# C771 — Forty-step synthesis checkpoint

## Question

Which common mechanism now explains the Rounded family?

## Inputs

```json
{}
```

## Sources

```json
[
  "C732–770"
]
```

## Opened utc

2026-09-28T01:59:04.586015+00:00

## Results

```json
{
  "checkpoint": {
    "path": "deliverables/490d_Chronological_Families_Checkpoint_C771.md",
    "sha256": "4c032c5d12943f45cc600e2db12f4d16ad34f83fea9776731e994d301a974820",
    "bytes": 1493
  }
}
```

## Finding

The general object is an ordered source path with mode-specific row measurements and a recoverable rounding field. Finite variants are the next discriminating test.

## Reassessment

Reconstruct the finite variant masks against literal source examples.

## Checks

```json
{
  "forty": true
}
```

## Closed utc

2026-09-28T01:59:04.586382+00:00

## Record provenance

Exact record hash: `e3f27dc311662c3f87b33e3b8aea36e2840b1fcb531973d8916b821f493d4a0e`

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