Two pools you buy from must end at the same price
If they don't, moving one share from the dearer to the cheaper would have cost less — so you weren't finished. That single condition fixes how much goes to each pool, and it is all Shim solves for.
Live on Robinhood Chain
Shim
One share. One price.
A tokenized share on this chain does not have a price — it has a dozen. AAPL trades in eleven Uniswap pools at once, and your wallet sends the whole order to one of them. Shim works out the single price at which every pool agrees, buys from each one below it, sells into any that are above it, and hands you the shares. One transaction, and no contract of ours in it.
Shares it prices
49
279 pools read at one block
Pools that can't take $1.00
11
they quote a price and hold nothing
Our contracts
0
Uniswap's router, already live
One transaction, all or nothing
A floor the router enforces, not us
No contract of ours is deployed
Nothing is left in the router
The price at which every pool agrees
Call it lambda. Buy from every pool whose price, marked up by its own fee, is below it. Sell into every pool whose price, marked down by its fee, is above it. Trade each one exactly as far as lambda and no further. That is the cheapest fill that exists, and it is not a heuristic: profit is dollars out minus dollars in subject to the shares balancing, and the multiplier on that constraint is lambda.
A fee is not a gap
Two pools quoting the same number with a 0.30% fee each look 0.60% apart if you compare an ask to a bid. There is nothing there. Fees are why lambda sits strictly between the best ask and the best bid — and why most shares here have no gap at all.
The arbitrage is the same number
At zero net demand, buying below lambda and selling above it is the arbitrage. When your order passes a pool that is too high, it sells into it on the way past and the proceeds pay part of your bill.
What we found, which is not what we went looking for
The first version of this reported gaps of three to seven per cent on a dozen shares, and we nearly shipped it.
Every one of them was a pool holding a price and no liquidity. Its whole position sits outside the price window, so the price walks for free and the pool will not sell you a cent's worth. CRCL shows 574 basis points between its pools if you count every pool that quotes. Counting only the pools that can fill a $1.00 order, it shows -53.
So every pool is now asked, in both directions, whether it can absorb $1.00 inside the tick data Shim has actually read. Of 279 pools read across 49 shares, 11 cannot absorb $1.00 in either direction and 100 charge more than 1%. Of the 168 that are left, the pools of 48 shares out of 49 agree inside their own fees.
This chain is level. What it is not is deep. The disagreement worth money is not between the pools today — it is the one your own order creates, and it grows with size.
What it saves, by size
Measured against the best single pool — what a router that quotes every pool and picks the cheapest would charge for the same number of shares. Not the biggest pool, and not the worst: beating the worst is not a claim worth making.
| Order | Shares it helps | Median saved | In dollars | Split over 2+ pools | Chain can't fill |
|---|---|---|---|---|---|
| $1k | 44 | 0 bps | $0.00 | 55% | 5 |
| $10k | 42 | 1 bps | $1.05 | 69% | 7 |
| $50k | 36 | 6 bps | $32.76 | 81% | 11 |
| $250k | 24 | 13 bps | $343 | 88% | 23 |
On $1k it is worth 0 basis points and Shim says so. On $250k the median share saves 13 — $343 — and 23 of 49 shares cannot be filled at that size at all. The biggest single saving at $250k is MSTR, at $2,647 against its own best pool (v4 0.290%).
Proof
The same modules the page runs on, checked three ways. Every claim about a refusal has a control proving the same call goes through when the guard is not there.
On the real chain
39/39
Solidity properties executed by an eth_call with no to on Robinhood Chain itself — real creation code on the real evaluator, costing nothing and leaving nothing behind. 19 of 21 deliberate defects were caught by a named property; 2 are declared unobservable with the property that proves why.
Against frozen pool state
10,890
Assertions over 600 random orders against real pools, plus 15 named properties. 19 of 20 deliberate bugs caught. The fuzz found a real one: an order whose pools could not all be reached put the whole budget into the one pool it could, at six times the price next door.
Executed on a fork
21/21
A real wallet, the real Universal Router, real pools. A $100k order arrived with the shares the plan predicted, to the wei, and beat the best single pool by 27 basis points — executed, not simulated.
Price an order against every pool at once.
Shim shows you the split, the pools it refuses and why, and what the same order costs the ordinary way. Nothing is signed until you say so.
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