# C964 — Late begetting constraint rank

## Question

What do the three capped lives determine about four late begetting intervals?

## Inputs

```json
{
  "matrix": [
    [
      1,
      1,
      1,
      1
    ],
    [
      0,
      0,
      1,
      1
    ],
    [
      0,
      0,
      0,
      1
    ]
  ],
  "rhs": [
    246,
    119,
    52
  ]
}
```

## Sources

```json
[
  "C961",
  "File18 §3.1"
]
```

## Opened utc

2026-09-28T03:47:51.282317+00:00

## Results

```json
{
  "rank": 3,
  "kernel": [
    1,
    -1,
    0,
    0
  ],
  "recoverable": {
    "Lamech_completed": 52,
    "Methuselah": 67,
    "Jared_plus_Enoch": 127
  }
}
```

## Finding

The cap equations recover Lamech52, Methuselah67, and Jared+Enoch127; they do not separate Jared from Enoch.

## Reassessment

Add the independently retained Enoch65 row and test the complete late reconstruction.

## Checks

```json
{
  "kernel": true,
  "rank_three": true,
  "recovered": true
}
```

## Closed utc

2026-09-28T03:47:51.282519+00:00

## Record provenance

Exact record hash: `e0fefcf74ffb218e7dac9b3ae1c816bf6c7b3a534f297da3fc5d97eba4206073`

Source journal: `Research_Cycles/C0932_C1131/journal.json`