# C688 — Explain the two completed volume registers

## Question

What operation distinguishes12600 from12740 at the same35 count?

## Inputs

```json
{
  "count": 35,
  "calendar_lengths": [
    360,
    364
  ],
  "root_volume": 12558
}
```

## Sources

```json
[
  "Supplement A §6"
]
```

## Opened utc

2026-09-28T01:13:50.854956+00:00

## Results

```json
{
  "volumes": [
    12600,
    12740
  ],
  "difference": 140,
  "calendar_ratio": "91/90",
  "cross_products": [
    4586400,
    4586400
  ],
  "root_outputs": [
    12600,
    12740
  ]
}
```

## Finding

The12600/12740 pair uses the same completed count35 with360/364 calendar lengths. Their ratio91/90 and shared cross-product follow from this construction; the product is a register equality, not an additional chronology or independent witness.

## Reassessment

Account for the PhaseNorm40 volume and its residual relative to12600.

## Checks

```json
{
  "outputs": true,
  "difference": true,
  "cross_products": true
}
```

## Closed utc

2026-09-28T01:13:50.855260+00:00

## Record provenance

Exact record hash: `6a57b724fbf99b68c4140eb5feef5e5089bec76a4cf0b92c0e3e3e75c48f3ba4`

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