$500 Starting MC

🎯 Goal

Update Moonbound’s bonding curve so that:

• The first buyers pay non-zero price

• The bonding curve starts at a $500 market cap

• The curve still graduates at exactly $50,000 market cap

• All pricing remains consistent across different token supplies

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✅ Updated Pricing Formula

Replace your current pricing logic with this:

price(s)=Pgraduation⋅(s+s0S)2\boxed{ \text{price}(s) = P_{\text{graduation}} \cdot \left( \frac{s + s_0}{S} \right)^2 }price(s)=Pgraduation​⋅(Ss+s0​​)2​

Where:

• s: tokens sold so far from the curve

• S: total bonding curve supply = maxSupply × 0.75

• P_graduation = 50,000 / maxSupply

• s₀: a small offset to shift the curve right and lift early prices

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🧮 Offset Calculation (for $500 starting cap)

To preserve a total curve market cap of exactly $50,000, calculate:

s0=−S2−3⋅S⋅−Pgraduation⋅S+6000006⋅Pgraduation\boxed{ s_0 = -\frac{S}{2} - \frac{\sqrt{3} \cdot \sqrt{S} \cdot \sqrt{-P_{\text{graduation}} \cdot S + 600000}}{6 \cdot \sqrt{P_{\text{graduation}}}} }s0​=−2S​−6⋅Pgraduation​​3​⋅S​⋅−Pgraduation​⋅S+600000​​​

This offset only affects the price curve, not token accounting. It ensures the area under the curve (total raised KAS) still sums to $50,000 equivalent.

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🔢 Examples

Example 1 — 1,000,000 Max Supply

• maxSupply = 1,000,000

• S = 750,000

• P_graduation = 50,000 / 1,000,000 = 0.05

Plug into the formula:

s0≈426.776s_0 \approx 426.776s0​≈426.776

So pricing becomes:

price(s)=0.05⋅(s+426.776750000)2\text{price}(s) = 0.05 \cdot \left( \frac{s + 426.776}{750000} \right)^2price(s)=0.05⋅(750000s+426.776​)2

This starts the curve at ~$0.000002 or higher, generating ~$500 from early buys, and still ends at exactly $50k market cap when s = S.

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Example 2 — 10,000,000 Max Supply

• S = 7,500,000

• P_graduation = 0.005

s0≈1347.150s_0 \approx 1347.150s0​≈1347.150

Pricing formula becomes:

price(s)=0.005⋅(s+1347.1507,500,000)2\text{price}(s) = 0.005 \cdot \left( \frac{s + 1347.150}{7,500,000} \right)^2price(s)=0.005⋅(7,500,000s+1347.150​)2

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Example 3 — 100,000 Max Supply

• S = 75,000

• P_graduation = 0.5

s0≈45.825s_0 \approx 45.825s0​≈45.825

Pricing becomes:

price(s)=0.5⋅(s+45.82575000)2\text{price}(s) = 0.5 \cdot \left( \frac{s + 45.825}{75000} \right)^2price(s)=0.5⋅(75000s+45.825​)2

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💡 Implementation Notes

• Keep your existing S and P_graduation logic

• Inject this new pricing formula into the contract or pricing helper

• s₀ can be calculated off-chain at token launch and stored as a constant for that token