}^{\infty} M\_n = \frac{M\_0}{1 - r}
$$

***

#### Token Issuance Schedule per Cycle

Assuming $$M0$$ =4,200,000,000,000 tokens in the first cycle.

<table data-header-hidden><thead><tr><th></th><th></th><th></th><th width="196"></th><th></th></tr></thead><tbody><tr><td>Cycle (nnn)</td><td>Block Reward (RnR_nRn​)</td><td>Tokens Mined ( <span class="math">Mn)</span></td><td>Cumulative Tokens Mined</td><td>Percentage of Total Supply</td></tr><tr><td>1</td><td><span class="math">R0</span></td><td><span class="math">M0</span></td><td><span class="math">M0</span></td><td><span class="math">M0S×100%\frac{M_0}{S} \times 100\%SM0​​×100%</span></td></tr><tr><td>2</td><td></td><td><span class="math">M0×0.85</span></td><td><span class="math">M0×(1+0.85)</span></td><td>...</td></tr><tr><td>3</td><td>R0×0.852R_0 \times 0.85^2R0​×0.852</td><td>M0×0.852M_0 \times 0.85^2M0​×0.852</td><td>M0×(1+0.85+0.852)M_0 \times (1 + 0.85 + 0.85^2)M0​×(1+0.85+0.852)</td><td>...</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

**Calculations:**

* **Block Reward (** $$R0$$ **​)**:&#x20;

$$
R\_0 = \frac{M\_0}{B\_c} = \frac{4.200,000,000,000}{518,400} \approx 8,101,851.85 \text{ tokens per block}
$$

* **Subsequent Block Rewards**:

$$
R\_n = 8,101,851.85 \times 0.85^{n-1}
$$

## &#x20;Detailed Token Issuance for First 10 Cycles

<table data-header-hidden><thead><tr><th width="94"></th><th width="146"></th><th width="194"></th><th width="204"></th><th></th></tr></thead><tbody><tr><td>Cycle (n)</td><td>Block Reward (Rn)</td><td>Tokens Mined (Mn)</td><td>Cumulative Tokens Mined (tokens)</td><td>Percentage of Total Supply (%)</td></tr><tr><td>1</td><td>81,018,518.52</td><td>42,000,000,000,000</td><td>42,000,000,000,000</td><td>2%</td></tr><tr><td>2</td><td>68,865,740.74</td><td>35,700,000,000,000</td><td>77,700,000,000,000</td><td>3.7%</td></tr><tr><td>3</td><td>58,535,879.63</td><td>30,345,000,000,000</td><td>108,045,000,000,000</td><td>5.15%</td></tr><tr><td>4</td><td>49,755,497.68</td><td>25,793,250,000,000</td><td>133,838,250,000,000</td><td>6.37%</td></tr><tr><td>5</td><td>42,292,173.03</td><td>21,924,262,500,000</td><td>155,762,512,500,000</td><td>7.41%</td></tr><tr><td>6</td><td>35,948,347.08</td><td>18,635,623,125,000</td><td>174,398,135,625,000</td><td>8.30%</td></tr><tr><td>7</td><td>30,555,094.02</td><td>15,840,279,656,250</td><td>190,238,415,281,250</td><td>9.06%</td></tr><tr><td>8</td><td>25,971,829.92</td><td>13,464,237,707,813</td><td>203,702,653,989,063</td><td>9.70%</td></tr><tr><td>9</td><td>22,076,055.44</td><td>11,444,602,051,641</td><td>215,147,256,040,703</td><td>10.25%</td></tr><tr><td>10</td><td>18,764,647.12</td><td>9,727,911,744,895</td><td>224,875,167,785,598</td><td>10.71%</td></tr></tbody></table>

<figure><img src="https://2639828105-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FDLeIVJqHiDrf1ktdSCyh%2Fuploads%2FnGlZj9ACYk8n2nGhMSxe%2FBlock%20Reward%20vs%20Cycle.png?alt=media&amp;token=5accfda8-d047-49c7-8d31-f4af42f97c7c" alt=""><figcaption></figcaption></figure>