# C1216 — Reconstruct the hidden interior effect of head cancellation

## Question

Which cumulative boundaries move even though the head error is zero?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1215"
]
```

## Opened utc

2026-09-28T05:29:12.387992+00:00

## Results

```json
{
  "interior_field": {
    "path": "model/whole_genealogy_rounding_interior_field.json",
    "sha256": "6d567b190a9b6394b05ca6e81b64f7eefde7f8e2021b4b92f407e75e25fa0c2d",
    "bytes": 916
  },
  "nonzero_boundaries": [
    {
      "boundary": "Noah",
      "difference_error": -4
    },
    {
      "boundary": "Shem",
      "difference_error": -4
    },
    {
      "boundary": "Arphaxad",
      "difference_error": -4
    },
    {
      "boundary": "Shelah",
      "difference_error": -2
    }
  ]
}
```

## Finding

The head cancellation hides a−4 comparison shift at Noah, Shem and Arphaxad, followed by−2 at Shelah. Adjacent differences recover the three local rounding changes exactly.

## Reassessment

Check compatibility with separately rounded remaining years and identify the carry change.

## Checks

```json
{
  "head_terminal_zero": true,
  "recurrence": true,
  "nonzero4": true
}
```

## Closed utc

2026-09-28T05:29:12.390524+00:00

## Record provenance

Exact record hash: `05c9eb4596a23c5d92a7bf787703c21929e0f1b60b2a915d78004a7236b807d1`

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