# C554 — Separate endpoint and whole-rail translation

## Question

Which spans contract when the clutch moves only a parent boundary?

## Inputs

```json
{
  "lifespans": [
    175,
    180,
    147,
    137,
    133,
    137
  ],
  "clutch": 14
}
```

## Sources

```json
[
  "File61 §7.4; §§17.2–17.3"
]
```

## Opened utc

2026-09-28T00:12:55.834605+00:00

## Results

```json
{
  "parent_only": [
    161,
    166,
    133,
    123,
    119,
    123
  ],
  "both_ends": [
    175,
    180,
    147,
    137,
    133,
    137
  ],
  "Isaac_only_Abraham_fixed": 189,
  "derived_terminal_to_fixed_Exodus": 66
}
```

## Finding

One-end translation contracts each lifespan; whole-rail translation preserves it. Outputs166 and119 remain part of the family. Moving Isaac alone makes189, showing why endpoint roles are indispensable.

## Reassessment

Determine the exact local composition law for half and full clutch.

## Checks

```json
{
  "contractions": true,
  "opposite_endpoint": true,
  "terminal": true
}
```

## Closed utc

2026-09-28T00:12:55.834804+00:00

## Record provenance

Exact record hash: `a626ce59056739d0391c7896af2c112ae74e728c23542e34a73ce7be958ab294`

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