# C1185 — Compare complete row recovery with two head differences

## Question

Can regular and cumulative totals distinguish the same five coefficients?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1182"
]
```

## Opened utc

2026-09-28T05:21:06.762307+00:00

## Results

```json
{
  "head_information": {
    "path": "model/whole_genealogy_head_information.json",
    "sha256": "855645f2d27bb371e76a02f8b5dcc6b46e64ebdaa303b4c33eb8bf74b49071c6",
    "bytes": 487
  },
  "head_differences": [
    1250,
    430
  ],
  "rank": 2,
  "lost_dimensions": 3
}
```

## Finding

The two heads see12.5u and3u+lambda+2a+e+n. Their values1250 and430 leave three coefficient directions invisible, even though all local row changes are recoverable from five named observations.

## Reassessment

Check whether the four-amplitude restriction restores that missing information.

## Checks

```json
{
  "expected_heads": true,
  "rank2": true,
  "kernel3": true
}
```

## Closed utc

2026-09-28T05:21:06.763813+00:00

## Record provenance

Exact record hash: `6a67cf88a2e9cc4663e984eccabf03a1a65a3b9aa0c8ac3871d288c473e99c5a`

Source journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`