C558 — Generate the fixed-Joseph comparison family

Question

Can one flank-transfer formula reproduce all nine comparison states?

Inputs

{
  "regular_Joseph": [
    1915,
    1805
  ],
  "phases": [
    0,
    3,
    "7/2"
  ],
  "clutch": [
    0,
    7,
    14
  ]
}

Sources

[
  "File62 §§6.1–6.4"
]

Opened utc

2026-09-28T00:13:53.938889+00:00

Results

{
  "partitions": [
    [
      18,
      9,
      83
    ],
    [
      11,
      16,
      83
    ],
    [
      4,
      23,
      83
    ],
    [
      "43/2",
      "11/2",
      83
    ],
    [
      "29/2",
      "25/2",
      83
    ],
    [
      "15/2",
      "39/2",
      83
    ],
    [
      21,
      6,
      83
    ],
    [
      14,
      13,
      83
    ],
    [
      7,
      20,
      83
    ]
  ],
  "formula": [
    "18+p−d",
    "9−p+d",
    "83"
  ]
}

Finding

The clutch transfers duration between two flanks while preserving their27 total and the83 overlap. All nine states follow without moving regular Joseph1915–1805.

Reassessment

Test whether the reported cyclic symmetry acts on dates or on duration components.

Checks

{
  "nine": true,
  "totals": true
}

Closed utc

2026-09-28T00:13:53.939439+00:00

Record provenance

Exact record hash: b91c3ca9bc4a64f1989f0bd86f9b584dec686a7ba001f9a48b4ae95796aa0f35

Source journal: Research_Cycles/C0532_C0631/journal.json