# C641 — Identify the calendar compatibility period

## Question

Why is the full congruence period32760, and how does it meet the earlier common-volume family?

## Inputs

```json
{
  "half_calendars": [
    168,
    180,
    182
  ],
  "full_calendars": [
    336,
    360,
    364
  ]
}
```

## Sources

```json
[
  "C640; File12 calendar definitions; C575"
]
```

## Opened utc

2026-09-28T00:58:58.617439+00:00

## Results

```json
{
  "half_calendar_lcm": 32760,
  "full_calendar_lcm": 65520,
  "previous_volume_coefficient": 327600,
  "ratios": [
    2,
    10
  ]
}
```

## Finding

The period32760 is the least common multiple of the three half-calendars. Doubling gives65520 for full calendars; the earlier327600 common-volume coefficient is ten half-periods. The numerical link comes from the same calendar denominators, with units retained.

## Reassessment

Execute the no-Cainan rail companion and locate which calendar divisibilities it preserves.

## Checks

```json
{
  "period": true,
  "previous_volume": true,
  "counts_increment": true
}
```

## Closed utc

2026-09-28T00:58:58.617609+00:00

## Record provenance

Exact record hash: `aca507fc8cb4d8a7ff368876b5cf8e91a3c68205120bedafce3f964c098b542e`

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