# C1133 — Form the joint SP age constraints

## Question

How many free age coordinates remain after the explicit source relations and inherited cap equations?

## Inputs

```json
{
  "variables": [
    "Adam",
    "Seth",
    "Enosh",
    "Kenan",
    "Mahalalel",
    "Jared",
    "Enoch",
    "Methuselah",
    "Lamech"
  ]
}
```

## Sources

```json
[
  "C1132",
  "File18 §3.1",
  "File51a §8.3"
]
```

## Opened utc

2026-09-28T04:57:51.938865+00:00

## Results

```json
{
  "age_constraints": {
    "path": "model/SP_age_constraints.json",
    "sha256": "a424c44212d21411e61116d36dad64234cf5602e9c4578c3989ac79f8ab308fd",
    "bytes": 1226
  },
  "rank": 6,
  "free_coordinates": 3
}
```

## Finding

The six retained relations have rank6 on nine ages, leaving three free coordinates. They reduce the local input model without uniquely recovering the whole age sequence.

## Reassessment

Describe the three remaining freedoms explicitly to see which source values are still needed.

## Checks

```json
{
  "all_source_equations": true,
  "rank6": true
}
```

## Closed utc

2026-09-28T04:57:51.941254+00:00

## Record provenance

Exact record hash: `8864da50f84957f28dd0b217d4758a05a60155c6269126a2de444e9ec7d449dd`

Source journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`