# C1050 — Exact-phase and lifespan constraints

## Question

How do source equalities reduce the array without merging distinct phase policies?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1048",
  "C1049",
  "File62 §1.3"
]
```

## Opened utc

2026-09-28T04:06:39.794808+00:00

## Results

```json
{
  "dimension_phase_only": 8,
  "dimension_equal_lives_only": 8,
  "dimension_both": 7,
  "exact_phase_residual": 0,
  "whole_year_phase_residual": 1
}
```

## Finding

The exact7=2×3.5 link and repeated137 life each remove one degree of freedom; together they leave seven. The whole-year phase3 does not satisfy the same equality and stays a separate model.

## Reassessment

Generate the seven base boundaries from the source lifespan path.

## Checks

```json
{
  "independent_constraints": true,
  "exact_vs_whole": true
}
```

## Closed utc

2026-09-28T04:06:39.795440+00:00

## Record provenance

Exact record hash: `6a0b3a36270f54441c0f2c9b1b21816a76866ac87a766052863c10dd837d3e4d`

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