# C1309 — Register measure-preserving grouping and symmetry descent

## Question

What additionalcondition letsreflection act onagroupedobject?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1308",
  "inherited/model/toledot_quotient.json",
  "C1024–C1029 inherited"
]
```

## Opened utc

2026-09-28T06:12:25.483264+00:00

## Results

```json
{
  "grouping_relation": {
    "path": "model/relation_grouping_reflection.json",
    "sha256": "4c6ff0cb4fb2a646e79edc4982ea4aaa54b2a197bb01ec1f55131bbfa7b2425b",
    "bytes": 745
  }
}
```

## Finding

Toledot’scollapsedEsauoccurrences reflectintodifferentsections, soitsreflectiondoesnotdescend even thoughmultiplicitypreserves themeasure. TheNT groupingworks becauseitsfibres respectitsreflection.

## Reassessment

Register theinversefamily’s dependenceontheoriginalpartition.

## Checks

```json
{
  "different_classes": true,
  "images": true,
  "occurrence_count": true
}
```

## Closed utc

2026-09-28T06:12:25.483729+00:00

## Record provenance

Exact record hash: `aec788c1a21015282640fcdc1446ed46d6e1926cd6c6cef01c2792438d82b6ee`

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