# C884 — Keep civil counts distinct from Rounded widths

## Question

What arithmetic changes if neighboring width labels are substituted?

## Inputs

```json
{}
```

## Sources

```json
[
  "File51a C versus W_R",
  "C883"
]
```

## Opened utc

2026-09-28T02:49:14.772691+00:00

## Results

```json
{
  "responses": [
    {
      "civil": 10051,
      "Rounded_width": 10050,
      "difference": 1,
      "E_width": "251250/23",
      "EE_width": "6281250/529",
      "E_difference": "25/23",
      "EE_difference": "625/529"
    },
    {
      "civil": 55016,
      "Rounded_width": 55015,
      "difference": 1,
      "E_width": "1375375/23",
      "EE_width": "34384375/529",
      "E_difference": "25/23",
      "EE_difference": "625/529"
    }
  ],
  "artifact": {
    "path": "model/civil_Rounded_input_distinction.json",
    "sha256": "2818366718815ab42ed4bfa9fed56973a9eca69ecd8a361434b9b59ddeead1ca",
    "bytes": 399
  }
}
```

## Finding

The one-unit source-type difference propagates as25/23 after E and625/529 after E². Replacing the civil inputs by neighboring Rounded widths destroys the stated integral chains; matching near labels does not authorize type substitution.

## Reassessment

Test the predetermined six distinct-Key orders as a bounded confirmation of the prefix theorem.

## Checks

```json
{
  "one_unit": true,
  "not_integral": true
}
```

## Closed utc

2026-09-28T02:49:14.773333+00:00

## Record provenance

Exact record hash: `34d59c102e42aebe0080d9e4634eca0b74cb00ca46ca9fc9ddba4a161552b479`

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