KARST
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Depth adds up.
Liquidity does not.

Every venue reports a sum — total value locked, aggregate depth, liquidity across chains. What you can actually get out is capped by the narrowest cut between you and the exit, and widening anything outside that cut changes it by nothing at all.

Aquifer · plan30 × 22 · seed 20250830
carrying water rock sinks spring
step
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discharge
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vs start
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rock widened
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fractures in the cut
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as a share of the rock
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solver residual
·

A limestone massif, dissolving — not a loop and not a video. Rain enters at the sinks, leaves at the spring, and takes the easy way, and flow between two rock faces goes as the cube of the gap, so the easy way gets easier. Watch it long enough and one route breaks through. Every figure above, including the solver's own residual, is read out of the same state the drawing is.

S-01The claim

A sum is not a ceiling

Liquidity is a minimum, not a sum. Depth is reported as a total across a system; what leaves is capped by the narrowest point on one route, and no amount of depth elsewhere widens it.

This is not a hunch about market structure. It is Ford and Fulkerson's theorem: the most that can flow from a source to a sink is exactly the capacity of the cheapest set of edges whose removal separates them. Every edge outside that set can be widened without end, and the answer does not move.

The number a protocol prints is the sum over every edge. The number that decides your trade is a subset — usually a very small one. On the model above, after breakthrough, the cut is 7 fractures out of 2,218: 0.59% of the massif's cross-section. Widen the other 2,211 fiftyfold — total cross-section ×49.7 — and what the rock can deliver moves by 0.000000%. G5

S-02The same thing, in real pools

Two hops, and one of them is free

A trade routed through a token's own pool usually goes through WETH first. That first hop is the deepest pool on the chain: on its own it absorbs at least $1,000,000 inside one per cent. Of 52 two-hop routes here, 28 have a limit inside the sizes quoted at all, and their median is $1,498667× less than the hop they all pass through. It is not what stops them. G5

Read each of those at its own limit and ask what the deep hop contributed to the cost: at worst 6.66% of it, and at the median 0.013%. The other 24 routes reach one per cent below $100, the second size quoted, where the deep pool's own cost interpolates out of the reference itself — so their ratio would be a clamp, and they are left out and counted here instead.

Being routed through enormous liquidity buys you nothing. Your capacity is the other hop, and it always was.

The whole measurement, and a live quote →

0.001%0.010%0.10%1%slippage, log scale● what the deep pool cost◆ what the whole route cost — one per cent, by constructioncbBTC · 0.05%15×cbBTC · 0.3%15×wstETH · 0.01%292×cbBTC · 1%555×rETH · 0.05%588×AERO · 0.3%595×VIRTUAL · 0.05%641×wstETH · 0.05%1,417×cbETH · 0.05%1,488×USDT · 0.3%1,593×MORPHO · 0.3%1,962×the thin hop, ×
The eleven deepest of 28 two-hop routes with a measurable limit, each read at the size where its own slippage reaches one per cent — so every diamond sits on the same total, and the dot is what the WETH/USDC pool contributed to it. Log scale, because on a linear one the dot is narrower than a pixel. Uniswap V3 on Base, block 50,629,127. Aerodrome is not read — see the note on Conduit.
S-03The cliff
$10$1k$10k$100k$1000k0%25%50%75%100%trade size, USDCshare that holds within 1%— 20 tokens, best route— 97 pools, one at a time$100k — 2 of 20
Of 20 tokens verified on chain and 97 pools with live in-range liquidity, this is the share that absorbs a given size within one per cent. It is not a slope. 2 tokens hold $100,000; 2 hold a million.

The last stretch is the steep one

This paragraph said "it does not decay, it stops" until the curve was measured, and that was wrong: across 49 routes the median slippage grows as size to the 1.25 — worse than linear, and not a wall.

The wall is at the end. Going from a tenth of a per cent of slippage to one per cent takes only 2.0× more size at the median route, where a constant-product pool would need ten times more. And 12 of the 49 are steeper than a square law, up to size to the 6.2 — concentrated liquidity leaving the range it was placed in. G5

Meanwhile 60 of 97 pools — 62% of them — cannot absorb a thousand dollars within one per cent while still reporting live in-range liquidity.

S-04What is being built

Four instruments, and one number beside each

One of the four runs today. Route is live against Base — real pools, real quotes, a real swap. The vault and the receipt are written and their properties are executed on an EVM by the build, and they are not deployed. The other two are sentences. The state table says which is which and how to check each one.

S-05Why every number here has a letter next to it

The survey grade

Cavers grade a survey by how it was measured. A compass-and-tape traverse closed against a known station and a sketch drawn from memory are both surveys, and a drawing that does not say which one it is, is a drawing asking to be believed.

Every figure on this site carries that grade. The scale runs from G5 — read from a published standard or from the chain, reproducible by anybody — down to G1, which means nothing measured it and it is a plan or a preference, named as one.

The grade table, the constants, and the checks