# C997 — Recovered magnitudes versus retained roles

## Question

Does recovering two numerical components identify their chronological realization?

## Inputs

```json
{}
```

## Sources

```json
[
  "C994",
  "C996"
]
```

## Opened utc

2026-09-28T03:54:34.573243+00:00

## Results

```json
{
  "numerically_recovered": [
    "converted magnitude u",
    "retained magnitude v"
  ],
  "not_recovered": [
    "order along the path",
    "which named interval is converted",
    "absolute anchor",
    "permission to use the route"
  ]
}
```

## Finding

A measurement inverse recovers magnitudes, not source identities, order or placement. The compact algebra must carry those tags alongside its numbers.

## Reassessment

Derive the fixed-pivot integer-domain theorem for two staged Keys.

## Checks

```json
{
  "two_magnitudes": true,
  "required_tags": true
}
```

## Closed utc

2026-09-28T03:54:34.573532+00:00

## Record provenance

Exact record hash: `7d7abe1f3b751463c3d9a696801ca28e47c9910ac78b4851c97d2c524040e197`

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