# C770 — Identify a recoverable shared source object

## Question

What must accompany Rounded to preserve the original family?

## Inputs

```json
{}
```

## Sources

```json
[
  "C754–769"
]
```

## Opened utc

2026-09-28T01:58:40.489217+00:00

## Results

```json
{
  "reconstruction": "Actual boundary = Rounded boundary − D; actual row = rounded row − e",
  "affine_obstruction": {
    "fixed_dates": [
      1406,
      1526
    ],
    "moved_date": [
      1663,
      1661
    ]
  },
  "retained_data": [
    "ordered source rows",
    "typed path and terminal",
    "mode selector",
    "rounding residual field"
  ]
}
```

## Finding

Rounded plus its residual field recovers Actual exactly. Rounded alone loses information; no one affine date map works, since two fixed dates force identity while Amram moves.

## Reassessment

Integrate the 40-step checkpoint and move to finite variant configurations.

## Checks

```json
{
  "all_reconstructed": true,
  "two_fixed": true,
  "nonidentity": true
}
```

## Closed utc

2026-09-28T01:58:40.489528+00:00

## Record provenance

Exact record hash: `ef5dcc23f56156470f8e22dfe0a204c11dad7e8b4e1b1f8fc182bf3345ba596e`

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