# C1139 — Complete the age reconstruction with a stated source basis

## Question

Which retained source coordinates close the unconstrained linear age model?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1133–C1134",
  "File18 §3.1"
]
```

## Opened utc

2026-09-28T04:59:58.322531+00:00

## Results

```json
{
  "age_basis": {
    "path": "model/SP_age_basis_completion.json",
    "sha256": "b4a86d46e1fe491032030e01dbd19b5f4be75570e41dd6ec824d20c3883fe9de",
    "bytes": 1248
  },
  "rank": 9,
  "reconstructed": [
    130,
    105,
    90,
    70,
    65,
    62,
    65,
    67,
    52
  ]
}
```

## Finding

The shared65 age and two interior ages provide an exact full-rank reconstruction after the six stated relations are retained. The distinction between a rational model and a bounded grid explains their different identification costs.

## Reassessment

Audit the full input cost so reverse cap recovery is not counted as a new independent source explanation.

## Checks

```json
{
  "full_rank": true,
  "actual_recovered": true
}
```

## Closed utc

2026-09-28T04:59:58.331325+00:00

## Record provenance

Exact record hash: `2380f5ec86d29a6854949064dffb7d07a6b59091aaa7cdb5ba3ee7bb8ed6b3bf`

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