# C1564 — Compress the partition family by local merges

## Question

Can one local quantity describe every retained-boundary choice?

## Sources

```json
[]
```

## Opened utc

2026-09-29T02:42:15.195307+00:00

## Results

```json
{
  "MT": {
    "full_total": 7290,
    "D_a_600": -990,
    "D_600_950": 4320,
    "D_950_c": 4320,
    "D_a_1550": 0,
    "D_1550_c": -990,
    "D_a600_950": 5310
  },
  "LXX": {
    "full_total": 12230,
    "D_a_600": 0,
    "D_600_950": 4320,
    "D_950_c": -1710,
    "D_a_1550": 0,
    "D_1550_c": -7020,
    "D_a600_950": 4320
  },
  "SP": {
    "full_total": 5690,
    "D_a_600": 0,
    "D_600_950": 4320,
    "D_950_c": 4320,
    "D_a_1550": 0,
    "D_1550_c": 0,
    "D_a600_950": 4320
  }
}
```

## Finding

Define D(x,y)=I(x+y)−I(x)−I(y). The same merge rule covers all named partitions, with the sharedD(600,950)=4320 andD(a,1550)=0.

## Reassessment

Check the relation between two different orders of merging the same three source legs.

## Checks

```json
{}
```

## Closed utc

2026-09-29T02:42:15.195854+00:00

## Record provenance

Exact record hash: `bd30a1fd6f2d3a55dc69376848456e2726a0881d28f683796a6c436ff678c729`

Source journal: `Research_Cycles/C1483_C1582/c1483_c1582/journal.json`