# C487 — A shared row grammar

## Question

What common rule generates divergent regular and cumulative changes?

## Inputs

```json
{
  "compatible_row": [
    "b",
    "r"
  ],
  "lifespan": "b+r",
  "regular_selector": [
    1,
    0
  ],
  "cumulative_selector": [
    1,
    1
  ]
}
```

## Sources

```json
[
  "Strategy §§3.2,5B",
  "C485–C486"
]
```

## Opened utc

2026-09-27T22:39:11.631579+00:00

## Results

```json
{
  "row_moves": {
    "repartition_100": {
      "regular_effect": 100,
      "cumulative_effect": 0,
      "remainder_effect": -100
    },
    "LXX_Lamech": {
      "regular_effect": 0,
      "cumulative_effect": -24,
      "remainder_effect": -24
    },
    "insert_Cainan": {
      "regular_effect": 130,
      "cumulative_effect": 460,
      "remainder_effect": 330
    }
  },
  "regular_formula": "anchor_R + sum(selected begetting intervals) + declared boundary terms",
  "cumulative_formula": "anchor_C + sum(selected lifespans) + declared phase terms",
  "projection_matrix": [
    [
      1,
      0
    ],
    [
      1,
      1
    ]
  ],
  "determinant": 1
}
```

## Finding

A richer source row supports two distinct measurements. Repartition lies in the cumulative kernel; a lifespan-only change can leave the regular projection fixed. This explains family divergence without a universal map between their endpoints.

## Reassessment

Test the admitted Cainan insertion as a concrete cross-mode vector.

## Checks

```json
{
  "repartition_kernel": true,
  "insertion": true
}
```

## Closed utc

2026-09-27T22:39:11.631755+00:00

## Record provenance

Exact record hash: `cf03e97da2b1013fa5cbae893db9813e84e6a7d80e85f5acb0531ac9f1c5b81f`

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