C707 — Derive the fixed-template placement condition

Question

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

Inputs

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

Sources

[
  "Supplement A §13.4"
]

Opened utc

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

Results

{
  "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

{
  "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