# C1191 — Count the exact residual fibre

## Question

How many original decompositions share B,R,L away from zero?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1190"
]
```

## Opened utc

2026-09-28T05:22:33.812921+00:00

## Results

```json
{
  "fibre_count": {
    "path": "model/joint_rounding_fibre_count.json",
    "sha256": "675aded4ec0b4aa373b5fb41a62a59b066ba872990fb481b07f80f5fd2ee610f",
    "bytes": 388
  },
  "counts": {
    "-5": 0,
    "-4": 1,
    "-3": 2,
    "-2": 3,
    "-1": 4,
    "0": 5,
    "1": 4,
    "2": 3,
    "3": 2,
    "4": 1,
    "5": 0
  }
}
```

## Finding

Interior joint fibres have5−|z| members for |z|<=4. A singleton occurs only at z=±4, where both residuals must be the same extreme ±2.

## Reassessment

Apply this criterion to the complete55-row ordinary source domain.

## Checks

```json
{
  "all_counts": true,
  "singletons": true
}
```

## Closed utc

2026-09-28T05:22:33.813364+00:00

## Record provenance

Exact record hash: `a7bac3e57a118615956bdade02d54316c9c306183c353f7e4b805504c61bb97f`

Source journal: `Research_Cycles/C1132_C1431_Recovered/journal.json`