# C1452 — Identify the complementary manuscript-mode pairings

## Question

When is invariance genuine at both merges, and when does it arise from cancellation?

## Sources

```json
[
  "Partition law"
]
```

## Opened utc

2026-09-29T01:16:15.053664+00:00

## Results

```json
{
  "(0, 0)": [
    "MT_regular",
    "SP_cumulative"
  ],
  "(-990, -990)": [
    "MT_cumulative",
    "LXX_regular"
  ],
  "(0, -990)": [
    "LXX_cumulative"
  ],
  "(-4500, 1800)": [
    "SP_regular"
  ]
}
```

## Finding

MT Regular and SP Cumulative have two zero defects; LXX Regular and MT Cumulative have two equal−990 defects. The second pair preserves coarse totals by cancellation while refinement adds990.

## Reassessment

Inspect the complete source-node displacement vectors for an actual multi-node translation.

## Checks

```json
{
  "stable_pair": true,
  "balanced_pair": true
}
```

## Closed utc

2026-09-29T01:16:15.054244+00:00

## Record provenance

Exact record hash: `2f4f935ce19aeaa54efac9d623fa13026d4a35fa482210a628dae010f28aef5f`

Source journal: `Research_Cycles/C1433_C1482/journal.json`