# C705 — Verify the whole-set affine mirror

## Question

Does the declared5842 translation match the mirror for every fixed node?

## Inputs

```json
{
  "center": -2921,
  "template_coefficients": [
    15,
    2,
    "1/4"
  ],
  "translation": 5842
}
```

## Sources

```json
[
  "Supplement A §13.2; C704"
]
```

## Opened utc

2026-09-28T01:18:37.278527+00:00

## Results

```json
{
  "transpositions": [
    [
      "-11753/4",
      "-11615/4"
    ],
    [
      "-11751/4",
      "-11617/4"
    ],
    [
      "-11745/4",
      "-11623/4"
    ],
    [
      "-11743/4",
      "-11625/4"
    ],
    [
      "-11737/4",
      "-11631/4"
    ],
    [
      "-11735/4",
      "-11633/4"
    ]
  ],
  "fixed_points": 0,
  "translated_equals_mirrored": true
}
```

## Finding

The5842 translation sends the entire fixed field onto its mirror; the associated reflection permutes it in six pairs with no fixed node. This is affine reflection of phase coordinates, distinct from decimal digit reversal and from File52c’s rounded mirror chart.

## Reassessment

Compare all four source-listed cycle totals against the same fixed set.

## Checks

```json
{
  "set_reflection": true,
  "double_reflection": true,
  "translation": true,
  "six_pairs": true
}
```

## Closed utc

2026-09-28T01:18:37.278975+00:00

## Record provenance

Exact record hash: `3ca6c07e4fdfc146cf513c30c5638764db6f6517c8e69613dc0b5d44257409bf`

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