# C524 — Why the common grammar needs richer objects

## Question

Does a universal scalar affine regular-to-cumulative conversion fit the current controlled comparison states?

## Inputs

```json
{
  "MT": [
    4114,
    14004
  ],
  "LXX_full430_nativeCainanON": [
    5494,
    14894
  ],
  "SP_equalized_OFF": [
    4414,
    13396
  ]
}
```

## Sources

```json
[
  "Strategy §3.1; current File18 completion rows",
  "C483–C491"
]
```

## Opened utc

2026-09-27T22:52:37.021443+00:00

## Results

```json
{
  "required_slopes": {
    "LXX_vs_MT": "89/138",
    "SP_vs_MT": "-152/75"
  },
  "cross_product_obstruction": 1106040
}
```

## Finding

The required slopes89/138 and−152/75 have opposite signs. Thus the current native-Cainan/full-frame comparison also excludes one scalar affine mode conversion. This confirms why the shared object must retain genealogical rows and state choices, not just a Creation number.

## Reassessment

Specify the smallest useful typed operation inventory supported by the completed reconstructions.

## Checks

```json
{
  "incompatible": true,
  "sign": true
}
```

## Closed utc

2026-09-27T22:52:37.021720+00:00

## Record provenance

Exact record hash: `bca61d0407d48b80bb3b0c632653569ecf5bc6d508fed8d0a337df4bee3a1384`

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