# C1199 — Derive the row rounding carry from the hidden residual sum

## Question

How does the joint observation control the difference between rounded life and rounded parts?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1191",
  "C1192"
]
```

## Opened utc

2026-09-28T05:25:01.340720+00:00

## Results

```json
{
  "carry_bridge": {
    "path": "model/joint_rounding_carry_bridge.json",
    "sha256": "09df548a9ff72ded568e716ef1fca3f0cb17d025f60f6662d99181bdcbd7b46e",
    "bytes": 4134
  },
  "branches": {
    "-4": -5,
    "-3": -5,
    "-2": 0,
    "-1": 0,
    "0": 0,
    "1": 0,
    "2": 0,
    "3": 5,
    "4": 5
  }
}
```

## Finding

The same residual sum that measures joint ambiguity determines the carry between rounded lifespan and rounded parts. Carry is−5 for z≤−3, zero for |z|≤2, and+5 for z≥3.

## Reassessment

Check whether the carry by itself retains the exact joint recovery information.

## Checks

```json
{
  "all_rows": true,
  "three_branches": true
}
```

## Closed utc

2026-09-28T05:25:01.341533+00:00

## Record provenance

Exact record hash: `6b92f05310cbabfa085134c859ff27941d3690ae2debfe145287ead85194d7fc`

Source journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`