# C764 — Attach the residual decomposition to the Strategy rectangle

## Question

What part of the SP equal-gain rectangle is now explained?

## Inputs

```json
{
  "regular_head": 4206,
  "cumulative_head": 13406,
  "origin": 1446,
  "target": 1406
}
```

## Sources

```json
[
  "Strategy §4.3; C763"
]
```

## Opened utc

2026-09-28T01:56:59.196107+00:00

## Results

```json
{
  "native_spans": [
    2760,
    11960
  ],
  "expanded_spans": [
    2800,
    12000
  ],
  "gains": [
    40,
    40
  ],
  "preserved_gap": [
    9200,
    9200
  ],
  "new_explanation": "conditional cumulative-head provenance+2/+3/+5",
  "remaining_input": "the regular4206 branch and application status remain source-controlled"
}
```

## Finding

The existing rectangle survives exactly. This cycle adds a row-based explanation for its cumulative-head offset, not a new independent rectangle or permission to tune other heads.

## Reassessment

Test how lifespan splitting changes the whole accumulated comparison.

## Checks

```json
{
  "same_gain": true,
  "gap": true
}
```

## Closed utc

2026-09-28T01:56:59.197379+00:00

## Record provenance

Exact record hash: `3c9f212f167946a02885e388e7a5d4aff3a7c77dea3a32dfaf5760bb156bb85e`

Source journal: `Research_Cycles/C0732_C0831/journal.json`