# C977 — Local counting paths preserve capacity

## Question

Do the three admitted Noah/Shem paths share the ancestral Flood distance?

## Inputs

```json
{
  "paths": [
    [
      52,
      500,
      100
    ],
    [
      53,
      499,
      100
    ],
    [
      53,
      500,
      99
    ]
  ],
  "Lamech_birth": 3545
}
```

## Sources

```json
[
  "File18 §3.1.2",
  "C976"
]
```

## Opened utc

2026-09-28T03:50:38.163313+00:00

## Results

```json
{
  "completed_path_lengths": [
    652,
    652,
    652
  ],
  "Flood_starts": [
    2893,
    2893,
    2893
  ],
  "Lamech_inclusive_capacity": [
    653,
    653,
    653
  ]
}
```

## Finding

All three source-qualified local paths preserve the652 completed distance and653 inclusive capacity. Noah/Shem station choices do not move the ancestral births.

## Reassessment

Apply nearest-five rounding to resolved count values.

## Checks

```json
{
  "same_path": true,
  "same_boundary": true
}
```

## Closed utc

2026-09-28T03:50:38.163526+00:00

## Record provenance

Exact record hash: `f1c631462682752fffd70a94527bd6e7349ccd9ccbf15962e514ea370807f734`

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