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

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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.

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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)

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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 ( $Tmined$)

$$T_{\text{mined}} = \sum_{n=1}^{\infty} M_n = \frac{M_0}{1 - r}$$

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Token Issuance Schedule per Cycle

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

Cycle (nnn)	Block Reward (RnR_nRn​)	Tokens Mined ( $Mn)$	Cumulative Tokens Mined	Percentage of Total Supply
1	$R0$	$M0$	$M0$	$M0S×100$
2		$M0×0.85$	$M0×(1+0.85)$	...
3	R0×0.852R_0 \times 0.85^2R0​×0.852	M0×0.852M_0 \times 0.85^2M0​×0.852	M0×(1+0.85+0.852)M_0 \times (1 + 0.85 + 0.85^2)M0​×(1+0.85+0.852)	...
...	...	...	...	...

Calculations:

• Block Reward ( $R0$ ​):

$$R_0 = \frac{M_0}{B_c} = \frac{4.200,000,000,000}{518,400} \approx 8,101,851.85 \text{ tokens per block}$$

• Subsequent Block Rewards:

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

Detailed Token Issuance for First 10 Cycles

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