# C784 — Transfer full residual vectors through finite variants

## Question

Does rounding retain its coordinate discrepancies throughout the admitted MT configuration?

## Inputs

```json
{}
```

## Sources

```json
[
  "File51a 23 regular and26 cumulative paired rows; C760,C772"
]
```

## Opened utc

2026-09-28T02:02:37.310204+00:00

## Results

```json
{
  "residuals": {
    "path": "model/variant_residual_vectors.json",
    "sha256": "8ec539b81d93e426a3dbfa143ea51f46d05c08288af75e4b302b27093a9040b8",
    "bytes": 4203
  },
  "basis": "row-level Q(n+5k)=Q(n)+5k; coordinate calculation is its consequence"
}
```

## Finding

All existing23 regular and26 cumulative MT residual coordinates persist under their compatible admitted state moves. This transfers the whole field, while keeping raw cumulative Terah/Sojourn choices forgotten.

## Reassessment

Evaluate the new Cainan coordinate on both Actual and Rounded rails.

## Checks

```json
{
  "regular_invariance": true,
  "cumulative_invariance": true
}
```

## Closed utc

2026-09-28T02:02:37.311994+00:00

## Record provenance

Exact record hash: `bbe773e0c0e26b1aac28252a5c8a04b235f602ccf6a82a9ed75e2bc002bbdc4c`

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