# C875 — Explain the existing completions by domain membership

## Question

Do established source scalars have different compatibility profiles?

## Inputs

```json
{
  "source_scalars": [
    460,
    690,
    483,
    12558
  ]
}
```

## Sources

```json
[
  "File46",
  "File63",
  "C831 inherited examples",
  "C874"
]
```

## Opened utc

2026-09-28T02:47:05.936749+00:00

## Results

```json
{
  "profiles": [
    {
      "input": 460,
      "images": {
        "E": 500,
        "P": "1400/3",
        "J": "6000/13"
      },
      "integer_keys": [
        "E"
      ],
      "input_on5Z": true
    },
    {
      "input": 690,
      "images": {
        "E": 750,
        "P": 700,
        "J": "9000/13"
      },
      "integer_keys": [
        "E",
        "P"
      ],
      "input_on5Z": true
    },
    {
      "input": 483,
      "images": {
        "E": 525,
        "P": 490,
        "J": "6300/13"
      },
      "integer_keys": [
        "E",
        "P"
      ],
      "input_on5Z": false
    },
    {
      "input": 12558,
      "images": {
        "E": 13650,
        "P": 12740,
        "J": 12600
      },
      "integer_keys": [
        "E",
        "P",
        "J"
      ],
      "input_on5Z": false
    }
  ],
  "artifact": {
    "path": "model/existing_key_profiles.json",
    "sha256": "f60bf0b288ce5e0edc4f6928749c64bacca0016149bfab9f40dbe827cccc2b6f",
    "bytes": 716
  }
}
```

## Finding

The familiar460,690,483 and12558 completions occupy different exact domains. Their compatibility follows from denominator divisibility; the new explanation is the shared criterion, not the old scalar outputs.

## Reassessment

Evaluate every row of the quarter-carrier family under the three Keys.

## Checks

```json
{
  "profiles": true,
  "all_three": true
}
```

## Closed utc

2026-09-28T02:47:05.937316+00:00

## Record provenance

Exact record hash: `eee6ede40cae40b2fa558ffecbf7ab870d84fac7ebb4883076f16d78147e0dd8`

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