# C772 — Define the finite source configuration

## Question

What is the smallest regular birth-state formula consistent with the declared variant domains?

## Inputs

```json
{
  "s": "0/1 minimum/full430",
  "t": "0/1 baseline/+60 Terah",
  "c": "0/1 Cainan OFF/ON"
}
```

## Sources

```json
[
  "File18 §§1.3–1.6; model/variant_inputs.json"
]
```

## Opened utc

2026-09-28T01:59:36.002851+00:00

## Results

```json
{
  "rule": {
    "path": "model/variant_rule.json",
    "sha256": "58ac54c59156d94eeedd4313111bbd2ec5edcb91af5eab442f2e2251878fb5b5",
    "bytes": 516
  },
  "masks": {
    "Adam–Arphaxad": [
      1,
      1,
      1
    ],
    "Shelah–Terah": [
      1,
      1,
      0
    ],
    "Abraham–Joseph/Levi": [
      1,
      0,
      0
    ],
    "Aaron/Moses terminal": [
      0,
      0,
      0
    ]
  }
}
```

## Finding

Three finite choices have nested supports. The rule predicts placements within each source domain while preserving native LXX Cainan and unassigned regular births.

## Reassessment

Recover the four literal Terah states before extending the rule.

## Checks

```json
{
  "nested": true
}
```

## Closed utc

2026-09-28T01:59:36.003316+00:00

## Record provenance

Exact record hash: `3af63638f3027a8078f580010e6f0b62199336c09a6fbfdbcba020353820bc16`

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