C559 — Locate the Joseph cyclic symmetry

Question

Does a three-cycle act consistently on the complete component family?

Inputs

{
  "rotation": "(a,b,c)→(b,c,a)"
}

Sources

[
  "File62 §§6.1–6.4; C558"
]

Opened utc

2026-09-28T00:14:08.923110+00:00

Results

{
  "states": 9,
  "component_displays": 27,
  "example": [
    [
      4,
      23,
      83
    ],
    [
      23,
      83,
      4
    ],
    [
      83,
      4,
      23
    ]
  ],
  "action_domain": "ordered duration triples"
}

Finding

A genuine C3 action rotates duration components and returns after three applications. It does not establish a permutation of historical people or complete chronology states.

Reassessment

Test how whole-year and exact phase choices change crossed containers.

Checks

{
  "all_rotations": true,
  "third_power_identity": true
}

Closed utc

2026-09-28T00:14:08.923700+00:00

Record provenance

Exact record hash: a22fb0384fb192c1b75b6ee07ee84c20b8fb963fa4a8e3f94493c549c335dd5a

Source journal: Research_Cycles/C0532_C0631/journal.json