# C785 — Distinguish zero row residual from zero coordinate residual

## Question

What residual does the inserted MT Cainan boundary inherit?

## Inputs

```json
{
  "regular_Shelah": [
    2421,
    2421
  ],
  "cumulative_Shelah": [
    4393,
    4396
  ]
}
```

## Sources

```json
[
  "File51a paired rows; File18 Cainan130/460"
]
```

## Opened utc

2026-09-28T02:02:48.677719+00:00

## Results

```json
{
  "regular_Cainan": [
    2551,
    2551
  ],
  "cumulative_Cainan": [
    4853,
    4856
  ],
  "residuals": [
    0,
    3
  ]
}
```

## Finding

The inserted local durations are already round, but the cumulative Cainan coordinate inherits Shelah’s+3 residual:4853→4856. Local exactness and coordinate exactness are different properties.

## Reassessment

Check Terah triangle compatibility with both rounding selectors.

## Checks

```json
{
  "regular": true,
  "cumulative": true
}
```

## Closed utc

2026-09-28T02:02:48.677947+00:00

## Record provenance

Exact record hash: `76684580621cf081e99ba1ffd4554760a41ffeca85473f02b1256844bad31b59`

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