# C842 — Separate scale, order and accumulation

## Question

Which operations commute, and which change the internal chronological field?

## Inputs

```json
{}
```

## Sources

```json
[
  "File58 declared order and×7; C839–841"
]
```

## Opened utc

2026-09-28T02:32:58.085858+00:00

## Results

```json
{
  "scale_order_commutes": true,
  "scale_accumulation_commutes": true,
  "forward_prefix_years": [
    210,
    413,
    609,
    798,
    980,
    1155,
    1323,
    1393
  ],
  "reverse_prefix_years": [
    70,
    238,
    413,
    595,
    784,
    980,
    1183,
    1393
  ]
}
```

## Finding

Scaling commutes with both declared reordering and accumulation. Reordering preserves the total but changes the intermediate prefix field; that distinction is the same one needed for genealogical and Rounded paths.

## Reassessment

Construct the complete sex-by-purity measurement table for Esau’s ledger.

## Checks

```json
{
  "linear_scaling": true,
  "total_preserved": true,
  "internal_change": true
}
```

## Closed utc

2026-09-28T02:32:58.086086+00:00

## Record provenance

Exact record hash: `014b2520d366a31afb8baa60bf99cdab71294276d587139eb6fc4243b4b5e6ae`

Source journal: `Research_Cycles/C0832_C0931/journal.json`