# C516 — The Cainan-associated trio as one transformed object

## Question

What does one common dilation explain about the complete trio?

## Inputs

```json
{
  "inverse_Eber_Shelah_Mahalalel": [
    9321,
    2421,
    1731
  ],
  "anchor": 14726
}
```

## Sources

```json
[
  "File52c §3.12.1–3.12.2"
]
```

## Opened utc

2026-09-27T22:49:14.668348+00:00

## Results

```json
{
  "input_triple": [
    9321,
    2421,
    1731
  ],
  "output_triple": [
    8851,
    1351,
    601
  ],
  "input_gaps": [
    6900,
    690
  ],
  "output_gaps": [
    7500,
    750
  ],
  "outer_widths": [
    7590,
    8250
  ],
  "radius_23_coefficients": [
    235,
    535,
    565
  ],
  "P_integral": [
    false,
    false,
    false
  ],
  "J_integral": [
    false,
    false,
    false
  ]
}
```

## Finding

The6900:690 partition becomes7500:750, preserving10:1. Its7590 outer width becomes8250. All three E results are integral, while P and J are fractional on these radii. The trio is one structured object with dependent displays.

## Reassessment

Test the mixed original/generated Cainan midpoint, which is not forced by transforming the trio alone.

## Checks

```json
{
  "outputs": true,
  "ratio": true,
  "outer": true
}
```

## Closed utc

2026-09-27T22:49:14.668625+00:00

## Record provenance

Exact record hash: `c0abbc9184128fcaa94ed52617f36dfb207e5bad7cd78c89052b62807b5e5ab8`

Source journal: `Research_Cycles/C0482_C0531/journal.json`