01
Why Backstop is needed
Most onchain trades take place between a buyer and a seller: the buyer pays an asset, the seller gives up a token, and liquidity comes from traders, market makers, or liquidity pools.
That structure completes an exchange, but it does not require token supply and settlement assets to move together. A trade can change ownership and market price without changing total supply, and the buyer’s payment does not automatically become a protocol reserve.
Backstop uses a different rule. While calculating price, the protocol also adjusts supply and reserve with every trade. A buy or sell is not merely a transfer between wallets; it changes protocol state.
The sections below explain how that state changes and how every transaction settles under the same rules.
02
What Backstop changes
Backstop ties trading and protocol state to the same curve.
Buying creates supply and adds to the reserve. Selling burns supply and settles from the reserve.
On a buy, the curve calculates the amount of BACKSTOP available and the protocol mints it; net ETH after fees enters the reserve.
On a sell, the same curve calculates the quote; the protocol settles ETH from the reserve and burns the BACKSTOP it receives.
Backstop therefore does not rely on a traditional external dual-asset liquidity pool as its core settlement source. Supply and reserve are driven by actual trading: both rise on buys and fall on sells.
BUYMint BACKSTOP. Add net ETH to the reserve.
SELLBurn BACKSTOP. Settle ETH from the reserve.
PRICEDetermined by the current phase and position within it.
03
How a buy works
A buy does not take existing tokens from another holder. It creates new supply on the current curve.
The user submits ETH to the protocol. A 1% Protocol Fee and the Dynamic Buy Fee for the current phase are deducted first. The remaining ETH enters the reserve and is used in the curve calculation.
Starting from the current position within the phase, the curve calculates how much BACKSTOP the net ETH can purchase. The protocol then mints that amount and sends it to the user’s wallet.
If the amount is large enough to complete the current phase, the order does not stop at the boundary. The protocol settles the current phase first, then carries the remaining amount into the next phase and continues under its capacity, price, and fee parameters.
The same amount of ETH does not always produce the same amount of BACKSTOP. The result depends on the phase, the position within that phase, fees, and whether the order crosses a phase boundary.
04
How a sell works
A sell settles backward along the current curve. The protocol calculates the sell quote, then burns the BACKSTOP it receives.
After the user submits a sell quantity, the protocol calculates a Gross Quote from the current position within the phase. A 1% Protocol Fee and a 3% Dynamic Sell Fee are deducted, and the remaining ETH is sent to the user.
If the quantity exceeds the amount sold within the current phase, the calculation rolls back into the previous phase. Each phase crossed by the order is settled separately and then aggregated into the final result.
Actual exit value cannot be calculated as “BACKSTOP balance × current displayed price.”
The displayed price is only the marginal price at the current point on the curve. The sell itself moves down the curve, while quantity, fees, slippage, and cross-phase settlement all affect the result.
05
Genesis: setting the starting point together
The initial Backstop price is determined by the effective Genesis raise and the fixed Genesis supply.
Genesis lasts for a maximum of 24 hours, has a cap of 20 ETH, and allocates a fixed 72,000,000 BACKSTOP. It ends when the cap is reached or when 24 hours have elapsed. Amounts above the cap are excluded from the effective raise.
Initial price
Let the effective Genesis raise be G ETH and the initial price be P0:
P0 = G72,000,000 ETH / BACKSTOP
A larger final effective raise produces a higher starting price for the protocol curve. Every participant uses the same final P0.
User allocation
A user’s allocation is proportional to their effective deposit as a share of the total raise. Let the user’s effective deposit be Du ETH and their allocation be Au:
Au = DuG × 72,000,000
Genesis does not require different prices for different participants. Participants differ only in their share of the effective raise.
06
The ten-phase price curve
After Genesis, trading moves through ten continuous phases. Together, they form one curve that can advance and roll back.
Within each phase, price rises linearly from the phase starting price to twice that price. The next phase begins at the previous phase’s ending price, so pricing remains continuous at the boundary.
Phase capacity halves as the curve advances. Phase 1 has a capacity of 36,000,000 BACKSTOP; Phase 10 has a capacity of 70,312.5 BACKSTOP. The Dynamic Buy Fee falls from 3.00% to 0.25%, while the Dynamic Sell Fee remains 3.00%.
Buying advances to the next phase after filling the current one. Selling rolls back when the net quantity sold within the current phase reaches zero. Orders that cross a boundary are calculated separately in each phase.
| Phase | Capacity (BACKSTOP) | Price range | Dynamic buy fee | Dynamic sell fee |
|---|
| 1 | 36,000,000 | 1P0 → 2P0 | 3.00% | 3.00% |
| 2 | 18,000,000 | 2P0 → 4P0 | 2.69% | 3.00% |
| 3 | 9,000,000 | 4P0 → 8P0 | 2.39% | 3.00% |
| 4 | 4,500,000 | 8P0 → 16P0 | 2.08% | 3.00% |
| 5 | 2,250,000 | 16P0 → 32P0 | 1.78% | 3.00% |
| 6 | 1,125,000 | 32P0 → 64P0 | 1.47% | 3.00% |
| 7 | 562,500 | 64P0 → 128P0 | 1.17% | 3.00% |
| 8 | 281,250 | 128P0 → 256P0 | 0.86% | 3.00% |
| 9 | 140,625 | 256P0 → 512P0 | 0.56% | 3.00% |
| 10 | 70,312.5 | 512P0 → 1024P0 | 0.25% | 3.00% |
07
How reserve and supply move together
In Backstop, a single transaction changes both supply and reserve.
A buy mints BACKSTOP and adds net ETH to the reserve; a sell settles ETH from the reserve and burns BACKSTOP.
SUPPLY +Occurs when the protocol completes a buy and mints.
SUPPLY −Occurs when the protocol completes a sell and burns.
RESERVE +Comes from the effective Genesis raise and net ETH from buys.
RESERVE −Comes from sells calculated and settled under the curve.
The current reserve is not a fixed exit amount for any one user. The ETH a user receives must still be calculated from the curve position and the actual path of the full sell order.
08
Beyond Phase 10
Phase 10 is the end of the parameter transition, not the end of protocol trading.
After Phase 10, the protocol continues with a base phase capacity of 70,312.5 BACKSTOP, a 0.25% Dynamic Buy Fee, a 3.00% Dynamic Sell Fee, and a 1.00% Protocol Fee.
Price calculation remains continuous. Buying continues to mint and selling continues to burn, so the protocol does not set a fixed maximum supply. Supply remains a result of actual buying and selling activity.
09
Protocol parameters
The following parameters define the Backstop mechanism described in this paper.
| Parameter | Value |
|---|
| Maximum Genesis duration | 24 hours |
| Genesis cap | 20 ETH |
| Genesis fixed supply | 72,000,000 BACKSTOP |
| Protocol Fee | 1% on buys and sells |
| Dynamic Buy Fee | 3.00% → 0.25% |
| Dynamic Sell Fee | 3.00% |
| Phase 1 capacity | 36,000,000 BACKSTOP |
| Phase capacity change | Halves each phase |
| Price range within a phase | Rises linearly from the starting price to 2× |
| Phase 10 base capacity | 70,312.5 BACKSTOP |
| Maximum supply | Not fixed |
10
Mathematical appendix
The main text explains how trading works. This appendix expresses the same mechanism in calculation form.
Phase capacity
The capacity of Phase i is:
Ci = 36,000,0002i−1
Phase starting price
Li = 2i−1P0
Price within a phase
Let the net quantity sold within the current phase be x:
Pi(x) = Li(1 + xCi)
When x = 0, the price is Li. When x = Ci, the price is 2Li.
Net buy amount
Let a user submit X ETH and the Dynamic Buy Fee for the current phase be di:
A = X(1 − 1% − di)
Buy quantity
Let the phase starting price be L, capacity be C, net quantity sold within the phase be x, and the quantity bought in the current phase be q:
A = L[q + 2xq + q²2C]
q = −(C + x) + √((C + x)² + 2CAL)
Sell quote
When a user sells q BACKSTOP in the current phase, the Gross Quote is:
V = L[q + 2xq − q²2C]
After the 1% Protocol Fee and 3% Dynamic Sell Fee:
UserReceive = V(1 − 1% − 3%) = 0.96V
Cross-phase settlement
If a buy exceeds the remaining capacity of the current phase, the protocol first calculates the amount needed to complete that phase, then carries the remainder into the next one. If a sell exceeds the amount available for rollback in the current phase, the protocol settles that phase first and returns to the previous one. The result of the full order is the sum of calculations across every phase crossed.
Per-phase reserve relation
The net ETH required to enter the curve reserve to complete any full phase is:
∫0CᵢPi(x)dx = 32LiCi
Because LiCi = 36,000,000P0 and P0 = G / 72,000,000:
LiCi = G2
StageNetReserve = 34G
Under the defined parameters, the net ETH required to enter the curve reserve to complete any full phase is therefore 75% of the effective Genesis raise.
11
Conclusion
Backstop turns every trade into a synchronized change in supply and reserve.
On a buy, the protocol mints new BACKSTOP under the curve and adds net ETH to the reserve. On a sell, it settles ETH from the reserve under the same curve and burns the BACKSTOP it receives.
Genesis establishes the shared starting point. The ten-phase parameters determine how price moves forward and backward. Beyond Phase 10, the protocol continues to operate on a continuous curve.
Backstop does not attempt to promise price or returns. It provides a public, consistent, and computable set of trading rules.