# C1045 — Residual source freedoms

## Question

Which biological or household data remain unidentifiable after normalization?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1044"
]
```

## Opened utc

2026-09-28T04:05:21.631745+00:00

## Results

```json
{
  "formal_null_directions": [
    [
      0,
      0,
      0,
      0,
      -1,
      1,
      0,
      0,
      0,
      0,
      0,
      0,
      0
    ],
    [
      0,
      0,
      -1,
      -1,
      1,
      0,
      -1,
      0,
      1,
      1,
      0,
      0,
      0
    ]
  ],
  "node_effects": [
    {
      "Q": 0,
      "terminal": 0,
      "Ishmael_birth": 0,
      "Isaac_birth": 0,
      "Ishmael_death": 0,
      "Jacob_birth": 1,
      "Jacob_call": 0,
      "Jacob_death": 1,
      "Levi_birth": 0,
      "Levi_death": 0,
      "Joseph_birth": 0,
      "Joseph_death": 0
    },
    {
      "Q": 0,
      "terminal": 0,
      "Ishmael_birth": 1,
      "Isaac_birth": 1,
      "Ishmael_death": 0,
      "Jacob_birth": 0,
      "Jacob_call": 0,
      "Jacob_death": 0,
      "Levi_birth": 1,
      "Levi_death": 0,
      "Joseph_birth": 0,
      "Joseph_death": 0
    }
  ],
  "status": "sensitivity directions only; no new source state"
}
```

## Finding

One direction exchanges Isaac→Jacob age with Jacob’s call age; another adjusts several source offsets and equal lives together. Both preserve the selected pattern totals while changing local data.

## Reassessment

Test which retained source ages close those remaining freedoms.

## Checks

```json
{
  "both_null": true,
  "independent_directions": true
}
```

## Closed utc

2026-09-28T04:05:21.633042+00:00

## Record provenance

Exact record hash: `aeb76bd8f30ca5d42f83e97d33c7388ad858f27d9f25749ec661e0e8e69f3f16`

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