# C766 — Join rounding to the mode bridge

## Question

Does bridge rounding follow the difference of the two boundary residuals?

## Inputs

```json
{}
```

## Sources

```json
[
  "File51a §3.1 strict regular and §16.2 cumulative tables"
]
```

## Opened utc

2026-09-28T01:57:42.205748+00:00

## Results

```json
{
  "source_packet": {
    "path": "model/variant_inputs.json",
    "sha256": "637ee29c7bcb34fbdf313690535d3f2035837e6f77940bc0580e5a90295f8cf0",
    "bytes": 187357
  },
  "bridge": {
    "path": "model/MT_rounding_bridge.json",
    "sha256": "8b8c6c130a8aaf156453fe1b74b3ffa72d29a9529134efc1678b7f8234a8732f",
    "bytes": 2560
  },
  "common_nodes": 22,
  "Adam": {
    "name": "Adam",
    "G_actual": 9894,
    "G_rounded": 9900,
    "delta_G": 6,
    "D_C_minus_D_R": 6
  }
}
```

## Finding

On the literal strict regular comparison, rounded G−actual G equals D_C−D_R at every common node. Rounding modifies the mode bridge through two fields, not one date offset.

## Reassessment

Check the local bridge-generator identity from adjacent differences.

## Checks

```json
{
  "all_nodes": true,
  "enough_nodes": true
}
```

## Closed utc

2026-09-28T01:57:42.212412+00:00

## Record provenance

Exact record hash: `e712d08ab051d820a79d4d24055738c06d738082f19da55b1959e11d44007b3b`

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