# C866 — Classify the complete finite E return family

## Question

Which positive display indices return to display indices under E?

## Inputs

```json
{
  "domain": "r=0,...,76",
  "E": "25/23"
}
```

## Sources

```json
[
  "File43 complete display",
  "File54 Enoch fork"
]
```

## Opened utc

2026-09-28T02:44:22.442355+00:00

## Results

```json
{
  "returns": [
    {
      "r": 0,
      "image_r": 0,
      "source": "Jesus",
      "image": "Jesus",
      "source_BC": 6,
      "image_BC": 6
    },
    {
      "r": 23,
      "image_r": 25,
      "source": "Melki",
      "image": "Cosam",
      "source_BC": 1616,
      "image_BC": 1756
    },
    {
      "r": 46,
      "image_r": 50,
      "source": "Salmon",
      "image": "Hezron",
      "source_BC": 3226,
      "image_BC": 3506
    },
    {
      "r": 69,
      "image_r": 75,
      "source": "Enoch",
      "image": "Creation of Adam",
      "source_BC": 4836,
      "image_BC": 5256
    }
  ],
  "artifact": {
    "path": "model/NT_E_returns.json",
    "sha256": "3fd2848a494b025de9c077ff77f10011cb24bf0a463fc3b1f5a7754b04e029d7",
    "bytes": 528
  }
}
```

## Finding

Coprimality of25 and23 makes 23-divisibility the complete return rule. The four finite returns, including the fixed hinge, follow from one lattice condition; only the Enoch fork carries the supplied interpretation.

## Reassessment

Classify P on the same fixed domain and compare its intersection with E.

## Checks

```json
{
  "complete": true,
  "bounded": true,
  "Enoch": true
}
```

## Closed utc

2026-09-28T02:44:22.442971+00:00

## Record provenance

Exact record hash: `7a7af985e43def3235d6fa05b9eb770002797be530012a5eb1ba9c126ab729df`

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