> ## Documentation Index
> Fetch the complete documentation index at: https://knot-38d8bd0e.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Adversarial results

> Every number, and the command that reproduces it.

These results keep the mechanism's favorable and unfavorable cases together. Every number below
comes from a named KNOT test that can be rerun from the repository.

```bash theme={null}
forge test --match-contract MEVProtectionTest -vv
forge test --match-contract EconomicViabilityTest -vv
forge test --match-contract RouterRealismTest -vv
```

## Constructed round-trip fixture

The same synthetic reserve sequence, run with and without the federation:

| | Attacker P\&L, 5-token stake |
| - | - |
| Independent pools | **+13.5843**, profitable |
| Under Knot | **-0.0298**, a loss |
| **Difference between fixtures** | **13.6141** |

The KNOT path is lower at every sampled size, from 0.1 to 20 tokens. This proves the mechanics of
that constructed sequence; it is not a historical replay or a production-profit forecast.

## Routing

The router fixtures check quote ordering, not organic order flow:

| | |
| - | - |
| Samples routed between the two members | **40**, all land on a member by construction |
| Deep member vs an identical outside pool | **0 wins · 40 ties · 0 losses** |

The external control has the same reserves and fee as the deep member, so a tie is the only honest
result. These tests do not establish how a production router or real flow would respond.

## Same-member sandwich fixtures

The attacker sells the exact output inventory acquired in the front-run, so both portfolios close
in currency0.

| Fixture | KNOT attacker delta | Hookless control |
| - | -: | -: |
| Skewed member | **-1.347578** | not the control used for this regression |
| Balanced member | **≈+0.393701** | **≈+1.803279** |

KNOT dampens the balanced fixture but does not eliminate the sandwich profit. The skewed fixture
closes at a loss. These are bounded simulation results, not a universal MEV claim.

## Skew sensitivity

| Skew | Isolated-quote reduction |
| - | - |
| 1× (balanced) | 0 bps |
| 2× | 4,299 bps |
| 4× | 6,674 bps |
| 6× | 7,466 bps |
| 8× | 7,862 bps |

An earlier version divided retained output tokens by hypothetical input-token fees. That ratio was
dimensionally invalid and has been removed. A normalized fixture can compare both values in one
numeraire, but it still would not measure routing loss or realised LP returns, so it is not used as
a headline claim.

## Stateful

Twelve sequential extraction attempts with state carried forward: the quote for a fixed size falls
from 1.2678 to 1.2406. The test advances the member and aggregate books with the gross input on
every step, matching `executeSwap`. In this sequence the fixed-size quote tightens as reserves move.


This documentation is built and hosted on [Mintlify](https://mintlify.com), a developer documentation platform.