# Finite Certificates

## Level-18 LP Certificate

Parameters:

```text
k                     18
gamma                 901/1000
principal rows        3^17 = 129,140,163
auxiliary rows        3^16 = 43,046,721
coefficient scale     2^28
minimum weight        2^20
payload bytes         516,560,652
```

The coefficient numerators are:

```text
lambda^(-2)           76,981,049
lambda^(alpha-2)     207,142,911
lambda^(alpha-1)     386,810,365
```

All `129,140,163` exact inequalities pass. The least integer margin is
`4,147,742,755`, at principal index `18,958,255` and residue `56,874,767`.

Payload SHA-256:

```text
fc96181c552398be8bbc4c0a47482a53c4ff847059bf7fd4b9be11837ca7c34c
```

## Adaptive-Potential Certificate

The potential has one unsigned byte for every level-18 principal residue and
lies in `0..34`. For each D1 and D3 auxiliary row, the policy keeps a lift of
least certified potential, with ties resolved in the order `0, 1, 2`.

Checked inequalities:

```text
principal             129,140,163
D1 adaptive            43,046,721
D3 adaptive            43,046,721
total                 215,233,605
```

The selected-lift counts for each auxiliary family are:

```text
lift 0                 42,561,920
lift 1                    484,085
lift 2                        716
```

Payload SHA-256:

```text
778584ce7635639ab2a0c7de766f81e8f551b0a52f96ca51eb2bb128c3248f52
```

## Transport Encoding

The two binary payloads are represented by 20 tracked hexadecimal chunks,
each below 64 MiB. Lean streams the chunks through
`ChunkedEncoding.lean`. The materializer reconstructs the binary forms for
external verification and checks aggregate byte counts and hashes.