C552 — Generate the cumulative root family

Question

Does one affine rule reconstruct all six source rails?

Inputs

{
  "base": [
    2435,
    2260,
    2080,
    1933,
    1796,
    1663,
    1526
  ],
  "phases": [
    0,
    "7/2"
  ],
  "clutch": [
    0,
    7,
    14
  ]
}

Sources

[
  "File62 §§1.2–1.4; File61 §§7.3A–7.6"
]

Opened utc

2026-09-28T00:12:31.275020+00:00

Results

{
  "rails": [
    [
      2435,
      2260,
      2080,
      1933,
      1796,
      1663,
      1526
    ],
    [
      2428,
      2253,
      2073,
      1926,
      1789,
      1656,
      1519
    ],
    [
      2421,
      2246,
      2066,
      1919,
      1782,
      1649,
      1512
    ],
    [
      "4877/2",
      "4527/2",
      "4167/2",
      "3873/2",
      "3599/2",
      "3333/2",
      "3059/2"
    ],
    [
      "4863/2",
      "4513/2",
      "4153/2",
      "3859/2",
      "3585/2",
      "3319/2",
      "3045/2"
    ],
    [
      "4849/2",
      "4499/2",
      "4139/2",
      "3845/2",
      "3571/2",
      "3305/2",
      "3031/2"
    ]
  ],
  "coordinate_matches": 42
}

Finding

C(p,d)=C0+p−d reconstructs all42 source coordinates. This is one family generated from seven inputs and two local state parameters, not42 independent successes.

Reassessment

Establish why the source clutch is14 and whether its three envelopes are independent.

Checks

{
  "six_rails": true,
  "invariant_spans": true
}

Closed utc

2026-09-28T00:12:31.275664+00:00

Record provenance

Exact record hash: ed4d4ba1528f03351c874e6224383840e9da8b1b703b22a8c50818d742eda54a

Source journal: Research_Cycles/C0532_C0631/journal.json