# C978 — Rounding the cap counts

## Question

Does nearest-five rounding commute with the source minimum?

## Inputs

```json
{}
```

## Sources

```json
[
  "C953",
  "C955",
  "C956",
  "File51a nearest-five policy"
]
```

## Opened utc

2026-09-28T03:50:40.100297+00:00

## Results

```json
{
  "field": {
    "path": "model/sp_cap_rounded_counts.json",
    "sha256": "ec28f7907b254a793adc02ef6124384b9be3e2f6bf7b3ce347bd2708b35ae779",
    "bytes": 332
  },
  "rounded_lives": [
    930,
    910,
    905,
    910,
    895,
    845,
    365,
    720,
    655
  ],
  "proof": "A monotone map on a total order preserves binary minima."
}
```

## Finding

Count rounding commutes with the cap across all nine rows because the rounding map is monotone. This does not yet define Rounded date labels.

## Reassessment

Check whether this source field keeps the same strict active support.

## Checks

```json
{
  "commutes_all_rows": true,
  "expected_counts": true
}
```

## Closed utc

2026-09-28T03:50:40.100762+00:00

## Record provenance

Exact record hash: `fc8fb73429f76d6d11bad550902e0a5f1f589f89f4f4e0e7a1fabc19ea6591ff`

Source journal: `Research_Cycles/C0932_C1131/journal.json`