# C650 — Locate the common coarse rail

## Question

Which supplied triples share the same bilateral projection?

## Inputs

```json
{
  "triples": [
    [
      4121,
      4114,
      4107
    ],
    [
      4251,
      4244,
      4237
    ],
    [
      2296,
      2226,
      2156
    ],
    [
      1929,
      1922,
      1915
    ],
    [
      1885,
      1878,
      1871
    ]
  ],
  "centers": [
    4114,
    4244,
    2226,
    1922,
    1878
  ],
  "steps": [
    7,
    7,
    70,
    7,
    7
  ]
}
```

## Sources

```json
[
  "File70 §§3–6; A.3,A.5,A.6"
]
```

## Opened utc

2026-09-28T01:04:52.873999+00:00

## Results

```json
{
  "normalized": [
    [
      1,
      0,
      -1
    ],
    [
      1,
      0,
      -1
    ],
    [
      1,
      0,
      -1
    ],
    [
      1,
      0,
      -1
    ],
    [
      1,
      0,
      -1
    ]
  ],
  "refinement_projection": [
    0,
    2,
    4
  ]
}
```

## Finding

All five supplied triples normalize to1|0|-1. Creation and Terah additionally share the five-node refinement; Jacob and Joseph establish the coarse rail only. A shared outer shape does not supply missing inner events.

## Reassessment

Consolidate the first20 steps into an explanation of geometry versus selected calendar placement.

## Checks

```json
{
  "all_triples": true,
  "projection": true
}
```

## Closed utc

2026-09-28T01:04:52.874257+00:00

## Record provenance

Exact record hash: `e4c24280b4d4426f3ceec817198a956ebe03ed332b45f3e95d2b601944e35429`

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