# C883 — Explain the authorized File51a Key chains

## Question

Do the exact civil inputs satisfy the full stagewise domains?

## Inputs

```json
{}
```

## Sources

```json
[
  "File51a author clarification lines26–66",
  "C880–881"
]
```

## Opened utc

2026-09-28T02:49:00.773966+00:00

## Results

```json
{
  "chains": [
    {
      "civil_input": 10051,
      "EE_chain": [
        10051,
        10925,
        11875
      ],
      "multiple529": 19
    },
    {
      "civil_input": 55016,
      "EE_chain": [
        55016,
        59800,
        65000
      ],
      "multiple529": 104,
      "EJ_chain": [
        55016,
        59800,
        60000
      ],
      "multiple6877": 8
    }
  ],
  "artifact": {
    "path": "model/File51a_authorized_key_chains.json",
    "sha256": "164285d8a6e23e20bbf840fa4de7a8c12dd5f5467fd650e8021a0ede0778a34c",
    "bytes": 330
  }
}
```

## Finding

Both source E² chains satisfy the529 domain; the55016→59800→60000 E→J chain satisfies6877. The general criterion explains their intermediate integrality while preserving their civil-count input roles.

## Reassessment

Test why the neighboring Rounded widths cannot replace those civil counts.

## Checks

```json
{
  "all_EE": true,
  "EJ": true
}
```

## Closed utc

2026-09-28T02:49:00.774613+00:00

## Record provenance

Exact record hash: `491c2725d66ca43170b69db7da36d6bb67121cb67c028da3d7732b7d31145dfb`

Source journal: `Research_Cycles/C0832_C0931/journal.json`