# C1365 — Preserve the inverse register proof in the companion

## Question

What exact hypotheses support the aggregate convergence?

## Inputs

```json
{}
```

## Sources

```json
[
  "prep/final_inverse_keys_draft.md",
  "C1352"
]
```

## Opened utc

2026-09-28T06:36:17.980344+00:00

## Results

```json
{
  "supplement": {
    "path": "draft/technical_04_inverse.md",
    "sha256": "9c40e316533e3f5be3bce7ed2b629c54ca3a313adea1db781d6ba1af4f4dfa4c",
    "bytes": 1289
  }
}
```

## Finding

The companion retains the full register theorem with its two-component domain, carry alternatives and source-selected cumulative branch.

## Reassessment

Write the anchored-Key domain supplement.

## Checks

```json
{
  "domain": true,
  "branches": true,
  "source_cores": true
}
```

## Closed utc

2026-09-28T06:36:17.980859+00:00

## Record provenance

Exact record hash: `ad7bb8b329e68c998f1fa70a1df73a3491fb0cb8ef0cfce7a4866cafcdb81789`

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