# C1301 — Register grouping and source-qualified reflection

## Question

When can acoarserrepresentation preserve ameasureorsymmetry?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1300",
  "inherited/model/toledot_quotient.json",
  "C1009–C1029 inherited"
]
```

## Opened utc

2026-09-28T06:09:05.694281+00:00

## Results

```json
{
  "group_reflection": {
    "path": "model/operations_group_and_reflect.json",
    "sha256": "e544e9ff27d160fd1748095fbf88dbbc486a9c463725d99acc71e9833ca11448",
    "bytes": 1268
  }
}
```

## Finding

Groupingpreservesaselectedmeasure whenitsweightsandmultiplicitiesarecarried. Reflectionrequiresadditionalcompatibilityofthesourcegrouping, explainingwhytheNT andToledot examplesdiffer.

## Reassessment

Assemble theoperationinventory andlink eachoperationtoitsretainedsourcepremises.

## Checks

```json
{
  "two_ops": true,
  "multiplicity": true
}
```

## Closed utc

2026-09-28T06:09:05.694717+00:00

## Record provenance

Exact record hash: `d46a7b25090a715b0561dae5a68340b81f909a783861446584e1e182af46ac2e`

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