# C526 — The forwarded axis joins the529 grammar

## Question

What does the existing three-axis diagram’s forwarded family share with the studied ladders?

## Inputs

```json
{
  "forwarded_shift_magnitudes": [
    4232,
    8464,
    12696
  ],
  "scope": "duration algebra only; existing source-authorized forwardings keep their own endpoint domains"
}
```

## Sources

```json
[
  "Chronology_Three_Axis_Mirrors.png supplied schematic",
  "C505–C507; inherited C480 controls"
]
```

## Opened utc

2026-09-27T22:53:47.842209+00:00

## Results

```json
{
  "ladders": [
    {
      "source_shift": 4232,
      "529_coefficient": 8,
      "first_E": 4600,
      "second_E": 5000,
      "translation_dilation_difference": 368
    },
    {
      "source_shift": 8464,
      "529_coefficient": 16,
      "first_E": 9200,
      "second_E": 10000,
      "translation_dilation_difference": 736
    },
    {
      "source_shift": 12696,
      "529_coefficient": 24,
      "first_E": 13800,
      "second_E": 15000,
      "translation_dilation_difference": 1104
    }
  ],
  "operator_relation": "D_E,a T_t = T_(E*t) D_E,a",
  "shared_middle_duration": "8464 ->9200 ->10000"
}
```

## Finding

The diagram’s8,16,24 multiples of529 become4600/9200/13800, then5000/10000/15000. The middle ladder shares the9200→10000 duration used by the SP rectangle and Shem partition. This connects all three schematic families at the operator level; identical durations do not identify their source nodes or license new forwardings.

## Reassessment

Use the proven interfaces to replace a merely spatial reading of the axes with a map of actual operations.

## Checks

```json
{
  "coefficients": true,
  "first": true,
  "second": true
}
```

## Closed utc

2026-09-27T22:53:47.842480+00:00

## Record provenance

Exact record hash: `6fa98efea2e8df1c8aa277bd2566ff2c354e7f81c46617fe5a1fa88da4d398d1`

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