# C709 — Separate Short and Long whole-field translations

## Question

Does a50-shifted center preserve the5842 whole-field closure requirement?

## Inputs

```json
{
  "Short_center": -2921,
  "Long_center": -2871,
  "shape": "same fixed phase template"
}
```

## Sources

```json
[
  "Supplement A §13.9; C707"
]
```

## Opened utc

2026-09-28T01:19:36.381089+00:00

## Results

```json
{
  "self_mirror_lengths": [
    5842,
    5742
  ],
  "length_difference": 100,
  "Long_center_residual_under5842": 100
}
```

## Finding

The supplied Long center requires5742 for its own mirror closure,100 less than the Short field’s5842. A50 center displacement doubles in the required translation. No adjacent state or remote extension is introduced to erase this distinction.

## Reassessment

Compare the conserved quantities across the now-completed chronological mechanisms.

## Checks

```json
{
  "lengths": true,
  "double_shift": true,
  "fixed5842_fails": true
}
```

## Closed utc

2026-09-28T01:19:36.381472+00:00

## Record provenance

Exact record hash: `f699d548aa4d3dbd3fc8d791a624fc57e81fed7ac6e8617c0c6dbd76278467fc`

Source journal: `Research_Cycles/C0632_C0731/journal.json`