Economic Model

I. Block Rewards

We adopt a Logarithmic Decay Algorithm based on issuance ratio (LSED model).

The core logic is based on the formula log2(1 / (1 - ratio)), and the emission decay presents a 1/2ⁿ pattern.

1. Mathematical Expression of the Decay Algorithm

• R is the current total issuance (total_issuance)

• S is the total supply (total_supply) = 21,000,000 HETU

• E₀ is the default block reward: 1 HETU/block

• r = R / S is the current issuance ratio (0 ≤ r < 1)

• E(r) is the current actual reward

Then:

$$E(r) = E_0 \times \frac{1}{2^{\lfloor \log_2 \left( \frac{1}{1-r} \right) \rfloor}}$$

• If r ≥ 1, E(r) = 0

2. Trigger Points of Each Decay Cycle

Halving Cycle	r (Issuance Ratio)	Block Reward (HETU)
0	0% ~ 50%	1
1	50% ~ 75%	0.5
2	75% ~ 87.5%	0.25
3	87.5% ~ 93.75%	0.125
4	93.75% ~ 96.875%	0.0625
5	96.875% ~ 98.4375%	0.03125
6	98.4375% ~ 99.21875%	0.015625
...	...	...

3. Cycle Schedule Calculated Based on 12-Second Blocks

• Total supply: 21,000,000 HETU

• Initial reward per block: 1 HETU

• Block generation speed: 12 seconds/block ≈ 5 blocks/minute

We estimate the duration based on the amount of HETU that can be released in each stage:

Decay Cycle	Block Reward (HETU)	Ratio Range	Stage Supply (HETU)	Time (Years)	Block Height Range
0	1	0% ~ 50%	10,500,000	~4	0 ~ 10.5M
1	0.5	50% ~ 75%	5,250,000	~4	10.5M ~ 15.75M
2	0.25	75% ~ 87.5%	2,625,000	~4	15.75M ~ 18.375M
3	0.125	87.5% ~ 93.75%	1,312,500	~4	...
...	...	...	...	~4	...

4. Reward Decay Curve (Issuance Ratio vs. Block Reward)

(Exponential decay graph with issuance ratio on the horizontal axis and block reward on the vertical axis)

Reward Decay Curve

• Horizontal axis: proportion of total issuance (0% to 100%)

• Vertical axis: block reward (unit: HETU)

• The reward decreases exponentially, and a halving is triggered whenever the issuance ratio reaches 1 - 1/2ⁿ

5. Release Model Curve

Release Model Curve

II. Block Reward Allocation

1. Introduction to Block Rewards

• Stakework rewards (subnet rewards)

• Main network rewards

  • Community (community pool): 2%

  • Validator (commission): 5%

  • Validator (validator rewards, allocated according to weight and delegation): 93%

Block Reward Allocation

2. Introduction to Subnet Rewards

(1) Algorithm Introduction

Logarithmic Subnet Incentive (LSI) "logarithmic" subnet reward mechanism

Calculation formula:

subnet_reward_ratio = min( max_ratio, base + k * log(1 + subnet_count) )

Where:

• base: Initial subnet reward ratio (e.g., 0.10)

• k: Growth rate coefficient (e.g., 0.16)

• max_ratio: Maximum subnet reward ratio (e.g., 0.9)

(2) Calculation Process

subnet_count	subnet_reward_ratio
0	0
1	0.1109035489
2	0.1757779662
3	0.2218070978
4	0.257510066
5	0.2866815151
6	0.3113456238
7	0.3327106467
8	0.3515559324
9	0.3684136149
10	0.3836632436

(3) Subnet Reward Growth Curve Chart:

Subnet Reward Growth Curve

• As the number of subnets increases, the reward ratio gradually increases.

• The growth rate is controlled by the parameter k.

• The reward ratio is limited by the maximum value of max_ratio = 0.9, and it will not increase after reaching the upper limit.

Explanation:

1. Initial stage (number of subnets < 50)

   • The ratio starts from base=0.10 and grows slowly with log(1+subnet_count).

   • For example:

     • 1 subnet: 0.10 + 0.1*log(2) ≈ 0.17

     • 10 subnets: 0.10 + 0.1*log(11) ≈ 0.34

2. Rapid growth stage (50 ≤ number of subnets < 300)

   • The logarithmic function enters a significant growth interval, and the ratio rises rapidly.

   • For example:

     • 100 subnets: 0.10 + 0.1*log(101) ≈ 0.56

     • 200 subnets: 0.10 + 0.1*log(201) ≈ 0.66

3. Saturation stage (number of subnets ≥ 300)

   • When the ratio is close to max_ratio=0.9, the formula triggers the min() function to limit growth.

   • Calculation of the turning point:

     0.10 + 0.1*log(1+x) = 0.9 → log(1+x)=8 → x≈e⁸≈2981

     Actually, due to the limitation of calculation accuracy, it is close to the upper limit when x≈300 in the figure.

   • After that, the ratio remains unchanged at 0.9 (horizontal line).

3. Incentive Sharing Curve Chart

Incentive Sharing Curve