# C555 — Specify the finite clutch action

## Question

What symmetry is licensed by the three admitted displacement states?

## Inputs

```json
{
  "displacements": [
    0,
    7,
    14
  ],
  "example": 1933
}
```

## Sources

```json
[
  "File61 §7.3A; File62 §1"
]
```

## Opened utc

2026-09-28T00:13:07.094413+00:00

## Results

```json
{
  "rail": [
    1933,
    1926,
    1919
  ],
  "half_step_edges": [
    [
      0,
      7
    ],
    [
      7,
      14
    ]
  ],
  "composite_edge": [
    0,
    14
  ],
  "third_half_step": 1912,
  "third_step_admitted": false
}
```

## Finding

H7 composed twice equals T14 on the declared original-to-full domain. The admitted rails form a finite directed chain, not a closed translation group. Historical event anchors remain fixed.

## Reassessment

Generate Joseph collateral intervals from the same root boundaries.

## Checks

```json
{
  "composition": true,
  "finite_domain": true
}
```

## Closed utc

2026-09-28T00:13:07.094612+00:00

## Record provenance

Exact record hash: `0d829b55576be04021e284e9c95f41054fe5e95b28d71c356cc7c4f65789d568`

Source journal: `Research_Cycles/C0532_C0631/journal.json`