# C1028 — General reflection descent criterion

## Question

When does a source grouping carry an existing involution?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1025",
  "C1027"
]
```

## Opened utc

2026-09-28T04:00:42.389009+00:00

## Results

```json
{
  "point_quotient": "q(x)=q(y) implies q(Rx)=q(Ry).",
  "boundary_subset": "Selected boundaries must be invariant under R.",
  "interval_coarsening": "R must permute complete coarse blocks.",
  "proof": "The proposed map q(x)↦q(Rx) is well-defined exactly when representatives of one class have a common image class."
}
```

## Finding

Reflection can pass to a grouped object only when the grouping respects its action. Point identification, interval coarsening and boundary selection require their own checks.

## Reassessment

Test the source NT490 coarsening as a contrasting complete field.

## Checks

```json
{
  "Toledot_counterexample": true,
  "representative_condition_explicit": true
}
```

## Closed utc

2026-09-28T04:00:42.389353+00:00

## Record provenance

Exact record hash: `5653889cd9b0ba5b0bdabd7dffa729ca3c51cbf82040188864e6115170a16e11`

Source journal: `Research_Cycles/C0932_C1131/journal.json`