# C742 — Explain equal births with unequal cumulative boundaries

## Question

Why does the entireLXX/SP birthsuffix coincide while itscumulativeprofilediverges?

## Inputs

```json
{
  "nodes": [
    "Shelah",
    "Eber",
    "Peleg",
    "Reu",
    "Serug",
    "Nahor",
    "Terah",
    "Abraham"
  ],
  "native_Cainan": [
    "LXXON",
    "SPOFF"
  ],
  "regular_frame": "commonfull430"
}
```

## Sources

```json
[
  "File18 §§3–4,6C–D; C738"
]
```

## Opened utc

2026-09-28T01:44:58.868367+00:00

## Results

```json
{
  "regular_differences": [
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0
  ],
  "cumulative_differences": [
    547,
    520,
    420,
    320,
    220,
    120,
    60,
    0
  ],
  "lifespan_changes": [
    27,
    100,
    100,
    100,
    100,
    60,
    60
  ]
}
```

## Finding

All eightLXX/SP birthpositionsShelah throughAbraham coincide. Their cumulative differences547→520→420→320→220→120→60→0 are exactly generated by the local lifespan changes. This is a complete positive example of shared regular geometry with divergent cumulative realization.

## Reassessment

Insert the single admittedCainan row intoSP and test how far the shared birthsuffix extends.

## Checks

```json
{
  "same_births": true,
  "cumulative_profile": true,
  "local_cause": true
}
```

## Closed utc

2026-09-28T01:44:58.868769+00:00

## Record provenance

Exact record hash: `7d48feefa5ce07e9b29d58a4588ba5dcf022c193c8e691361d07812b220d9d89`

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