# C1220 — Prove coherence of consecutive rounded-residual translations

## Question

Does the lifted action depend on how an admitted total shift is decomposed?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1218",
  "C1219"
]
```

## Opened utc

2026-09-28T05:30:59.326469+00:00

## Results

```json
{
  "composition": {
    "path": "model/rounded_translation_composition.json",
    "sha256": "75a28f7bb3d4a6f20397c95c1ee5d51b30d61bd6dc6d190fbb0db940da93dba8",
    "bytes": 384
  },
  "diagnostic_cases": 25
}
```

## Finding

The lifted translations compose exactly because they retain the full original value. Their coherence is mathematical; source authorization of each intermediate state remains separate.

## Reassessment

Determine precisely when the residual may be dropped without breaking a universal shift rule.

## Checks

```json
{
  "all_cases": true,
  "25cases": true
}
```

## Closed utc

2026-09-28T05:30:59.326980+00:00

## Record provenance

Exact record hash: `c74d03e7bb0f6fd6dc2f9508f6ca8d8f644702e763748aefb46f89434f09b18d`

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