# C561 — Resolve the two Joshua translations

## Question

Which Joseph states yield the source430 and460 routes?

## Inputs

```json
{
  "target": [
    1476,
    1366
  ],
  "source_intervals": [
    [
      1906,
      1796
    ],
    [
      1936,
      1826
    ],
    [
      1933,
      1823
    ],
    [
      "3873/2",
      "3653/2"
    ]
  ]
}
```

## Sources

```json
[
  "File61 §§14.1–14.3"
]
```

## Opened utc

2026-09-28T00:14:34.271558+00:00

## Results

```json
{
  "translations": [
    [
      430,
      430
    ],
    [
      460,
      460
    ],
    [
      457,
      457
    ],
    [
      "921/2",
      "921/2"
    ]
  ],
  "states": [
    "backward Nisan",
    "forward Aaron whole-year",
    "forward Nisan diagnostic",
    "forward Aaron exact diagnostic"
  ]
}
```

## Finding

The430/460 pair is exact in its declared mixed states. Other forward phases require457 or460.5, so460 is not a phase-independent property of Joseph.

## Reassessment

Follow the fixed regular Joshua interval into the cumulative Joshua interval.

## Checks

```json
{
  "routes": true
}
```

## Closed utc

2026-09-28T00:14:34.271787+00:00

## Record provenance

Exact record hash: `d89a2f0a37c2f3bd6fe0a40ed73b2f7ecfb8193f1ad3d56f229552e1a7b1bde3`

Source journal: `Research_Cycles/C0532_C0631/journal.json`