> ## Documentation Index
> Fetch the complete documentation index at: https://docs.vibetoken.cn/llms.txt
> Use this file to discover all available pages before exploring further.

# Token Pricing: Supply-Based Bonding Curve Explained

> Learn how Vibe Token calculates price using a square root bonding curve, and why this rewards early contributors while dampening volatility.

Token price in Vibe Token is not set by a founder, an exchange, or a vote. It emerges automatically from the circulating supply using a bonding curve. As more tokens enter circulation, the price rises. As tokens are burned during exits, the price falls. This creates a self-regulating market that reflects the scale of contribution activity in your business.

## The Pricing Formula

```
P = k × √S
```

| Variable | Meaning                                                     |
| -------- | ----------------------------------------------------------- |
| `P`      | Current token price in USD                                  |
| `k`      | Pricing constant anchored to your business's MRR            |
| `S`      | Circulating supply — issued tokens only (excludes treasury) |
| `√S`     | Square root of circulating supply                           |

All three inputs are always knowable. There are no hidden parameters, oracle feeds, or discretionary adjustments.

## Price at a Glance

The table below shows how price responds to different supply levels and values of `k`.

| Circulating Supply (S) | k     | Price (P) |
| ---------------------- | ----- | --------- |
| 1,000 (floor)          | 0.005 | \$0.158   |
| 10,000                 | 0.005 | \$0.50    |
| 10,000                 | 0.01  | \$1.00    |
| 10,000                 | 0.1   | \$10.00   |

Notice that `k` acts as a direct multiplier: doubling `k` doubles the price at any given supply level.

## Why a Square Root?

A linear curve — `P = k × S` — would make early tokens almost free and later tokens extremely expensive, concentrating value sharply at the start. A square root curve compresses that range in a predictable way:

* Doubling supply increases price by roughly **41%**, not 100%.
* Tripling supply increases price by roughly **73%**, not 200%.

This dampens volatility as your contributor community grows. A contributor joining when `S = 40,000` pays only twice the price of someone who joined when `S = 10,000` — not four times.

## The Supply Floor: Smin = 1,000

When `S = 0`, the formula produces `P = $0`, which would make the first tokens free and create a mathematical singularity. To prevent this, Vibe Token enforces a minimum circulating supply:

```
Smin = 1,000
```

Even before any tokens are issued, `S` is treated as at least 1,000 for pricing purposes. At `k = 0.005`, this floor produces a minimum price of:

```
P = 0.005 × √1,000 = 0.005 × 31.62 ≈ $0.158
```

This ensures every first token grant happens at a meaningful, non-zero price.

## How Price Moves Over Time

Price changes in two directions:

* **Minting (earnings and grants)** increases circulating supply → `S` rises → `P` rises.
* **Burning (exits)** decreases circulating supply → `S` falls → `P` falls.

Neither direction is artificially suppressed. If your contributor community grows, price reflects that. If contributors exit, price adjusts downward — transparently and immediately.

## Early Contributor Advantage

Because price is lower when supply is low, early contributors earn more tokens per dollar of contribution than later contributors do. A referral that earns `$100` of attributed revenue when `P = $0.50` yields twice as many tokens as the same referral made when `P = $1.00`.

This is intentional. Early contributors take the most risk and uncertainty. The bonding curve rewards that timing automatically, without requiring the founder to manually set different token prices for different cohorts.

## Choosing the Right k

The pricing constant `k` is calculated from your business's monthly recurring revenue (MRR) at the time of launch:

```
k = max(MRR ÷ 1,000,000, 0.005)
```

This anchors token price to your actual business scale. A bootstrapped tool with $2K MRR gets a modest `k`; a growing SaaS at $100K MRR gets a `k` that puts tokens in a price range meaningful to that business.

| MRR      | k     | Starting Price at S=1,000 |
| -------- | ----- | ------------------------- |
| $0 – $5K | 0.005 | \~\$0.158                 |
| \$10K    | 0.01  | \~\$0.316                 |
| \$100K   | 0.1   | \~\$3.16                  |

<Info>
  `k` anchors token value to business scale. A higher `k` doesn't make your tokens more valuable in isolation — it means the token price is calibrated to a business where each token represents a proportionally larger claim on revenue.
</Info>

### Rule of thumb for initial grants

When you launch, you may want to grant tokens to founding contributors before any revenue events have occurred. As a guideline, **initial grants should total less than 50% of the tokens you expect to be earned in year one** through revenue-linked activity. Granting too many tokens at launch dilutes the incentive for future contributors and compresses the price appreciation that makes early contribution meaningful.