# C586 — Unify calendar and paired-endpoint equalities

## Question

What single normalized comparison underlies the calendar Keys and earlier common endpoints?

## Inputs

```json
{
  "calendars": [
    336,
    360,
    364
  ],
  "Keys": [
    "25/23",
    "70/69",
    "300/299"
  ]
}
```

## Sources

```json
[
  "File12 §§2,6.3; C535; C568–C575"
]
```

## Opened utc

2026-09-28T00:20:35.611996+00:00

## Results

```json
{
  "calibration_constant": [
    "8400/23",
    "8400/23",
    "8400/23"
  ],
  "Key_ratios": [
    "15/14",
    "13/12",
    "91/90"
  ],
  "calendar_decomposition": [
    336,
    364,
    360
  ]
}
```

## Finding

All Keys satisfy d×K_d=8400/23, hence K_d(s)=(8400/23)(s/d). Equal normalized durations explain the calendar-volume agreements and the earlier1566/2926 paired endpoints when anchor and direction also agree.

## Reassessment

Test the Enochic source family for a similarly compact parameter rule.

## Checks

```json
{
  "constant": true,
  "ratios": true,
  "calendars": true
}
```

## Closed utc

2026-09-28T00:20:35.612360+00:00

## Record provenance

Exact record hash: `512b300884f11f09a386de89339f2159011ff73fce2f80bb436d553548622961`

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