# C1042 — Independence changes with held source values

## Question

Are the centered and E-completed radius conditions still independent when175/147 are supplied?

## Inputs

```json
{}
```

## Sources

```json
[
  "File60 §2.6",
  "C1041"
]
```

## Opened utc

2026-09-28T04:04:41.562315+00:00

## Results

```json
{
  "identity": "25A8−2A7 = 21·Abraham_life−25·Jacob_life",
  "held_rhs": 0,
  "consequence": "with175/147 held, the two radius conditions are equivalent"
}
```

## Finding

The two radius conditions are independent only while the relevant lifespans vary. With source175 and147 held, one condition implies the other. Constraint counts must state their held premises.

## Reassessment

Reduce the entire selected Covenant claim list to a precise row basis.

## Checks

```json
{
  "coefficient_identity": true,
  "source_rhs_zero": true
}
```

## Closed utc

2026-09-28T04:04:41.563266+00:00

## Record provenance

Exact record hash: `f8fc7ab12886e6ede3b60312a8d1839116124cd21d82e8850a59feb20969de25`

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