# C844 — Derive the equal-marginal constraint

## Question

What exactly must be true for purity and sex totals to coincide?

## Inputs

```json
{}
```

## Sources

```json
[
  "C843"
]
```

## Opened utc

2026-09-28T02:33:26.480421+00:00

## Results

```json
{
  "clean_minus_female": 0,
  "unclean_minus_male": 0,
  "fixed_margin_family": "[[490−t,t],[t,60−t]], 0≤t≤60",
  "source_t": 50,
  "constraint_count": 1,
  "independence_determinant": 1900
}
```

## Finding

The double490/60 display imposes one cross-category balance, b=c. Given those margins, one cell parameter remains; the source selects50. Distinct category definitions and equal marginals do not establish statistical independence.

## Reassessment

Recover the exact rank of the nine-row measurement map.

## Checks

```json
{
  "equal_marginals": true,
  "source_family": true,
  "not_product_table": true
}
```

## Closed utc

2026-09-28T02:33:26.480756+00:00

## Record provenance

Exact record hash: `344cf2ae2e5dc74547b9ec04e7fd7fa744e0dcbed85e398976fb9811b1e47a1e`

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