# C1250 — Determine the arithmetic freedom in the430/490 bridge

## Question

Does the integer bridge430m−490n=130 have only the source solution?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1238",
  "File51a §7A.2"
]
```

## Opened utc

2026-09-28T05:43:46.390359+00:00

## Results

```json
{
  "bridge_family": {
    "path": "model/Moses_cycle_bridge_integer_family.json",
    "sha256": "5511afbe3ed58ac79ffe1d94b93293f8fab73e811d91fa86e0454fffd7af8275",
    "bytes": 587
  }
}
```

## Finding

The bridge has infinitely many positive integer solutions, with6/5 the smallest in this fixed430/490 equation. That arithmetic property is separate from the source path’s identification ofMoses.

## Reassessment

Assess the minimal source packet that regenerates the completeMosesfamily rather than just itscyclelabels.

## Checks

```json
{
  "source_equation": true,
  "step_homogeneous": true,
  "examples": true
}
```

## Closed utc

2026-09-28T05:43:46.390729+00:00

## Record provenance

Exact record hash: `0677fb515a567213d1cedea44caa1354604c9c1a595221eb22190378fe30c3e2`

Source journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`