# C1059 — All proper E prefixes remain fractional

## Question

Does an integral outer completion imply integral internal coordinates?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1058",
  "File52c §3.4"
]
```

## Opened utc

2026-09-28T04:09:17.331603+00:00

## Results

```json
{
  "prefix_field": {
    "path": "model/completed_path_prefix_field.json",
    "sha256": "c98eb407ba3004a21db63eb3b15047d068852f258f3c057c20f80431d6650339",
    "bytes": 1594
  },
  "residues_by_path": [
    [
      6,
      2,
      0
    ],
    [
      6,
      4,
      0
    ],
    [
      6,
      2,
      4,
      0
    ],
    [
      6,
      9,
      0
    ]
  ]
}
```

## Finding

All four paths complete14720→16000, but every proper E prefix remains fractional with denominator23. Integral outer completion is weaker than integral preservation of all source boundaries.

## Reassessment

Identify the finest numerical coarsening compatible with integral E block lengths.

## Checks

```json
{
  "whole_duration": true,
  "only_final_integral": true
}
```

## Closed utc

2026-09-28T04:09:17.332262+00:00

## Record provenance

Exact record hash: `00fa9a8467856f507863ed572ae15a8b117434c60c60ee28defc04087c4238ad`

Source journal: `Research_Cycles/C0932_C1131/journal.json`