# C508 — SP equal-gain rectangle

## Question

Can the calendar grammar reconstruct the Strategy’s separately declared SP rectangle?

## Inputs

```json
{
  "Strategy_ReportIV_comparison_heads": [
    4206,
    13406
  ],
  "Exodus": 1446,
  "Conquest": 1406,
  "state_note": "historical Strategy SP−215 rectangle; not the File18 completion pair used in C483"
}
```

## Sources

```json
[
  "Strategy §4.3"
]
```

## Opened utc

2026-09-27T22:46:21.831060+00:00

## Results

```json
{
  "input_radii": [
    2760,
    11960
  ],
  "P_and_J_outputs": [
    2800,
    12000
  ],
  "gains": [
    40,
    40
  ],
  "preserved_difference": [
    9200,
    9200
  ],
  "E_difference": 10000,
  "general_rule": "69m ->70m and299m ->300m; common gain m and preserved separation230m"
}
```

## Finding

At m=40, two distinct Keys add the same40, preserving9200 while terminating at the shared1406 target with the two heads held. This is a reusable equal-gain construction, separate from the newer File18 completion comparison.

## Reassessment

Derive how anchor changes affect otherwise identical expansions, needed to relate the14726 family’s two presentations.

## Checks

```json
{
  "radii": true,
  "gain": true,
  "difference": true,
  "E": true
}
```

## Closed utc

2026-09-27T22:46:21.831361+00:00

## Record provenance

Exact record hash: `2ef24055f1beab32a97f09e24cd39b9112cab3fa4561d565eb93cf445d5ffb2b`

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