C705 — Verify the whole-set affine mirror

Question

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

Inputs

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

Sources

[
  "Supplement A §13.2; C704"
]

Opened utc

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

Results

{
  "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

{
  "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