# C776 — Test the finite switch algebra

## Question

Do variant switches commute without becoming unlimited translations?

## Inputs

```json
{}
```

## Sources

```json
[
  "C772–775"
]
```

## Opened utc

2026-09-28T02:00:33.461502+00:00

## Results

```json
{
  "state_count": 8,
  "switch_amount_rule": "weight*(1−2*current_bit)*support_mask",
  "domain": "finite source labels; not repeated positive additions"
}
```

## Finding

The three switches commute and undo themselves on binary state labels. Their numeric direction changes on return; this supplies a bounded configuration rather than an unrestricted translation rule.

## Reassessment

Use support differences to predict entire interval responses.

## Checks

```json
{
  "involutions": true,
  "commutation": true
}
```

## Closed utc

2026-09-28T02:00:33.461832+00:00

## Record provenance

Exact record hash: `a3328635745bd28704c6b914c97cc5d930d6754f75bf209c21ab50d060c3260b`

Source journal: `Research_Cycles/C0732_C0831/journal.json`