Refresh Interval Economics for Fragmented AMM Settlement Networks

Fragmentation Doesn’t Scale Gracefully

If every asset must trade directly with every other asset, the number of liquidity pools grows quadratically. Hub architectures reduce this to linear growth — but linear growth is still expensive when liquidity must be pre-funded in parallel.

Even with a hub, thousands of pools still require thousands of buffers.

Prior research showed that fragmentation increases required liquidity dramatically.
What it did not show was whether velocity could realistically offset that cost — and under what conditions.That missing piece is what this paper resolves.

What Actually Scales With Time — and What Doesn’t

The Jackson Liquidity Framework defines total liquidity requirements as the maximum of several constraints:
- slippage tolerance (size-based)
- directional flow Value-at-Risk
- intraday peak depletion
- Basel-aligned buffers

Critically, not all of these respond to velocity in the same way.

Time-based buffers inherit a √T scaling from variance and stability conditions. Slippage constraints do not.

This creates two fundamentally different regimes:
- a buffer-limited regime, where faster refresh materially reduces required liquidity
- a slippage-limited regime, where speed no longer helps

This distinction turns out to be decisive.

The Hard Limit
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Why Velocity Stops Helping

Speed does not eliminate slippage.

When trade-size constraints dominate, liquidity requirements hit a floor that velocity cannot compress further.

The paper shows explicitly that once the slippage constraint binds, faster refresh yields diminishing — and eventually zero — benefit.

This is the critical reason why:
“Speed alone eradicates fragmentation” is directionally true but mechanically incomplete.

Any viable architecture must answer both:

- how fast liquidity can be reused
- and how trade size is controlled or netted