# C1029 — NT equal-block coarsening preserves reflection

## Question

Does the complete77-edge NT field carry reflection through seven-edge blocks?

## Inputs

```json
{
  "edges": 77,
  "block_size": 7
}
```

## Sources

```json
[
  "File43",
  "File54",
  "C1028"
]
```

## Opened utc

2026-09-28T04:01:19.343924+00:00

## Results

```json
{
  "block_map": [
    10,
    9,
    8,
    7,
    6,
    5,
    4,
    3,
    2,
    1,
    0
  ],
  "selected_boundaries": [
    0,
    7,
    14,
    21,
    28,
    35,
    42,
    49,
    56,
    63,
    70,
    77
  ],
  "reflected_boundaries": [
    77,
    70,
    63,
    56,
    49,
    42,
    35,
    28,
    21,
    14,
    7,
    0
  ]
}
```

## Finding

Reflection permutes all eleven equal seven-edge blocks, so the NT490 coarsening passes the criterion. This explains why one contraction preserves the reflection that the Toledot section quotient loses.

## Reassessment

Compare the three kinds of retained information now exposed.

## Checks

```json
{
  "all_blocks": true,
  "boundary_invariance": true,
  "eleven_blocks": true
}
```

## Closed utc

2026-09-28T04:01:19.344406+00:00

## Record provenance

Exact record hash: `fceec64736d298c84820860ac60bcf8a9becb90c69fa152136e26fc41d36ce65`

Source journal: `Research_Cycles/C0932_C1131/journal.json`