# C668 — Generate the whole alternating720/30 ladder

## Question

Can the source’s ten coordinates be recovered without separate date fitting?

## Inputs

```json
{
  "head": 4326,
  "core": 690,
  "flank": 30,
  "source": [
    4326,
    4296,
    3606,
    3576,
    2886,
    2856,
    2166,
    2136,
    1446,
    1416
  ]
}
```

## Sources

```json
[
  "Supplement A §1.3; admitted source ladder only"
]
```

## Opened utc

2026-09-28T01:09:07.681958+00:00

## Results

```json
{
  "generated_nodes": [
    4326,
    4296,
    3606,
    3576,
    2886,
    2856,
    2166,
    2136,
    1446,
    1416
  ],
  "gaps": [
    30,
    690,
    30,
    690,
    30,
    690,
    30,
    690,
    30
  ],
  "same_rail_steps": [
    [
      720,
      720,
      720,
      720
    ],
    [
      720,
      720,
      720,
      720
    ]
  ],
  "width": 2910
}
```

## Finding

The ten supplied positions are two720-step rails separated by30. Their interleaving generates the alternating30|690 path and2910 outer width. Source, dependency and generated-companion roles remain attached to the original positions; no new SKL transport is inferred.

## Reassessment

Extract the six-node1470 cell and explain its alternative partitions.

## Checks

```json
{
  "whole_ladder": true,
  "gaps": true,
  "width": true
}
```

## Closed utc

2026-09-28T01:09:07.682365+00:00

## Record provenance

Exact record hash: `ebb63304f38feeb2026c85d30e53b38622a7cd2260ae47abc076d873610e9378`

Source journal: `Research_Cycles/C0632_C0731/journal.json`