# C757 — Transfer the residual field to SP

## Question

Why does SP gain three at the cumulative head?

## Inputs

```json
{}
```

## Sources

```json
[
  "File18 SP inclusive lifespan ledger; C756"
]
```

## Opened utc

2026-09-28T01:55:12.782893+00:00

## Results

```json
{
  "row_support": {
    "Methuselah": -1,
    "Lamech": 4
  },
  "boundary_differences": {
    "Adam": 3,
    "Seth": 3,
    "Enosh": 3,
    "Kenan": 3,
    "Mahalalel": 3,
    "Jared": 3,
    "Enoch": 3,
    "Methuselah": 3,
    "Lamech": 4
  },
  "head_actual_rounded": [
    13398,
    13401
  ]
}
```

## Finding

SP rounding changes the cumulative head by+3, entirely from Methuselah−1 and Lamech+4 relative to MT residuals. The inclusive ledger remains the input type.

## Reassessment

Determine cross-tradition interval families preserved by rounding.

## Checks

```json
{
  "support": true,
  "head": true,
  "downstream": true
}
```

## Closed utc

2026-09-28T01:55:12.783236+00:00

## Record provenance

Exact record hash: `9436f33d7f8f2a9ea18288d69d28a0cb181026754919387530d91ba1dfb5af12`

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