# C536 — Equal lives preserve birth and death displacement

## Question

Which161 equality is forced by the supplied biographies?

## Inputs

```json
{
  "Ishmael": [
    1865,
    1728
  ],
  "Levi": [
    1704,
    1567
  ],
  "terminal": 1406
}
```

## Sources

```json
[
  "File60 §§3.1–3.2"
]
```

## Opened utc

2026-09-28T00:00:02.228191+00:00

## Results

```json
{
  "lifespans": [
    137,
    137
  ],
  "birth_gap": 161,
  "death_gap": 161,
  "terminal_arm": 161,
  "identity": "(B1−L1)−(B2−L2)=(B1−B2)−(L1−L2)"
}
```

## Finding

Equal137-year lives force equal161 birth/death displacement. The further161 from Levi’s death to the terminal is an additional source placement. Separating these two facts avoids treating the biography rectangle as several independent alignments.

## Reassessment

Reconstruct the bilateral spine and its expansion with a single held midpoint.

## Checks

```json
{
  "equal_lives": true,
  "gap": true,
  "terminal": true
}
```

## Closed utc

2026-09-28T00:00:02.228393+00:00

## Record provenance

Exact record hash: `142c706a4184de93dfcb4408f1dd102e6f418fcec4b89cad711bb2ccc7be3ec0`

Source journal: `Research_Cycles/C0532_C0631/journal.json`