# C538 — The14 gain links reconciliation and clutch scales

## Question

What common arithmetic underlies147/161/175 and the full/half clutch values?

## Inputs

```json
{
  "source_values": [
    147,
    161,
    175
  ],
  "calendar_factor": "25/23"
}
```

## Sources

```json
[
  "File60 §§2.6,3.3; File62 dependency note"
]
```

## Opened utc

2026-09-28T00:00:48.866885+00:00

## Results

```json
{
  "coefficients_over7": [
    21,
    23,
    25
  ],
  "E_gain": 14,
  "half_relation": {
    "input": "161/2",
    "output": "175/2",
    "gain": 7
  },
  "center_identity": 322
}
```

## Finding

The progression is7×(21,23,25). E raises161 to175 by14; halving gives80.5→87.5 by7. This provides a value-level bridge to T14/H7, while their chronology domains still require the File61/62 source rules.

## Reassessment

Reconstruct the ordered147 rails, testing translation of both endpoints rather than isolated widths.

## Checks

```json
{
  "progression": true,
  "half": true,
  "center": true
}
```

## Closed utc

2026-09-28T00:00:48.867078+00:00

## Record provenance

Exact record hash: `a9fd20f178bc310ed114e04f8fd566d51261b678e7b14c344f59fc875e6c7940`

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