# C1259 — Derive the necessary and sufficient coefficient-five calibration

## Question

When do the row gaps equal5(C+2T) and5C?

## Inputs

```json
{}
```

## Sources

```json
[
  "C1254",
  "C1256",
  "Strategy §4.1"
]
```

## Opened utc

2026-09-28T05:46:43.651080+00:00

## Results

```json
{
  "calibration": {
    "path": "model/regular_kernel_five_calibration.json",
    "sha256": "df161a85a5d0da068398d3c6e22e3232084ff1ded55eb7929261cbd762d6b63a",
    "bytes": 474
  },
  "ratios": [
    "3/5",
    "13/10"
  ]
}
```

## Finding

The fivefoldexpression holds exactly whenT=3u/5 andC=13u/10. These match60 and130 at u100, but the ratios are additional source relations; the row supports alone do not generate them.

## Reassessment

Separate compatibility ofa commoncoefficient fromthe choice thatcoefficient equalsfive.

## Checks

```json
{
  "ratios": true,
  "sourcevalues": true,
  "reconstruction": true
}
```

## Closed utc

2026-09-28T05:46:43.652027+00:00

## Record provenance

Exact record hash: `eca1b4576c3639111eecd6e4283671e4b0a3343ec75c6a6a9d7b0ba981e2d7fa`

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