Orbital

Research · 3 of 3

Against the paper

The paper ends with the authors noting that “Today, Orbital is just a design.” Turning it into a contract meant one correction, one new algorithm and two designs the paper leaves open.

8 min read

Contents

1The map

Each line pairs what the paper says with what the contract does, and links to the reasoning. Each result carries its evidence: proved on the stored integers, tested against independent oracles, or measured on a local chain.

In the paperIn this implementationRead
The Global Trade Invariant takes the boundary radius as a root of the summed (r,k)(r, k). Corrected sbound=∑sis_{bound} = \sum s_i, as the Tick Consolidation section states. The marginal price stays continuous when a tick crosses. Math 2
A trade is split at every tick crossing, with a closed-form crossover and Newton on each segment. Replaced That segmentation does not survive integer rounding. We solve the trade's endpoint directly, prove every stored state is on the pool side of the surface, and read each tick's fees from the trade's two ends. Math 3–5
“Each tick has only a single LP”; deposits and withdrawals are not described. Designed Several LPs per tick. Deposits keep the state's depth, and the LP pays the rounding. Math 7
Fees are not discussed. Designed Each tick's fees are read from the trade's two ends, with no event path. Math 8
“Today, Orbital is just a design.” Measured Live on Polygon, with a TypeScript SDK that reproduces its quotes to the wei. With the same capital, Orbital beats three Uniswap V3 pools on slippage. It beats Curve at the peg when LPs concentrate, and loses to Curve against wider positions. Benchmarks

A smaller note: the paper's Computation formula sums xintx_{int} in its first term. The derivation just above it gives xtotalx_{total}, since αint=xtotal⋅v−kbound\alpha_{int} = x_{total} \cdot v - k_{bound}.

2Open questions

In shortFour questions we would like the paper's authors, and anyone who has thought about Orbital, to weigh in on.

  1. Question 1 · Math 8

    Net or gross absorption

    Our fees pay each tick its net absorption between a swap's two ends. Should a swap that turns at pair parity also pay for the input a tick absorbs and gives back? If so, can that flow be measured at constant cost without an event path?

  2. Question 2 · Math 8

    A cheaper fee model

    Fees are not in the paper. Ours no longer follow the path, but every flipped tick must still record its accrued fees, two words per asset, so this work grows with nn. Do you see a fee model for Orbital that needs less per-tick work at a flip?

  3. Question 3 · How it works 2

    Tick spacing

    Every flip costs gas, which argues for fewer planes, while LPs want fine choices near the peg. Our catalog now follows the Renard R40 series: forty ticks per decade of depeg distance, about 6% apart, so neighbouring ticks differ by at most about 7% in capital efficiency. Is there a better criterion?

  4. Question 4

    Other implementations

    Do you know of another implementation of Orbital, onchain or in production? If none exists more than a year after the paper, what do you see as the main obstacle: integer arithmetic, the gas of tick crossings, LP demand, or something else?

Have an answer, or a proof we should see?

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3Status

Live
On Polygon since 6 October 2026, redeployed on 21 October 2026 with the contract these pages describe.
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Notes
The full technical notes, the engine's decision record and its proofs are available on request.