05 / Mechanism lab

Explore the mechanics behind GridPad

Experiment with GridPad’s bonding curve, floor reserve and redemption mechanics. Change the inputs, follow the calculations, and compare the model with verified on-chain data.

Educational only: the lab sends no transaction and needs no wallet. Every number is computed in your browser with the hub’s exact integer math, rounding included. Hypothetical results say so; live values come from the contract at a stated block. Nothing here predicts a price or promises a dollar value.

The pool

Start from an example or enter your own pool. Each example is replayed from an empty pool with the hub’s math, so it is a state the hub can reach. All of them are hypothetical: no token on the hub is any of them.

hypothetical An empty pool after one buy of 0.01 ETH.

01 Purchase allocation

hypothetical Example pool: after a buy
xc=⌊34 x⌋,xf=x−xcΔS=⌊S2+2 xc/k⌋−S\begin{gathered} x_c = \left\lfloor \tfrac{3}{4}\,x \right\rfloor, \qquad x_f = x - x_c \\ \Delta S = \left\lfloor \sqrt{S^{2} + 2\,x_c/k} \right\rfloor - S \end{gathered}

A hypothetical purchase: the hub splits it 75/25, mints on the curve, caps the mint where it would dilute the floor, and sweeps whatever the mint does not use into the floor reserve.

Initial split
After the guard and the rounding
Tokens minted
6,902 tokens6,902.613504603754094059 tokens
Dilution guard
does not bindcap 14,142.135623730944831162 · curve mint 6,902.613504603754094059 tokens
Supply after
148,323 tokens148,323.969741913258974227 tokens
Curve reserve after
0.008250 ETH8,249,999,999,999,999 wei
Floor reserve after
0.002750 ETH2,750,000,000,000,001 weinothing swept from the curve share
Floor
0.0000000176777 ETH → 0.0000000185405 ETH17,677,669,529 → 18,540,496,217 wei per token
Spot
0.000000106066 ETH → 0.000000111243 ETH106,066,017,177 → 111,242,977,306 wei per token
ΔS≤⌊xf SRf⌋Rf′=Rf+xf+(Rc+xc−12 k S′2)\begin{gathered} \Delta S \le \left\lfloor \frac{x_f\,S}{R_f} \right\rfloor \\ R_f' = R_f + x_f + \bigl(R_c + x_c - \tfrac{1}{2}\,k\,S'^{2}\bigr) \end{gathered}
How this was calculated
  1. Split the purchase 75 / 25toCurve = ⌊3x ÷ 4⌋, toFloor = x − toCurve
    x
    1,000,000,000,000,000 wei (0.001 ETH)
    ⌊3 × 1,000,000,000,000,000 ÷ 4⌋ = 750,000,000,000,000; 1,000,000,000,000,000 − 750,000,000,000,000 = 250,000,000,000,000toCurve = 0.00075 ETH, toFloor = 0.00025 ETHRounded down, so any remainder of the division goes to the floor share. This is the initial split: the guard and the rounding below decide what each reserve finally keeps.GridPadMath.buy()
  2. Mint on the curvecurve mint = ⌊√(S² + ⌊toCurve × 2 · 10⁵⁴ ÷ k⌋)⌋ − S
    S
    141,421,356,237,309,504,880,168 token-wei
    toCurve
    750,000,000,000,000 wei
    k
    750,000,000,000,000,000,000,000
    ⌊√(141,421,356,237,309,504,880,168² + ⌊750,000,000,000,000 × 2 · 10⁵⁴ ÷ 750,000,000,000,000,000,000,000⌋)⌋ − 141,421,356,237,309,504,880,168 = 6,902,613,504,603,754,094,059curve mint = 6,902.613504603754094059 tokensThe integer square root rounds down, so the pool never mints more than the curve share pays for.GridPadMath.buy()
  3. The dilution guardcap = ⌊toFloor × S ÷ Rf⌋, minted = min(curve mint, cap)
    toFloor
    250,000,000,000,000 wei
    S
    141,421,356,237,309,504,880,168 token-wei
    Rf
    2,500,000,000,000,001 wei
    ⌊250,000,000,000,000 × 141,421,356,237,309,504,880,168 ÷ 2,500,000,000,000,001⌋ = 14,142,135,623,730,944,831,162The cap (14,142.135623730944831162 tokens) is not below the curve mint: 6,902.613504603754094059 tokens minted.The floor share has to back every new token at the current floor, so no buy lowers the floor.GridPadMath.buy()
  4. Settle the curveS′ = S + minted, Rc′ = ⌊k × S′² ÷ 2 · 10⁵⁴⌋, sweep = Rc + toCurve − Rc′
    S + minted
    148,323,969,741,913,258,974,227 token-wei
    Rc
    7,499,999,999,999,999 wei
    toCurve
    750,000,000,000,000 wei
    Rc′ = ⌊750,000,000,000,000,000,000,000 × 148,323,969,741,913,258,974,227² ÷ 2 · 10⁵⁴⌋ = 8,249,999,999,999,999; sweep = 7,499,999,999,999,999 + 750,000,000,000,000 − 8,249,999,999,999,999 = 0Rc′ = 0.008249999999999999 ETH; 0 ETH of the curve share moves to the floor reserveThe sweep is the rounding the integer curve could not absorb: a few wei at most when the guard does not bind.GridPadMath.buy()
  5. Fill the floor reserveRf′ = Rf + toFloor + sweep
    Rf
    2,500,000,000,000,001 wei
    toFloor
    250,000,000,000,000 wei
    sweep
    0 wei
    2,500,000,000,000,001 + 250,000,000,000,000 + 0 = 2,750,000,000,000,001Rf′ = 0.002750000000000001 ETHGridPadMath.buy()
  6. The new floorP_floor′ = ⌊Rf′ × 10¹⁸ ÷ S′⌋
    Rf′
    2,750,000,000,000,001 wei
    S′
    148,323,969,741,913,258,974,227 token-wei
    ⌊2,750,000,000,000,001 × 10¹⁸ ÷ 148,323,969,741,913,258,974,227⌋ = 18,540,496,21718,540,496,217 wei (0.000000018540496217 ETH) per token; before: 17,677,669,529 wei (0.000000017677669529 ETH) per tokenThe guard makes Rf′ × S ≥ Rf × S′, so the floor after a buy is never below the floor before it.GridPadMath.floorPrice()
  7. Every wei is accounted for(Rc′ + Rf′) − (Rc + Rf) = x
    Rc′ + Rf′
    11,000,000,000,000,000 wei
    Rc + Rf
    10,000,000,000,000,000 wei
    11,000,000,000,000,000 − 10,000,000,000,000,000 = 1,000,000,000,000,0000.001 ETH, the purchaseGridPadMath.buy()

The hub also refuses buys while they are paused and after a transaction’s deadline, and a buyer sets a minimum of tokens; the lab models none of these.

02 Floor & supply

hypothetical Example pool: after a buy
Pfloor=RfS,Pspot=k SRc=12 k S2\begin{gathered} P_{\mathrm{floor}} = \frac{R_f}{S}, \qquad P_{\mathrm{spot}} = k\,S \\ R_c = \tfrac{1}{2}\,k\,S^{2} \end{gathered}

Four numbers describe a pool. The floor is the floor reserve shared over the supply; spot is what the curve charges for the next token. They come from two different mechanisms, and the chart draws both reserves to scale.

Circulating supply
141,421 tokens141,421.356237309504880168 tokens
Curve reserve
0.007500 ETH7,499,999,999,999,999 wei
Floor reserve
0.002500 ETH2,500,000,000,000,001 wei
Spot price
0.000000106066 ETH106,066,017,177 wei per token
Redemption floor
0.0000000176777 ETH17,677,669,529 wei per tokenin ETH, not a dollar price
Floor ÷ spot
0.166never below a sixth, up to rounding
Spot − floor
0.0000000883883 ETH88,388,347,648 wei per token
Spot and floor against supplyAt a supply of 141,421 tokens, spot is 0.000000106066 ETH and the floor is 0.0000000176777 ETH per token. The triangle under the price line is the curve reserve, 0.007500 ETH; the rectangle under the floor is the floor reserve, 0.002500 ETH.
Curve reserve: the area under the price line, ½ · S · spot Floor reserve: floor × S
  • Passed: The slope is K0k = 750,000,000,000,000,000,000,000 (7.5 × 10⁻¹³ ETH per token², scaled by 10³⁶): since hub 1.1.0 no pool's slope changes, and an emptied pool restarts at K0.
  • Passed: The curve reserve is ½·k·S²curveValue(S, k) = ⌊k · S² ÷ (2 · 10⁵⁴)⌋ = 7,499,999,999,999,999 wei, the curve reserve: every token can be sold back to the curve.
  • Passed: The supply is within the capThe hub refuses any buy that would take the supply past 1,000,000,000,000,000 tokens (MAX_SUPPLY = 10³³ token-wei).
  • Passed: A pool with holders has a floor reserveEvery buy puts at least a quarter of its ETH into the floor reserve, and no exit empties it while tokens remain.
  • Passed: The floor reserve is at least a third of the curve reserve3 × 2,500,000,000,000,001 ≥ 7,499,999,999,999,999 wei. Each buy sends at least a third as much to the floor as to the curve, and sales, ragequits and rent only raise that share, so a reachable pool’s floor is at least a sixth of its spot price, up to rounding.
How this was calculated
  1. Redemption floorP_floor = ⌊Rf × 10¹⁸ ÷ S⌋
    Rf
    2,500,000,000,000,001 wei
    S
    141,421,356,237,309,504,880,168 token-wei
    ⌊2,500,000,000,000,001 × 10¹⁸ ÷ 141,421,356,237,309,504,880,168⌋ = 17,677,669,52917,677,669,529 wei (0.000000017677669529 ETH) per tokenEach token’s share of the floor reserve: what a ragequit of one whole token pays, in ETH. It is not a promised dollar price.GridPadMath.floorPrice()
  2. Spot priceP_spot = ⌊k × S ÷ 10³⁶⌋
    k
    750,000,000,000,000,000,000,000
    S
    141,421,356,237,309,504,880,168 token-wei
    ⌊750,000,000,000,000,000,000,000 × 141,421,356,237,309,504,880,168 ÷ 10³⁶⌋ = 106,066,017,177106,066,017,177 wei (0.000000106066017177 ETH) per tokenWhat the curve charges for the next token. It moves with every buy and sale; the floor moves only up.GridPadMath.spotPrice()
  3. Curve reserveRc = ⌊k × S² ÷ 2 · 10⁵⁴⌋ (½ · k · S²)
    k
    750,000,000,000,000,000,000,000
    S
    141,421,356,237,309,504,880,168 token-wei
    ⌊750,000,000,000,000,000,000,000 × 141,421,356,237,309,504,880,168² ÷ 2 · 10⁵⁴⌋ = 7,499,999,999,999,9990.007499999999999999 ETHThe area under the price line from 0 to S: enough to buy every token back on the curve.GridPadMath.curveValue()
  4. Floor against spotfloor ÷ spot, spot − floor
    floor
    17,677,669,529 wei
    spot
    106,066,017,177 wei
    17,677,669,529 ÷ 106,066,017,177 = 0.166; 106,066,017,177 − 17,677,669,529 = 88,388,347,648floor = 0.166 × spot; spot is 88,388,347,648 wei (0.000000088388347648 ETH) per token above the floorRent and sales raise the floor without raising spot, so the floor can sit above spot. It never falls below a sixth of spot, up to rounding.GridPadMath.floorPrice(), spotPrice()

03 Ragequit

hypothetical Example pool: after a buy
out(b)=⌊b RfS⌋,S′=S−bRf′=Rf−out(b)+12 k b (2S−b)b=S:  out=Rc+Rf\begin{gathered} \mathrm{out}(b) = \left\lfloor \frac{b\,R_f}{S} \right\rfloor, \qquad S' = S - b \\ R_f' = R_f - \mathrm{out}(b) + \tfrac{1}{2}\,k\,b\,(2S - b) \\ b = S:\ \ \mathrm{out} = R_c + R_f \end{gathered}

Burn tokens for exactly their share of the floor reserve. The payout does not depend on spot, and the burned tokens’ curve value stays behind for the holders who remain.

Payout
0.000250 ETH250,000,000,000,000 weiin ETH
Tokens burned
14,142 tokens14,142.135623730950488016 tokens
Supply after
127,279 tokens127,279.220613578554392152 tokens
Floor reserve after
0.003675 ETH3,675,000,000,000,000 wei
Curve value left to the floor
0.001425 ETH1,424,999,999,999,999 wei
Floor
0.0000000176777 ETH → 0.0000000288735 ETH17,677,669,529 → 28,873,526,898 wei per token+63.33% for the holders who stay
Reserves before
After, with the payout
How this was calculated
  1. The floor beforeP_floor = ⌊Rf × 10¹⁸ ÷ S⌋
    Rf
    2,500,000,000,000,001 wei
    S
    141,421,356,237,309,504,880,168 token-wei
    ⌊2,500,000,000,000,001 × 10¹⁸ ÷ 141,421,356,237,309,504,880,168⌋ = 17,677,669,52917,677,669,529 wei (0.000000017677669529 ETH) per tokenGridPadMath.floorPrice()
  2. The payoutout = ⌊b × Rf ÷ S⌋
    b
    14,142,135,623,730,950,488,016 token-wei
    Rf
    2,500,000,000,000,001 wei
    S
    141,421,356,237,309,504,880,168 token-wei
    ⌊14,142,135,623,730,950,488,016 × 2,500,000,000,000,001 ÷ 141,421,356,237,309,504,880,168⌋ = 250,000,000,000,000out = 0.00025 ETHThe contract multiplies before it divides, so the payout is b’s exact share of the floor reserve rounded down once, not b times the rounded floor price.GridPadMath.ragequit()
  3. The burned tokens’ curve value staysrelease = Rc − ⌊k × (S − b)² ÷ 2 · 10⁵⁴⌋ (½ · k · b · (2S − b))
    Rc
    7,499,999,999,999,999 wei
    S − b
    127,279,220,613,578,554,392,152 token-wei
    7,499,999,999,999,999 − 6,075,000,000,000,000 = 1,424,999,999,999,9990.001424999999999999 ETH moves from the curve reserve to the floor reserveThe curve no longer owes anything for the burned tokens, so their curve value backs the holders who remain.GridPadMath.ragequit()
  4. The pool afterS′ = S − b, Rf′ = Rf − out + release
    Rf
    2,500,000,000,000,001 wei
    out
    250,000,000,000,000 wei
    release
    1,424,999,999,999,999 wei
    2,500,000,000,000,001 − 250,000,000,000,000 + 1,424,999,999,999,999 = 3,675,000,000,000,000S′ = 127,279.220613578554392152 tokens, Rf′ = 0.003675 ETHGridPadMath.ragequit()
  5. The floor afterP_floor′ = ⌊Rf′ × 10¹⁸ ÷ S′⌋
    Rf′
    3,675,000,000,000,000 wei
    S′
    127,279,220,613,578,554,392,152 token-wei
    ⌊3,675,000,000,000,000 × 10¹⁸ ÷ 127,279,220,613,578,554,392,152⌋ = 28,873,526,89828,873,526,898 wei (0.000000028873526898 ETH) per token; before: 17,677,669,529 wei (0.000000017677669529 ETH) per tokenout × S ≤ b × Rf, so Rf′ ÷ S′ ≥ Rf ÷ S: a ragequit never lowers the floor for those who stay.GridPadMath.ragequit()
  • Not a transaction: the lab only calculates, and nothing is sent.
  • The payout is in ETH, and ETH’s dollar value changes.
  • Nothing here promises a profit or a fixed dollar value.
  • A real ragequit pays from the token’s state when it executes, which can differ from the state used here.

04 Protocol reference

The rules

Split
toCurve = ⌊3x ÷ 4⌋, the rest to the floor reserve
Slope
K0 = 750,000,000,000,000,000,000,000 (7.5 × 10⁻¹³ ETH per token², × 10³⁶), the same for every pool since v1.1.0
Smallest buy
MIN_BUY = 10⁹ wei (0.000000001 ETH)
Supply cap
MAX_SUPPLY = 10³³ token-wei (1,000,000,000,000,000 tokens)
Precision
18 decimals for ETH and for tokens; every division rounds down, in the pool’s favour

Where they live

  • GridPadMath.sol: buy, sell, ragequit, curveValue, spotPrice, floorPrice
  • GridPadHub.sol: the refusals (MIN_BUY, a zero payout, the supply cap) and the restart of an emptied pool at K0
  • src/lib/protocol/hub-math.ts: the exact mirror the lab runs, held to the wei against a local hub, a fork of the mainnet hub and the mainnet hub’s recorded trades
  • The ratchet math, formulas 1 to 9, and token analytics

The deployed contract

Network
Robinhood Chain Mainnet · chain 4663
Implementation
0x0115…5111 ↗ · v1.1.0 · verified source ↗
Verified
against the live hub on 17 October 2026 at block 90,882,978 (deployment record)