# C1174 — Test order against the biography domain

## Question

Can commuting formulas fail to define both source-compatible intermediate paths?

## Inputs

```json
{
  "row": [
    1,
    1,
    2
  ],
  "d": 2,
  "e": 1
}
```

## Sources

```json
[
  "C1173"
]
```

## Opened utc

2026-09-28T05:11:49.125757+00:00

## Results

```json
{
  "order_counterexample": {
    "path": "model/row_order_domain_counterexample.json",
    "sha256": "b7317aad0bab6daf107563c28761bb167acc40b4845d3452487bdd43095d171f",
    "bytes": 363
  }
}
```

## Finding

The formulas commute on unrestricted coordinates, yet R-first produces a negative remainder in this diagnostic while A-first remains valid. A common endpoint therefore does not authorize every intermediate route.

## Reassessment

Check how the complete source packet uses the domain-qualified operations.

## Checks

```json
{
  "same_endpoint": true,
  "R_invalid": true,
  "A_path_valid": true
}
```

## Closed utc

2026-09-28T05:11:49.126064+00:00

## Record provenance

Exact record hash: `a46f365e6e41597ffe79e56d7428e6324239db52b7bc6c9cf5cd7f7031046875`

Source journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`