# C706 — Recover the fixed-set overlap inventory

## Question

Which of the source-listed cycle totals closes the whole declared field?

## Inputs

```json
{
  "cycle_totals": [
    5840,
    5842,
    5844,
    5846
  ],
  "fixed_field_center": -2921
}
```

## Sources

```json
[
  "Supplement A §13.3; C704–C705"
]
```

## Opened utc

2026-09-28T01:18:51.229325+00:00

## Results

```json
{
  "columns": [
    "total",
    "overlap",
    "outside"
  ],
  "rows": [
    [
      5840,
      8,
      4
    ],
    [
      5842,
      12,
      0
    ],
    [
      5844,
      8,
      4
    ],
    [
      5846,
      4,
      8
    ]
  ],
  "fixed_source_set": true
}
```

## Finding

The complete fixed-set inventory is8/12/8/4 overlaps for5840/5842/5844/5846. Only5842 covers every node. Selected-route matches at other totals remain valid local comparisons but do not establish whole-field closure.

## Reassessment

Derive the conditional placement theorem from centers rather than searching more candidate dates.

## Checks

```json
{
  "inventory": true,
  "unique_listed_full": true
}
```

## Closed utc

2026-09-28T01:18:51.229744+00:00

## Record provenance

Exact record hash: `4423f316801b318a441eea5684f08048dcfccbdb184c7dfb6cfd040f5d51fc00`

Source journal: `Research_Cycles/C0632_C0731/journal.json`