# C1009 — Joint Esau reconstruction

## Question

Do combined source registers recover all nine original counts?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1008",
  "File58 §13"
]
```

## Opened utc

2026-09-28T03:57:22.081645+00:00

## Results

```json
{
  "measurement_field": {
    "path": "model/esau_joint_measurements.json",
    "sha256": "77a91c74e28f7c20eb73c4696dd716bf02c5dd479498c60cd93f15f7cde55c1c",
    "bytes": 1374
  },
  "rank": 9,
  "recovered": [
    200,
    20,
    200,
    20,
    40,
    10,
    30,
    20,
    10
  ]
}
```

## Finding

The two ordered registers plus grand total recover every supplied count. This extends the separate-register analysis to the whole list.

## Reassessment

Remove the grand total to identify its exact information contribution.

## Checks

```json
{
  "full_rank": true,
  "complete_reconstruction": true
}
```

## Closed utc

2026-09-28T03:57:22.087796+00:00

## Record provenance

Exact record hash: `a5d9dfdf1f3a063c81f43ffd9f4207ddc565c537d972d58c5d2947cb93d82763`

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