Glossary
Symbols, notation, and shorthand used throughout the protocol pages.
AMM state
| Symbol | Type | Meaning |
|---|---|---|
N | integer | Number of bins in the market. Set at creation, range [2, 256]. |
xᵢ | u64 | Position in outcome i. Zero-indexed i ∈ [0, N). |
x | u64[N] | Position vector across all outcomes |
hᵢ | u64 | AMM holding of outcome-i tokens. Related: hᵢ = k − xᵢ. |
k | u64 | L₂ norm: k = √(Σ xᵢ²). Fixed by invariant; updated only on liquidity events. |
‖x‖₂ | scalar | L₂ norm of position vector, equal to k. |
Probabilities
| Symbol | Type | Meaning |
|---|---|---|
pᵢ | scaled int | True (calibrated) probability of outcome i. |
p̂ᵢ | scaled int | Implied probability extracted from AMM state: p̂ᵢ = xᵢ²/k². Quadratically distorted. |
p | int[N] | Calibrated probability vector. Recoverable from p̂ via pᵢ = √p̂ᵢ / Σⱼ √p̂ⱼ. |
Continuous markets
| Symbol | Type | Meaning |
|---|---|---|
[a, b] | (u64, u64) | Range of the continuous outcome value. |
bin | integer | Bin index. Continuous range divided into N equal-width bins. |
centerⱼ | u64 | Midpoint of bin j: centerⱼ = a + (2j+1)(b−a)/(2N). |
μ | u64 | Trader's center: where they think the value lands. |
σ | u64 | Trader's conviction: standard deviation of the curve. |
zⱼ | scaled int | Standardized z-score for bin j: zⱼ = (centerⱼ − μ)/σ. |
wⱼ | scaled int | Unnormalized PDF weight: wⱼ = exp(−zⱼ²/2). |
Wⱼ | scaled int | Normalized weight: Wⱼ = wⱼ · S / Σ wⱼ. Integer-valued. |
S | constant | Weight scale: S = 10⁹. So Σ Wⱼ = S. |
Z_CUTOFF | constant | 5. Bins with ` |
Trading
| Symbol | Type | Meaning |
|---|---|---|
c | u64 | Collateral amount (in USDC base units) for a buy. |
t | u64 | Token amount returned to the AMM for a sell. |
T | u64 | Total token amount returned in a distribution sell. |
λ | u128 | Solved scalar for distribution buy: λ = √(XW² + W²(k'² − k²)) − XW. |
XW | u128 | Inner product: XW = Σⱼ xⱼ Wⱼ. |
W² | u128 | Squared L₂ norm of weights: W² = Σⱼ Wⱼ². |
k' | u64 | New L₂ norm after the operation. |
tokens_outⱼ | u64 | Tokens of outcome j received (positive = buy, negative = sell). |
Liquidity
| Symbol | Type | Meaning |
|---|---|---|
d | u64 | Collateral added in an LP deposit. |
s | u64 | LP shares burned in an LP withdraw. |
L_total | u64 | Total LP shares outstanding. |
L_initial | u64 | Initial liquidity at market creation. |
i_win | int | Bin index of the resolved outcome. |
Fees
| Symbol | Type | Meaning |
|---|---|---|
creation_fee_bps | u16 | Creation fee in basis points. Default 50 bps (0.5%). |
trade_fee_bps | u16 | Trade fee in basis points. Default 30 bps (0.3%). |
redemption_fee_bps | u16 | Redemption fee in basis points. Default 50 bps (0.5%). |
lp_fee_share_bps | u16 | LP share of trade fee in basis points. Default 5000 bps (50%). |
MAX_FEE_BPS | constant | 5000 (50%). Hard cap on any individual fee. |
Constants
| Symbol | Value | Meaning |
|---|---|---|
SCALE | 10⁹ | Fixed-point precision for non-collateral values. |
INVARIANT_TOL | 256 | Maximum allowed ` |
MAX_BINS | 256 | Cap on N (bins per market). |
Z_CUTOFF | 5 | σ multiples beyond which weight = 0. |
MIN_LIQUIDITY | 1 USDC | Floor for initial market liquidity. |
MIN_TRADE_AMOUNT | 0.001 USDC | Floor for any single trade. |
On-chain types
| Type | Bit width | Used for |
|---|---|---|
u64 | 64-bit unsigned | Token amounts, collateral, L₂ norms (USDC base units) |
u128 | 128-bit unsigned | Intermediate products that could overflow u64 × u64 |
Pubkey | 256-bit | Solana public keys for accounts and PDAs |
bps | u16 | Basis points (1 bp = 0.01%). All fees stored as u16. |
State machine
| State | Meaning |
|---|---|
Active | Market accepts trades and LP operations. Before deadline. |
PendingResolution | Deadline passed; awaiting oracle. New trades rejected; LP removes still allowed. |
Resolved | Oracle has reported a value. Claims open indefinitely. |
Operations (instruction names)
| Instruction | Effect |
|---|---|
create_market | Initialize a new market with parameters and seed liquidity. |
buy | Discrete buy on a single outcome. |
sell | Discrete sell of a single outcome's tokens. |
distribution_buy | Distribution buy with (μ, σ) over a continuous range. |
distribution_sell | Distribution sell of token holdings weighted by (μ, σ). |
add_liquidity | LP deposit. Mints LP shares. |
remove_liquidity | LP withdraw. Burns LP shares. |
resolve_market | Oracle posts the final value. |
claim_payout | Token holder redeems winning tokens for USDC. |