# C987 — Four relations contain three constraints

## Question

What is the exact dependence certificate for calibration and allocation?

## Inputs

```json
{
  "matrix": [
    [
      336,
      -360,
      0
    ],
    [
      336,
      0,
      -364
    ],
    [
      1,
      -6,
      0
    ],
    [
      1,
      0,
      -26
    ]
  ],
  "rhs": [
    0,
    0,
    -5,
    -25
  ]
}
```

## Sources

```json
[
  "C985",
  "C986"
]
```

## Opened utc

2026-09-28T03:53:02.193428+00:00

## Results

```json
{
  "basis": {
    "path": "model/key_calibration_basis.json",
    "sha256": "0cd31da8f6cd69b1b9a7f33ef4fc1994b80e977c2715a19b08cf9043e76d1155",
    "bytes": 365
  },
  "rank": 3,
  "augmented_rank": 3,
  "dependency_products": [
    0,
    0,
    0,
    0
  ]
}
```

## Finding

The four equations have rank three, with7A−6B−420C+84D=0 including constants. One relation is dependent.

## Reassessment

Identify the freedom left by calendar calibration alone.

## Checks

```json
{
  "rank_three": true,
  "certificate": true
}
```

## Closed utc

2026-09-28T03:53:02.194512+00:00

## Record provenance

Exact record hash: `4943fd50616d70bca539f25bdd91ca12d2ce73d480b2b4b55006098679591407`

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