# C759 — Test Cainan residual neutrality

## Question

Does insertion change existing rounding discrepancies?

## Inputs

```json
{
  "Cainan": {
    "b": 130,
    "r": 330,
    "L": 460
  }
}
```

## Sources

```json
[
  "File18 Cainan; C754–758"
]
```

## Opened utc

2026-09-28T01:55:40.386236+00:00

## Results

```json
{
  "results": {
    "MT_native_OFF": {
      "all_common_residuals_equal": true,
      "new_node_D": 3,
      "Shelah_D": 3
    },
    "LXX_native_ON": {
      "all_common_residuals_equal": true,
      "new_node_D": 1,
      "Shelah_D": 1
    },
    "SP_native_OFF": {
      "all_common_residuals_equal": true,
      "new_node_D": 3,
      "Shelah_D": 3
    }
  },
  "duration_residuals": [
    0,
    0,
    0
  ]
}
```

## Finding

Cainan insertion changes admitted durations but preserves every corresponding residual. Its new boundary inherits the local plateau; zero row residual does not imply zero boundary displacement.

## Reassessment

Prove rounding compatibility with admitted multiples-of-five changes.

## Checks

```json
{
  "common_fields": true,
  "new_boundary_plateau": true
}
```

## Closed utc

2026-09-28T01:55:40.387507+00:00

## Record provenance

Exact record hash: `cd85ec2c4401020e37048487163d33a63146f8f0701477b6a985ea7df6aec364`

Source journal: `Research_Cycles/C0732_C0831/journal.json`