# C1204 — Separate the two loss types by the known cap branch

## Question

Are rounding residual and cap excess independent missing quantities on every row?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1202",
  "C1203"
]
```

## Opened utc

2026-09-28T05:26:13.150833+00:00

## Results

```json
{
  "branch_information": {
    "path": "model/cap_round_branch_information.json",
    "sha256": "496cab05f8d37f8f3f5ac004911fb79736ca2e4435da321932625405a2f45d59",
    "bytes": 2128
  }
}
```

## Finding

The two loss registers are not two independent unknowns per row. A known clipped row has y=c, fixing its rounding residual; a known unclipped row has zero excess and needs only its rounding residual.

## Reassessment

Verify reconstruction of all nine baseline lives using the branch-appropriate register.

## Checks

```json
{
  "identity_all": true,
  "three_clipped": true,
  "branch_constraints": true
}
```

## Closed utc

2026-09-28T05:26:13.151348+00:00

## Record provenance

Exact record hash: `582d9b8d493849e89b92c6868c8b2072903e0d9da9fc0d9ed995d316d2ccdcc8`

Source journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`