Ascendium

Every buy on $ASC runs through a single deterministic function. no oracle. no order book. no counterparty. WalkForward(x, n, f) : you send x WETH, the hook walks the bonding curve bin by bin until your input is fully consumed. if you stay inside a bin : zero slippage. price is constant at P(n). if you cross a bin : price steps up by r. Deterministic. Predictable. Always.

We are live You can buy $ASC : Ascendium.sh CA: 0x0866F604cC353C7EA534617b0498972e4eF923Dd $ASC only tradeable on the official dapp. Custom Uniswap V4 hook. Ascendium is powered by a deterministic step-curve AMM on Uniswap v4.

Marginal price within a single fill is constant at P(n). slippage only appears at step boundaries. The AMM state is fully described by (step, fillInStep). nothing else matters. This is what trustless price discovery looks like. $ASC

MAX_STEP = 1000 is an engineering cap, not a mathematical limit. Reversibility is exact. Any forward walk from cursor c₀ → c₁ consuming x WETH has a backward walk from c₁ → c₀ returning exactly x WETH. no hysteresis. No path dependency.

Strict monotonicity. No asymptote. No plateau. every forward step boundary tightens the marginal price by a factor of r. permanently. Cumulative supply Σ T(k) = S · (1 - δᴺ) converges monotonically to S but remains strictly less than S for every finite N. the hook never reaches exhaustion.

Marginal slippage at step n : slip(n) = P(n+1)/P(n) - 1 = r - 1 = 0.10 Every bin you cross = exactly +10% spot price. c(n+1)/c(n) = δ·r = 1.045 in ETH cost. The curve doesn't estimate price impact. It proves it. ∎

Ascendium's bonding curve is a convergent geometric series. ∑ T(n) = S·(1-δ) · ∑ δⁿ⁻¹ = S·(1-δ) · 1/(1-δ) = S The entire supply is absorbed exactly as n → ∞. No rounding. No remainder.

No governance. No admin keys. No upgrades. Ascendium runs on math and rules alone a fixed supply, a curve, and a set of constraints that apply to everyone equally. DeFi the way it was supposed to be.

The construction is closed-form and reversible. Every quote is a deterministic function of three numbers: the current cursor (step, fillInStep), the input amount, and the direction. There is no oracle, no liquidity provider, no governance, no admin, no upgrade path.

with per-step ASC capacity T(n) decaying geometrically toward zero so that the cumulative supply released across all steps converges to the genesis cap of one million ASC without ever exceeding it.

Ascendium (ASC) is a fixed-supply ERC20 priced by a deterministic step-function automated market maker, deployed as a Uniswap v4 hook against WETH.