Glossary

Alphabetized definitions of terms used throughout the Taurus Swap documentation.

A

AMM (Automated Market Maker)

A decentralized exchange protocol that uses a mathematical formula (invariant) to price assets, rather than an order book. Examples: Uniswap, Curve, Orbital.

ASA (Algorand Standard Asset)

A token on Algorand, analogous to ERC-20 on Ethereum. Each ASA has a unique integer ID and metadata (name, decimals, total supply).

AVM (Algorand Virtual Machine)

The stack-based virtual machine that executes TEAL smart contracts. Provides opcodes for 512-bit math, square root, and box storage.

B

Box Storage

Algorand's key-value storage for smart contracts. Each box can hold up to 64KB, with a total limit of 64MB per app. Used for per-tick and per-position data in taurusSwap.

C

Concentrated Liquidity

A liquidity provision strategy where LPs provide capital only within a specific price range, rather than uniformly across all prices. Increases capital efficiency.

Consolidation

The process of combining multiple ticks into a single geometric object (a torus). Interior ticks sum their radii; boundary ticks contribute effective radii.

D

Depeg

When a stablecoin trades below its intended peg (e.g., USDC at $0.99 instead of $1.00). Orbital ticks are configured to cover specific depeg thresholds.

F

Fee Growth

A cumulative tracker of fees earned per unit of liquidity. Used to compute LP fee claims in O(1) time regardless of trade count.

I

Interior Tick

A tick whose reserves are strictly inside its boundary (x · v < k). The tick is actively providing liquidity.

O

Orbital AMM

An AMM design by Paradigm (White, Robinson, Moallemi, June 2025) that generalizes concentrated liquidity to n tokens using spherical geometry.

P

Polar Decomposition

The mathematical transformation x = αv + w that splits reserves into an equal-price component (α) and an orthogonal trading component (w).

S

Sphere Invariant

The equation Σ(r − xᵢ)² = r² that constrains reserves to an n-dimensional sphere. The foundation of Orbital AMM.

T

Tick

A concentrated liquidity zone defined by parameters (r, k). Geometrically, a spherical cap cut by a hyperplane.

Torus Invariant

The master equation r_int² = (α_int − r_int√n)² + (‖w‖ − s_bound)² that describes the consolidated pool state. Verified on every swap.

V

Virtual Reserves

The reserves a tick would have if it were the only liquidity source. Computed from tick parameters (r, k) using the virtual reserve formula.