# C672 — Generate the complete phase bracket

## Question

Can center, width and suffix offset recover all eight supplied endpoints?

## Inputs

```json
{
  "base_center": 2871,
  "widths": [
    34,
    40
  ],
  "phase_offsets": {
    "n": 0,
    "t": "1/2"
  },
  "BC_label_rule": "coord(tY)=Y−1/2"
}
```

## Sources

```json
[
  "Supplement A §§4.1,4.3"
]
```

## Opened utc

2026-09-28T01:10:25.916112+00:00

## Results

```json
{
  "phase_rows": [
    {
      "width": 34,
      "phase": "n",
      "coordinates": [
        2888,
        2854
      ],
      "labels": [
        2888,
        2854
      ]
    },
    {
      "width": 34,
      "phase": "t",
      "coordinates": [
        "5777/2",
        "5709/2"
      ],
      "labels": [
        2889,
        2855
      ]
    },
    {
      "width": 40,
      "phase": "n",
      "coordinates": [
        2891,
        2851
      ],
      "labels": [
        2891,
        2851
      ]
    },
    {
      "width": 40,
      "phase": "t",
      "coordinates": [
        "5783/2",
        "5703/2"
      ],
      "labels": [
        2892,
        2852
      ]
    }
  ],
  "formula": "x=C+epsilon±w/2"
}
```

## Finding

One center/width/phase formula generates all eight before/after positions. Corresponding suffix widths are34 and40; Tishri and Nisan centers remain separated by half a year in exact coordinates.

## Reassessment

Test whether one global affine date map can perform this entire phase change.

## Checks

```json
{
  "source_labels": true,
  "fixed_phase": true
}
```

## Closed utc

2026-09-28T01:10:25.916432+00:00

## Record provenance

Exact record hash: `7678cbcaa6477f93b68fab8add528ac5f16f45cd92d2602992138e0fc1a48d50`

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