# C500 — The calendar family’s common measure

## Question

Do the three Keys share a conserved quantity despite producing different year counts?

## Inputs

```json
{
  "ratios": {
    "E": "25/23",
    "P": "70/69",
    "J": "300/299"
  },
  "year_lengths": {
    "E": 336,
    "P": 360,
    "J": 364
  },
  "source_seed": 12558
}
```

## Sources

```json
[
  "Strategy §3.3",
  "File52c §3.15",
  "C481"
]
```

## Opened utc

2026-09-27T22:43:36.399128+00:00

## Results

```json
{
  "E": {
    "calibration": "8400/23",
    "seed_output": 13650,
    "modeled_day_volume": 4586400
  },
  "P": {
    "calibration": "8400/23",
    "seed_output": 12740,
    "modeled_day_volume": 4586400
  },
  "J": {
    "calibration": "8400/23",
    "seed_output": 12600,
    "modeled_day_volume": 4586400
  }
}
```

## Finding

All three use K=8400/23 and give the same modeled day-volume4586400 for seed12558. The reusable rule is K_d(s)=(K/d)s. This explains common measurement, not every selected chronological placement.

## Reassessment

Find the common integral input domain and apply it to the Jared–Noah–Flood field.

## Checks

```json
{
  "calibration": true,
  "volume": true
}
```

## Closed utc

2026-09-27T22:43:36.399427+00:00

## Record provenance

Exact record hash: `d42d5541b7b56a6b572d1f47c84cc3c164902a1d8468fc4199f99ad243a12eab`

Source journal: `Research_Cycles/C0482_C0531/journal.json`