# C991 — Allocation triangle

## Question

Do the three relative Key gains form one nested-selection law?

## Inputs

```json
{}
```

## Sources

```json
[
  "C985–C990"
]
```

## Opened utc

2026-09-28T03:53:30.018809+00:00

## Results

```json
{
  "E_to_P": "1/6",
  "P_to_J": "3/13",
  "E_to_J": "1/26",
  "nested_factor": "300/299"
}
```

## Finding

The fractions1/6,3/13 and1/26 satisfy the nested-selection product law. The derived3/13 alone supplies no source-appointed chronological cut.

## Reassessment

Separate this selection composition from sequential application of Keys.

## Checks

```json
{
  "product": true,
  "fractions": true,
  "nested": true
}
```

## Closed utc

2026-09-28T03:53:30.019141+00:00

## Record provenance

Exact record hash: `d3859ee65e2e01ec3ebe9099894e72e315b8591e00258c5b33308e3f9606d8d7`

Source journal: `Research_Cycles/C0932_C1131/journal.json`