# C642 — Reconstruct the no-Cainan companion

## Question

Which relations survive when the Creation rail alone moves130?

## Inputs

```json
{
  "standard_Creation": [
    4121,
    4114,
    4107
  ],
  "Joseph": [
    1885,
    1878,
    1871
  ],
  "standard_exposure": 4108
}
```

## Sources

```json
[
  "File70 §§6.1,6.6"
]
```

## Opened utc

2026-09-28T00:59:33.175668+00:00

## Results

```json
{
  "span_family": [
    2210,
    2222,
    2236,
    2250
  ],
  "corresponding_spans": [
    2236,
    2236,
    2236
  ],
  "calendar_half_counts": [
    "221/18",
    "1111/84",
    "86/7"
  ],
  "shift_from_restored": 130
}
```

## Finding

Removing130 preserves both7+7 rails and all their relative diagonals, giving2236 as the corresponding translation. It changes the calendar counts to nonintegers, so the restored state’s13/14/13 specialization is not automatic from rail shape alone.

## Reassessment

Ask whether the fixed standard state and three-calendar conditions select130 as the least nonnegative correction.

## Checks

```json
{
  "companion": true,
  "shape": true,
  "counts_changed": true
}
```

## Closed utc

2026-09-28T00:59:33.175833+00:00

## Record provenance

Exact record hash: `bfffe3745aa25cf6e552ea3071d48994bddd5bd76620a6756efff51414405fdc`

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