Numerical Simulation Example

Global parameters

$$\begin{array}{lcl} \text{Daily emission:} & R_{day} & = 10{,}000 \;\text{CHN} \\[6pt] \text{Split ratios:} & split_{creator} & = 0.7,\; split_{engager} = 0.3 \\[6pt] \text{DAO weights:} & & \alpha = 1,\; \beta = 2,\; \gamma = 3,\; \delta = 4 \end{array}$$

Inputs (Day 𝑡 )

• Post A: U=100,  L=50,  C=20,  S=10,  Q=0.8

• Post B: U=200,  L=80,  C=30,  S=25,  Q=0.9

• Post C: U=50,  L=20,  C=10,  S=5,  Q=0.7

Step 1 — Post Scores

$$\text{Score}_p = Q_p \times \left( \alpha U + \beta L + \gamma C + \delta S \right)$$

$$\begin{array}{rcl} \text{Score}_A &=& 0.8 \times (1\cdot 100 + 2\cdot 50 + 3\cdot 20 + 4\cdot 10) = 0.8 \times 300 = 240 \\ \text{Score}_B &=& 0.9 \times (200 + 160 + 90 + 100) = 0.9 \times 550 = 495 \\ \text{Score}_C &=& 0.7 \times (50 + 40 + 30 + 20) = 0.7 \times 140 = 98 \end{array}$$

Total Score =

$$\Sigma_{\text{all}} = 240 + 495 + 98 = 833$$

Step 2 — Post Rewards

$$R_p = R_{\text{day}} \times \frac{\text{Score}_p}{\Sigma_{\text{all}}}$$

$$\begin{array}{rcl} R_A &=& 10{,}000 \times \frac{240}{833} \approx 2{,}881 \text{ CHN} \\ \\ R_B &=& 10{,}000 \times \frac{495}{833} \approx 5{,}942 \text{ CHN} \\ \\ R_C &=& 10{,}000 \times \frac{98}{833} \approx 1{,}177 \text{ CHN} \end{array}$$

(Checks: 2881+5942+1177=10,000 CHN)

Step 3 — Split: Creator vs. Engagers

$$\begin{array}{rcl} \text{Creator share} &=& 0.7 \times R_p \\ \text{Engagers share} &=& 0.3 \times R_p \end{array}$$

Post	Total Rp	Creator (70%)	Engagers (30%)
A	2,881	2,017	864
B	5,942	4,160	1,782
C	1,177	824	353
Total	10,000	7,001*	2,999*

* Totals differ by ±1 CHN due to rounding; production systems should handle rounding at the end of aggregation to ensure exact conservation.

Interpretation

• Post B earns the largest share due to higher weighted engagement and quality factor (Q).

• Engagers as a group receive ~30% of daily emissions, aligned with Split_engager.

• The DAO can tune α,β,γ,δ, creator/engager splits, and reputation/staking multipliers to balance growth, quality, and Sybil resistance.