# C748 — Identify the ordered reconstruction operator

## Question

Does the complete boundary profile determine itslocalcontributionsuniquely once theterminal is fixed?

## Inputs

```json
{
  "local_vector": [
    27,
    100,
    100,
    100,
    100,
    60,
    60
  ],
  "terminal": 0,
  "operator": "uppertriangularsuffixsum"
}
```

## Sources

```json
[
  "C742,C747; Research Strategy §5F"
]
```

## Opened utc

2026-09-28T01:47:14.611732+00:00

## Results

```json
{
  "suffix_matrix": [
    [
      1,
      1,
      1,
      1,
      1,
      1,
      1
    ],
    [
      0,
      1,
      1,
      1,
      1,
      1,
      1
    ],
    [
      0,
      0,
      1,
      1,
      1,
      1,
      1
    ],
    [
      0,
      0,
      0,
      1,
      1,
      1,
      1
    ],
    [
      0,
      0,
      0,
      0,
      1,
      1,
      1
    ],
    [
      0,
      0,
      0,
      0,
      0,
      1,
      1
    ],
    [
      0,
      0,
      0,
      0,
      0,
      0,
      1
    ]
  ],
  "profile": [
    547,
    520,
    420,
    320,
    220,
    120,
    60,
    0
  ],
  "recovered_rows": [
    27,
    100,
    100,
    100,
    100,
    60,
    60
  ],
  "determinant": 1,
  "rank": 7
}
```

## Finding

The suffix-sum matrix is triangular with unit diagonal. With terminal fixed, every ordered boundary determines exactly one local row vector, recovered by adjacent differences. This gives theStrategy a small linear mechanism for whole-family explanation, while total-only evaluation loses theordering.

## Reassessment

Test thewhole rounded-row family for compatibility between lifespan projection androunding.

## Checks

```json
{
  "recovered": true,
  "unit_diagonal": true,
  "triangular": true
}
```

## Closed utc

2026-09-28T01:47:14.611940+00:00

## Record provenance

Exact record hash: `9191777041d2fcdd61aa3efbe11747e1d8a05d5c7f42ed72e8c0218cefbdfd3d`

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