# C523 — Connect SP’s two comparison families

## Question

Can declared frame and node-class changes explain the9200 versus8982 SP gaps?

## Inputs

```json
{
  "equalized_regular_completion": 4414,
  "cumulative_lower_completion": 13396,
  "native_week_opening": 4206,
  "cumulative_implied_Day1": 13406
}
```

## Sources

```json
[
  "File18 §3.1 Creation-week row; §6C decade display",
  "Strategy §4.3",
  "C483,C508"
]
```

## Opened utc

2026-09-27T22:52:23.265218+00:00

## Results

```json
{
  "regular_frame_and_head_change": [
    -215,
    7
  ],
  "cumulative_head_change": 10,
  "reconstructed_rectangle_heads": [
    4206,
    13406
  ],
  "completion_gap": 8982,
  "rectangle_gap": 9200,
  "gap_change": 218,
  "decomposition": "218=215+(10−7)"
}
```

## Finding

The two SP families connect through source-declared changes: return the regular head to its native frame and week opening, and select the cumulative decade opening. Their gap changes by218 exactly. The9200 rectangle can therefore join the grammar without pretending its heads are the completion pair.

## Reassessment

Check explicitly why these richer state changes cannot be replaced by one scalar map from regular to cumulative chronology.

## Checks

```json
{
  "heads": true,
  "gaps": true,
  "delta": true
}
```

## Closed utc

2026-09-27T22:52:23.265442+00:00

## Record provenance

Exact record hash: `1e919881168b12163f7200267e4146b359ad97d41f6421b87ea27da640c1cb5e`

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