# C1040 — Primitive common-Key landing condition

## Question

Which relation among source paths makes the two expanded points agree?

## Inputs

```json
{}
```

## Sources

```json
[
  "File60 common1566 comparison",
  "C1032",
  "C1039"
]
```

## Opened utc

2026-09-28T04:04:12.331008+00:00

## Results

```json
{
  "generated_radii": [
    299,
    276
  ],
  "primitive_residual": 0,
  "generated_points": [
    1566,
    1566
  ],
  "difference_formula": "pointE−pointJ = −25/299 · (13w−12u)"
}
```

## Finding

The two routes agree exactly when13 times the Joseph radius equals12 times the Levi radius. The radii299/276 and common1566 point are generated from the local source paths.

## Reassessment

Measure the additional constraint that this cycle imposes.

## Checks

```json
{
  "radii": true,
  "common": true,
  "identity": true
}
```

## Closed utc

2026-09-28T04:04:12.331604+00:00

## Record provenance

Exact record hash: `f96d1504ac6faa43ebfdcedbc85c4f8b127d075b0c0c85da056e5067b9bcb96c`

Source journal: `Research_Cycles/C0932_C1131/journal.json`