# C756 — Transfer the cumulative residual field to LXX

## Question

Which changed rows explain every LXX-versus-MT rounding difference?

## Inputs

```json
{}
```

## Sources

```json
[
  "File18 LXX main rows; File51a rounding rule"
]
```

## Opened utc

2026-09-28T01:54:26.912804+00:00

## Results

```json
{
  "fields": {
    "path": "model/all_rounding_fields.json",
    "sha256": "6ce58f06e5687e621578a52663a0d6f32b50d3b1cd1ad74ff2cc4225a359c6fe",
    "bytes": 7609
  },
  "row_support": {
    "Lamech": 4,
    "Arphaxad": -2,
    "Shelah": -2
  },
  "nonzero_boundary_differences": {
    "Noah": -4,
    "Shem": -4,
    "Arphaxad": -4,
    "Shelah": -2
  }
}
```

## Finding

Three LXX residual changes generate the complete comparison: Lamech+4, Arphaxad−2, Shelah−2. Their total cancels, but the Noah–Arphaxad plateau changes−4 and Shelah−2.

## Reassessment

Test SP support and explain its changed head residual.

## Checks

```json
{
  "support": true,
  "Cainan_zero": true,
  "head_cancellation": true
}
```

## Closed utc

2026-09-28T01:55:00.997945+00:00

## Record provenance

Exact record hash: `95754f018c38b8c8d789bc6f0a9e99c8b51be630e86637c2c458e77284441cb6`

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