# C758 — Classify cross-tradition interval preservation

## Question

When does rounding preserve a difference between traditions?

## Inputs

```json
{}
```

## Sources

```json
[
  "C754–757"
]
```

## Opened utc

2026-09-28T01:55:25.793261+00:00

## Results

```json
{
  "comparison_classes": {
    "LXX_native_ON": {
      "-4": [
        "Noah",
        "Shem",
        "Arphaxad"
      ],
      "-2": [
        "Shelah"
      ],
      "0": [
        "Adam",
        "Seth",
        "Enosh",
        "Kenan",
        "Mahalalel",
        "Jared",
        "Enoch",
        "Methuselah",
        "Lamech",
        "Eber",
        "Peleg",
        "Reu",
        "Serug",
        "Nahor",
        "Terah",
        "Abraham",
        "Isaac",
        "Jacob",
        "Levi",
        "Kohath",
        "Amram",
        "Moses"
      ]
    },
    "SP_native_OFF": {
      "0": [
        "Noah",
        "Shem",
        "Arphaxad",
        "Shelah",
        "Eber",
        "Peleg",
        "Reu",
        "Serug",
        "Nahor",
        "Terah",
        "Abraham",
        "Isaac",
        "Jacob",
        "Levi",
        "Kohath",
        "Amram",
        "Moses"
      ],
      "3": [
        "Adam",
        "Seth",
        "Enosh",
        "Kenan",
        "Mahalalel",
        "Jared",
        "Enoch",
        "Methuselah"
      ],
      "4": [
        "Lamech"
      ]
    }
  },
  "criterion": "DeltaD_i=DeltaD_j iff the cross-tradition interval difference is unchanged by rounding"
}
```

## Finding

Equal comparison-residual plateaus identify complete preserved interval families. Cross-tradition compatibility follows from two local field values, without a new list of isolated matches.

## Reassessment

Test whether admitted Cainan insertion preserves these residual fields.

## Checks

```json
{
  "LXX_classes": true,
  "SP_classes": true
}
```

## Closed utc

2026-09-28T01:55:25.793611+00:00

## Record provenance

Exact record hash: `5180a2af056b70ea8608a815c5c40b7409cfcd39df4f1881d14a4d897f01219f`

Source journal: `Research_Cycles/C0732_C0831/journal.json`