# C858 — Integrate the decimal module by its retained register

## Question

How does one-pass reversal join the common grammar without becoming a chronology-wide affine operation?

## Inputs

```json
{}
```

## Sources

```json
[
  "C852–857; C831 rounding/path model"
]
```

## Opened utc

2026-09-28T02:37:45.739658+00:00

## Results

```json
{
  "module": {
    "path": "model/inverse_module_summary.json",
    "sha256": "bde0cd431d5efd716efd80d92de26b2cf52ba7dd2128c23d73168826f5c48c1f",
    "bytes": 494
  }
}
```

## Finding

The shared model needs a digit register for decimal evaluation just as it needs categories for list measurement. The complete gain field explains route dependence while leaving source selection and historical interpretation open.

## Reassessment

Freeze the complete NT indexed-display family and its comparison domains.

## Checks

```json
{
  "no_universal_affine": true,
  "source_limit": true
}
```

## Closed utc

2026-09-28T02:37:45.740175+00:00

## Record provenance

Exact record hash: `58ad46b488dbc147ea157bf2adedf4032d910233ca00ff5cd0e3d295239d9363`

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