# C982 — Cap as an irreversible operation

## Question

Which structural properties distinguish the cap from a frame translation?

## Inputs

```json
{}
```

## Sources

```json
[
  "C968",
  "C970",
  "C978"
]
```

## Opened utc

2026-09-28T03:51:31.680453+00:00

## Results

```json
{
  "properties": [
    "monotone",
    "idempotent",
    "many-to-one"
  ],
  "inverse_available": false,
  "domain": "resolved count vector with fixed capacity vector"
}
```

## Finding

The cap is a monotone idempotent projection with demonstrated information loss. The family’s operation grammar therefore includes irreversible maps as well as reversible translations.

## Reassessment

Regenerate the complete source family from the output-free packet and close the block.

## Checks

```json
{
  "idempotent": true,
  "many_to_one": true,
  "monotone_increase": true
}
```

## Closed utc

2026-09-28T03:51:31.680750+00:00

## Record provenance

Exact record hash: `c92a1b9d04dd5c54b733e15c157528bc3412a102733741e9dedb918291cbffdf`

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