# C713 — Derive whole-total effects from a retained partition

## Question

Why does partialP produce the364/360 ratio in the new macro family?

## Inputs

```json
{
  "upper": 9660,
  "lower": 2940,
  "total": 12600
}
```

## Sources

```json
[
  "C690; Supplement A §10.3"
]
```

## Opened utc

2026-09-28T01:21:39.291265+00:00

## Results

```json
{
  "converted_fraction": "23/30",
  "retained_fraction": "7/30",
  "effective_total_ratios": [
    "91/90",
    "16/15"
  ],
  "calendar_ratios": [
    "91/90",
    "16/15"
  ]
}
```

## Finding

The converted upper arm is23/30 of12600. Therefore partialP has total ratio1+(P−1)23/30=91/90, and partialE has ratio16/15. These are consequences of this retained partition, explaining its calendar-body outputs without adding universal Keys.

## Reassessment

Compare the new partial-conversion mechanism with the earlier one-sixth and one-twenty-sixth bridges.

## Checks

```json
{
  "fractions": true,
  "effects": true,
  "outputs": true
}
```

## Closed utc

2026-09-28T01:21:39.291945+00:00

## Record provenance

Exact record hash: `4ade86b4f2907d8fc48a9379ec009003bfd126e453b701d6f273a2e02778ab15`

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