# C673 — Test one-map compression of the phase family

## Question

Can one affine function change34 to40 while preserving every half-year phase separation?

## Inputs

```json
{
  "width_change": [
    34,
    40
  ],
  "phase_change": [
    "1/2",
    "1/2"
  ]
}
```

## Sources

```json
[
  "C672",
  "Supplement A §4.3"
]
```

## Opened utc

2026-09-28T01:10:37.837145+00:00

## Results

```json
{
  "required_width_slope": "20/17",
  "required_phase_slope": 1,
  "false_global_phase_gap": "10/17",
  "role_specific_rule": "C+epsilon+(20/17)(x−C−epsilon)"
}
```

## Finding

A single affine date map is impossible: width demands slope20/17, while the preserved phase separation demands slope1. The valid expression dilates around each phase’s own center. This explains why the full object needs a phase coordinate.

## Reassessment

Compare the scalar34.5 Key input with the coordinate34-to40 construction.

## Checks

```json
{
  "incompatible": true,
  "phase_miss": true,
  "phase_specific": true
}
```

## Closed utc

2026-09-28T01:10:37.837450+00:00

## Record provenance

Exact record hash: `acb88dbed3d675e012284caf3a98ebde7ef4e3ebf8c24677937e2a5ce1694f19`

Source journal: `Research_Cycles/C0632_C0731/journal.json`