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Mechanism · 04

Mathematical model

Formal definition of the Burn Price, monotonicity proof, break-even and the relationship between the floor and the market price.

Definition

The protocol’s floor is defined by a division, with no price oracle, no adjustable parameter, and no governance able to change it:

The The Burn Vault Boost applies the same division to a guaranteed quota of 148,776 EVA: 37.43 wBTC ÷ 69,729 eligible EVA = 53,680 sats per EVA (~US$ 46.26). The value shown is the burn quote read from the Boost contract itself; the division above matches it to within ±1 sat of rounding. This guaranteed floor is the headline value displayed on the site; the break-even and the premium below are measured against it.

The variables

wBTC in the vault (numerator)Daily mining deposits; one-off contributions; feesOnly redemptions (which also burn EVA)
EVA in circulation (denominator)Nothing (fixed supply of 21,000,000, no mint)Burns, permanent and proportional to redemptions

Monotonicity

Only two events change the formula. An analysis of each:

Mining deposit

The numerator grows and the denominator stays constant. For any deposit d > 0:

(V + d) / S > V / S

The floor rises.

Redemption (burn)

A redemption of q tokens pays exactly q × BurnPrice in wBTC. The vault loses that fraction and the supply loses q:

(V − q·V/S) / (S − q) = V·(S − q)/S / (S − q) = V / S

Numerator and denominator fall in the same proportion. The floor stays the same.

Conclusion

One event raises the floor; the other keeps it unchanged. There is no third event in the contract. The Burn Price is therefore monotonically non-decreasing, as a property of the code.

Denominated in sats

The guarantee is denominated in Bitcoin, not in dollars. In USD, the floor’s value varies with the price of BTC. Details in the Bitcoin volatility.

Floor growth and break-even

The floor started at 357 sats at launch and has only risen since. The pace of the climb depends on two factors: the volume of mining deposited and the size of the remaining quota (the smaller the quota, the greater the per-token effect of each deposit).

The break-even is straightforward: a position bought at X sats reaches its guaranteed break-even point when the floor reaches X. From that point on, the minimum assured by the contract covers the amount paid, and any market premium is surplus.

Market premium

With the backing concentrated by the Boost, the guaranteed floor closely tracks the market price: the current gap between spot and floor, the premium, is 0.2% (~US$ 46.35 versus ~US$ 46.26). When positive, the premium reflects expectation: future mining deposits, the growth of the operation, and the ecosystem’s products.

The public sale followed the same structure: a price of 550 sats with an initial floor of 357 sats, the difference corresponding to the expectation premium.

The premium has a structural lower bound: if the market price falls below the floor, buying EVA on the market and redeeming the wBTC through the contract becomes profitable, which generates buying pressure for as long as the price stays below the floor.

Properties of the model

  • Predictable: two public variables and one division. Floor projections can be made directly from on-chain data.
  • Uniform: the formula assigns the same per-token floor to every holder.
  • Operator-independent: the central property (the floor never decreases) follows from immutable, Security and audits code.

Found something incorrect or outdated? Let us know on Telegram or check the data directly in the contracts.