# C1213 — Test row operations that translate by the five-year lattice

## Question

Which changes pass through nearest-five rounding without changing their amplitude?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1182",
  "C1199",
  "prep/review1182_1201 pending independent review"
]
```

## Opened utc

2026-09-28T05:29:06.281790+00:00

## Results

```json
{
  "equivariance": {
    "path": "model/round_lattice_equivariance.json",
    "sha256": "cd4cba7a1d4f52780ea7a1406c86691f7f48b8dbaefa232792e71ca96049ced1",
    "bytes": 504
  }
}
```

## Finding

All translations by multiples of five pass through rounding exactly, including the century, half-century, forty and sixty changes. The signed carry notation uses an algebraic extension, not negative source durations.

## Reassessment

Locate the only whole-genealogy amplitudes outside that lattice.

## Checks

```json
{
  "all_translation_cases": true,
  "two_off_lattice": true
}
```

## Closed utc

2026-09-28T05:29:06.282246+00:00

## Record provenance

Exact record hash: `d8888961095773dcd375ca4baa91c39f66218acc52b18322cd77ca1eb20e7ddb`

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