# C488 — Cainan as a cross-mode vector

## Question

Which shared structures survive the admitted 130/460 insertion?

## Inputs

```json
{
  "delta_R": 130,
  "delta_C": 460,
  "MT_bridge": 9890
}
```

## Sources

```json
[
  "Strategy §§3.2,4.4",
  "File18 Cainan controls"
]
```

## Opened utc

2026-09-27T22:39:26.289098+00:00

## Results

```json
{
  "bridge_change": 330,
  "weighted_point_change": 394,
  "restored_bridge": 10220,
  "Sothic_factor": 7,
  "finite_state_rule": "OFF -> ON once where admitted; native LXX starts ON"
}
```

## Finding

One inserted row accounts for both130 and460, increases the cumulative–regular bridge by330, and sends9890 to10220=7×1460. It shifts the weighted point by394, so it is not a12026-preserving operation.

## Reassessment

Check whether the rounded regular reversal construction survives native LXX inputs.

## Checks

```json
{
  "bridge": true,
  "weighted_shift": true
}
```

## Closed utc

2026-09-27T22:39:26.289320+00:00

## Record provenance

Exact record hash: `81ce12908cdbb31a2fea6cbebbe635805da6fc1db08b73041dcb9737a0999cf3`

Source journal: `Research_Cycles/C0482_C0531/journal.json`