# C666 — Generate the complete retained-flank table

## Question

Can one formula produce every native and converted bracket column?

## Inputs

```json
{
  "core": 690,
  "flank": 30,
  "operators": [
    "identity",
    "P",
    "E"
  ]
}
```

## Sources

```json
[
  "Supplement A §§1.1–1.2"
]
```

## Opened utc

2026-09-28T01:08:43.934003+00:00

## Results

```json
{
  "columns": [
    "core",
    "gain",
    "one_flank",
    "two_flanks"
  ],
  "rows": [
    [
      690,
      0,
      720,
      750
    ],
    [
      700,
      10,
      730,
      760
    ],
    [
      750,
      60,
      780,
      810
    ]
  ]
}
```

## Finding

Applying each Key to the core while retaining30-unit flanks generates the full source table:690/720/750,700/730/760 and750/780/810. The gain belongs to the core; a whole-bracket conversion is a different operation.

## Reassessment

Measure the exact difference between retained-flank and whole-bracket conversion.

## Checks

```json
{
  "source_table": true,
  "gains": true
}
```

## Closed utc

2026-09-28T01:08:43.934579+00:00

## Record provenance

Exact record hash: `13f081be334a5e06920e021097c80171ecc6103e09c820fb6f6241482071ebd6`

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