# C1208 — Explain the change from exact to rounded cap reduction

## Question

Why does total488 become485 under row rounding?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1204",
  "C1143",
  "C1131 inherited cap-round result"
]
```

## Opened utc

2026-09-28T05:27:09.166462+00:00

## Results

```json
{
  "loss_identity": {
    "path": "model/cap_round_loss_identity.json",
    "sha256": "238adb4d7804f3f7873b3ee15c3ac61e23e8c1f7b8bf0615c2b7b462b5c3cb14",
    "bytes": 1794
  },
  "exact_total": 488,
  "rounded_total": 485
}
```

## Finding

Rounded reduction equals exact removed life plus the difference of the two rounding errors. The three SP cap losses115/249/124 become115/250/120, explaining488→485 without a second cap rule.

## Reassessment

Check what commutes when both the cap and its input are rounded consistently.

## Checks

```json
{
  "identity_all": true,
  "totals": true
}
```

## Closed utc

2026-09-28T05:27:09.167822+00:00

## Record provenance

Exact record hash: `1244961a0b50d087dce02dadbe3282140ad91c9f13efd6c1ebc5df68703fb63c`

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