# C1306 — Register coherent translation through Rounded residuals

## Question

How does exactsourcechange remaincompatiblewiththeRoundedrepresentation?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1305",
  "C1218–C1221",
  "C1278"
]
```

## Opened utc

2026-09-28T06:10:25.090906+00:00

## Results

```json
{
  "residual_relation": {
    "path": "model/relation_rounded_residuals.json",
    "sha256": "1c0b4aa4f98bb9e353a968eb99533277ba860ce60b040fe488a24060ad35574e",
    "bytes": 839
  }
}
```

## Finding

TheRoundedplusresidual representation carries exactsourcechanges coherently, anditsaccumulatedresiduals recovercompletepaths. Itworks byretaininginformation, notby makingroundingadditive.

## Reassessment

Register uniformKeycompatibility withsums andthelimitforcomponent-specificKeys.

## Checks

```json
{
  "two_applications": true,
  "proof_bound": true
}
```

## Closed utc

2026-09-28T06:10:25.091366+00:00

## Record provenance

Exact record hash: `cd8423799fd21e6fc407edabdcdb75d6a5b7bbb127020996a63de30f268b80c9`

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