# C1011 — Integral Esau measurement basis

## Question

Is the nine-measurement inverse an integer change of coordinates?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1009",
  "C1010"
]
```

## Opened utc

2026-09-28T03:57:55.869076+00:00

## Results

```json
{
  "basis": {
    "path": "model/esau_unimodular_basis.json",
    "sha256": "83d11fc1240a420d893079b9221cd8a96975e05026795c616070d13a21c51b38",
    "bytes": 1936
  },
  "determinant": 1,
  "reconstructed": [
    200,
    20,
    200,
    20,
    40,
    10,
    30,
    20,
    10
  ]
}
```

## Finding

The compact Esau basis has determinant1 and an integer inverse. It changes coordinates without fractional adjustment; it does not reduce nine independent numbers to fewer than nine.

## Reassessment

Compare with the complete clean-plus-unclean walk basis.

## Checks

```json
{
  "unimodular": true,
  "integral_inverse": true,
  "recover_counts": true
}
```

## Closed utc

2026-09-28T03:57:55.872197+00:00

## Record provenance

Exact record hash: `bf52cb33ab85fe9d47f939003f22ab70bab079518eeeb2e0541e1219a569ae51`

Source journal: `Research_Cycles/C0932_C1131/journal.json`