# C845 — Measure the information retained by the category projections

## Question

How many independent totals do the four marginals supply?

## Inputs

```json
{}
```

## Sources

```json
[
  "File58 nine-row ledger; C843–844"
]
```

## Opened utc

2026-09-28T02:33:41.804403+00:00

## Results

```json
{
  "incidence_matrix": [
    [
      1,
      1,
      1,
      1,
      1,
      1,
      0,
      0,
      0
    ],
    [
      0,
      0,
      0,
      0,
      0,
      0,
      1,
      1,
      1
    ],
    [
      1,
      0,
      1,
      0,
      1,
      0,
      1,
      1,
      0
    ],
    [
      0,
      1,
      0,
      1,
      0,
      1,
      0,
      0,
      1
    ]
  ],
  "rank": 3,
  "kernel_dimension_on_unrestricted_nine_counts": 6,
  "row_relation": "clean+unclean=female+male"
}
```

## Finding

The four totals contain three independent linear measurements of nine source counts. Six numerical directions are invisible to these marginals; species, order and individual counts remain necessary source data.

## Reassessment

Regenerate the complete source-admitted clean category-order walk.

## Checks

```json
{
  "rank3": true,
  "row_relation": true
}
```

## Closed utc

2026-09-28T02:33:41.806576+00:00

## Record provenance

Exact record hash: `2632e305cdbf2bb4ff5b314986b760a4d0766745390a8e53ba2419cf81c17f79`

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