# C961 — Nonredundant synchronization

## Question

How many extra constraints join the three caps to one parameter?

## Inputs

```json
{}
```

## Sources

```json
[
  "C954",
  "C956",
  "C960"
]
```

## Opened utc

2026-09-28T03:47:16.038529+00:00

## Results

```json
{
  "k_from_each": [
    601,
    601,
    601
  ],
  "pairwise_residuals": [
    0,
    0,
    0
  ],
  "independent_synchronization_equations": 2
}
```

## Finding

One cap fixes k; two further equations synchronize the remaining caps. The third pairwise comparison is their sum.

## Reassessment

Determine how much weaker clipped-row support alone would be.

## Checks

```json
{
  "common_k": true,
  "dependent_third": true
}
```

## Closed utc

2026-09-28T03:47:16.038776+00:00

## Record provenance

Exact record hash: `659013cef1eeb9344f8f0afff07327a70bc198cd84a5dfb2fbbbd80bcde93671`

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