# C707 — Derive the fixed-template placement condition

## Question

What does whole-field mirror closure determine once the shape is fixed?

## Inputs

```json
{
  "translation": 5842,
  "symmetric_template_center": 0,
  "shape": "fixed literal twelve-node template"
}
```

## Sources

```json
[
  "Supplement A §13.4"
]
```

## Opened utc

2026-09-28T01:19:05.456745+00:00

## Results

```json
{
  "required_center": -2921,
  "center_equation": "c+L=−c",
  "template_symmetric": true,
  "scope": "unique placement conditional on fixed shape, chart and L"
}
```

## Finding

Whole-field closure forces c=−L/2=−2921, and the fixed symmetric template makes that condition sufficient. The period determines placement only after shape, phase chart and closure requirement have been supplied; it does not independently determine them.

## Reassessment

Compare the source’s anchored calendar-body placement packet with this fixed-template result.

## Checks

```json
{
  "necessary": true,
  "sufficient_shape": true,
  "center": true
}
```

## Closed utc

2026-09-28T01:19:05.457229+00:00

## Record provenance

Exact record hash: `062f407ed4f4fa4183b5ad1794b7a89688d417b795fa4d964b1782571a665f12`

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