# C576 — Generate the quarter-carrier ladder

## Question

Can all five source scales follow from40→40.25?

## Inputs

```json
{
  "multipliers": [
    3,
    10,
    12,
    30,
    300
  ],
  "base_pair": [
    40,
    "161/4"
  ]
}
```

## Sources

```json
[
  "File63 §§1.1–1.4,4.6"
]
```

## Opened utc

2026-09-28T00:18:24.889741+00:00

## Results

```json
{
  "multiplier_base_carrier_excess": [
    [
      3,
      120,
      "483/4",
      "3/4"
    ],
    [
      10,
      400,
      "805/2",
      "5/2"
    ],
    [
      12,
      480,
      483,
      3
    ],
    [
      30,
      1200,
      "2415/2",
      "15/2"
    ],
    [
      300,
      12000,
      12075,
      75
    ]
  ],
  "ratio": "161/160"
}
```

## Finding

One source replacement40→40.25 generates the entire ladder, including480→483 and12000→12075. The quarter-phase carrier is a scalar construction, not an additional biological generation unit.

## Reassessment

Compose the carrier replacement with existing Keys.

## Checks

```json
{
  "constant_ratio": true,
  "excess": true
}
```

## Closed utc

2026-09-28T00:18:24.889995+00:00

## Record provenance

Exact record hash: `e99629441764b84e4eac3ad5e1bfeabbd26db83aa4fefeb6fb127742e1df0e15`

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