# C1190 — Specify the joint Rounded-row observation

## Question

What exact data remain after begetting and remaining years are rounded separately?

## Inputs

```json
{
  "Q": "nearest multiple of5 on integer nonnegative durations"
}
```

## Sources

```json
[
  "C1189",
  "File51a",
  "File52c_latest.md",
  "C1131 inherited rounding analysis"
]
```

## Opened utc

2026-09-28T05:22:31.861791+00:00

## Results

```json
{
  "observation": {
    "path": "model/joint_rounding_observation.json",
    "sha256": "dda331935947e8bcd63cba12aa5afc9ec31aa3a07ca64995199c8529d7452d77",
    "bytes": 540
  },
  "cells": {
    "0": [
      0,
      1,
      2
    ],
    "5": [
      3,
      4,
      5,
      6,
      7
    ],
    "10": [
      8,
      9,
      10,
      11,
      12
    ]
  }
}
```

## Finding

Joint Rounded observations restrict two hidden residuals to a bounded line u+v=L−B−R. Nonnegative durations truncate the cell at zero; current derived remainders do not supply independent evidence.

## Reassessment

Derive and verify the exact size of that bounded line for interior cells.

## Checks

```json
{
  "zero_cell": true,
  "interior_cell": true
}
```

## Closed utc

2026-09-28T05:22:31.862131+00:00

## Record provenance

Exact record hash: `dfba833c7385eb1f5d5150fc3aebf4a3f3f7510f562aa74723fe41d442e5805a`

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