# C880 — Derive the prefix-denominator theorem

## Question

What must hold for every stage of a finite Key word to preserve a grid?

## Inputs

```json
{}
```

## Sources

```json
[
  "C873",
  "Strategy partial actions"
]
```

## Opened utc

2026-09-28T02:48:14.996601+00:00

## Results

```json
{
  "theorem": {
    "path": "model/key_word_domain_theorem.json",
    "sha256": "9e8fc429be24813a422a5cbe2e49b519cb624e2b33a35d21147754afe10f1623",
    "bytes": 369
  }
}
```

## Finding

The exact all-stage domain is h times the least common multiple of reduced prefix denominators. Final integrality is a weaker condition whenever cancellation occurs only later.

## Reassessment

Evaluate the complete fixed inventory of nine two-Key words.

## Checks

```json
{
  "criterion": true,
  "authorization_retained": true
}
```

## Closed utc

2026-09-28T02:48:14.996937+00:00

## Record provenance

Exact record hash: `3e927bc16221395b1cafd26aad913a64efb1c770c298ee662f946b03a6b7eebe`

Source journal: `Research_Cycles/C0832_C0931/journal.json`