# C1565 — Verify consistency of merge order

## Question

Do the two routes through the lower three original legs have the same total local effect?

## Sources

```json
[]
```

## Opened utc

2026-09-29T02:42:15.243222+00:00

## Results

```json
{
  "MT": {
    "left": 4320,
    "right": 4320
  },
  "LXX": {
    "left": 4320,
    "right": 4320
  },
  "SP": {
    "left": 4320,
    "right": 4320
  }
}
```

## Finding

Both routes give4320 in all three cases. The identity D(x,y)+D(x+y,z)=D(y,z)+D(x,y+z) follows by cancellation for any fixedI.

## Reassessment

Use that general relation as explanation of path consistency, not another independentnumerical result.

## Checks

```json
{}
```

## Closed utc

2026-09-29T02:42:15.243785+00:00

## Record provenance

Exact record hash: `fb6d3c4d630456d92076ff8c20d0d2dc87f6d45a319ca89b90c9105dd09b1740`

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