# C848 — Transfer the projection model to the four-household ledger

## Question

Do equal regrouped totals recover the ordered household inputs?

## Inputs

```json
{
  "source_vector": [
    33,
    16,
    14,
    7
  ]
}
```

## Sources

```json
[
  "File58 §1.4 Genesis46 printed-household subtotal register"
]
```

## Opened utc

2026-09-28T02:34:32.561601+00:00

## Results

```json
{
  "source_pair": [
    49,
    21
  ],
  "source_bracket": [
    40,
    30
  ],
  "source_prefix": [
    33,
    49,
    63,
    70
  ],
  "invisible_regrouping_direction": [
    1,
    -1,
    1,
    -1
  ],
  "diagnostic_prefix": [
    34,
    49,
    64,
    70
  ],
  "scope": "printed source subtotals only; no person-count repair or chronology projection"
}
```

## Finding

The same four counts produce49/21 and40/30 through two declared partitions. Both partitions miss one direction of change that the ordered prefix register detects. Retaining order adds information beyond shared totals.

## Reassessment

State the precise extension of the path grammar established by the list holdout.

## Checks

```json
{
  "pair_preserved": true,
  "bracket_preserved": true,
  "order_detects": true
}
```

## Closed utc

2026-09-28T02:34:32.561778+00:00

## Record provenance

Exact record hash: `d05d03a756cecf42b923038bf767ceba8209676005158203955d98d09d4a2626`

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