Liquidity topology

Because liquidity separates per asset, an asset becomes a vertex carrying its own liquidity, and a pool becomes the structure connecting vertices — a liquidity graph. The topology of that graph is a design choice, and it has consequences.

Delta liquidity

Each asset (vertex) is linked to every other asset through a dedicated liquidity edge — a complete graph. The graph contains cycles, so pairwise prices can disagree along a loop: delta topologies fit sets of assets with little internal arbitrage (e.g. stablecoins), where the cycles stay quiet.

In the implementation, a delta pool carries the $n(n-1)/2$ pairwise prices of its upper triangle ($P[i][j]$ = "asset $j$ per asset $i$") and supports up to 8 assets.

Star liquidity

All assets are linked through a single central hub: the star pool. Every pair is a path through the hub, and the graph is a tree — it contains no cycle, so no internal arbitrage path exists. The topology is non-arbitrageable by construction: every pair is priced consistently through the hub.

This property is where the design pays:

• For consumers and solvers — with no internal arbitrage to feed, the liquidity is more efficient, and optimal routing is explicit by design: there is exactly one path between any two assets. $n$ prices instead of $n(n-1)/2$.
• For producers — the hub liquidity serves every pair at once, so it is high-yield, and the fees that internal arbitrage would have extracted remain in the pool.
• Against fragmentation — one star pool replaces a mesh of pairwise pools.

In the implementation, a star pool carries $n$ prices ("LP per asset $i$") and supports up to 16 assets. Single-asset entry and exit (zaps) are native to the star topology.

The electrical similitude of the model becomes literal here: liquidity composes across the graph exactly as conductance composes across a circuit, and the star–mesh transform of circuit theory is the formal statement of the equivalence between the two topologies.

Gamma liquidity

TODO