# C721 — Relate the two exact phase charts

## Question

How does the earlier positiveBC phase chart connect to the fixed-set signed chart?

## Inputs

```json
{
  "earlier_chart": "q(Bn)=B; q(Bt)=B−1/2",
  "signed_chart": "x(Bn)=−B+1/4; x(Bt)=−B+3/4",
  "Short_center_labels": [
    "2922t",
    "2921n"
  ]
}
```

## Sources

```json
[
  "Supplement A §§4.1,13.1–13.2; reviewer C692–C709"
]
```

## Opened utc

2026-09-28T01:26:27.475595+00:00

## Results

```json
{
  "chart_map": "x=1/4−q",
  "sample_T_x": "-11753/4",
  "sample_N_x": "-11755/4",
  "center_pair_q": [
    "5843/2",
    2921
  ],
  "center_pair_x": [
    "-11685/4",
    "-11683/4"
  ],
  "January_center": -2921
}
```

## Finding

The charts are related by x=1/4−q. The2922t/2921n center pair brackets the January instant−2921 by a quarter-year on either side; neither labeled phase position alone is that instant. This resolves the chart relation without changing the source phases.

## Reassessment

Apply all independent review refinements to the final integrated manuscript.

## Checks

```json
{
  "T_rule": true,
  "N_rule": true,
  "center_pair": true,
  "January_center": true
}
```

## Closed utc

2026-09-28T01:26:27.476086+00:00

## Record provenance

Exact record hash: `05c0c928fe5398864d7f4c46c6e269862338e93e8a75004bf6efec16ae1258e5`

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