# C493 — Cumulative residuals and completion selection

## Question

Does cumulative rounding itself create the −2 change used in C481?

## Inputs

```json
{
  "MT_26_lifespans": [
    930,
    912,
    905,
    910,
    895,
    962,
    365,
    969,
    777,
    950,
    600,
    438,
    433,
    464,
    239,
    239,
    230,
    148,
    205,
    175,
    180,
    147,
    137,
    133,
    137,
    120
  ],
  "terminal_anchor": 1406,
  "actual_completion": 14004
}
```

## Sources

```json
[
  "File51a §§16.1–16.2",
  "File22 §5.1"
]
```

## Opened utc

2026-09-27T22:41:47.928076+00:00

## Results

```json
{
  "actual_sum": 12600,
  "rounded_sum": 12600,
  "positive_rounding": 12,
  "negative_rounding": -12,
  "Moses_line_heads": [
    14006,
    14006
  ],
  "completion_offset": -2
}
```

## Finding

Cumulative rounding preserves12600 and the14006 Moses-line head exactly. The−2 is the selected lower completion endpoint14004, not a cumulative rounding error. The bridge uses both row residuals and explicit endpoint selection.

## Reassessment

Combine the two separately explained shifts and test which endpoint alternatives preserve the anchor.

## Checks

```json
{
  "total": true,
  "residuals": true
}
```

## Closed utc

2026-09-27T22:41:47.928329+00:00

## Record provenance

Exact record hash: `191fcfd19b8f4216ab56a16ed411f0e8f1405b5a2eb2e1412f960d17370da41e`

Source journal: `Research_Cycles/C0482_C0531/journal.json`