{
  "id": "VAC-02",
  "uri": "https://cosmological-constant.org/claims/#VAC-02",
  "record_type": "Scientific claim",
  "status": "Derived",
  "dependencies": [
    "VAC-01"
  ],
  "downstream_claims": [
    "EXT-01",
    "CMP-01"
  ],
  "source_status": "Derived here",
  "technical_statement": "On compact round S4 without boundary, the vacuum-energy functional and cosmological counterterm are the same local volume operator, proportional to H^-4, with no intrinsic geometrical label separating them.",
  "public_statement": "On compact round S4, the ambiguity is especially sharp: the zero-point term and cosmological counterterm are literally the same local operator.",
  "qualifier": "",
  "source_in_paper": "CC Paper I v1.0, Sec. 3",
  "external_foundations": "BirrellDavies1982; Wald1994",
  "limits_open_issues": "This is a compact-background sharpening of standard renormalisation lore.",
  "relations": "",
  "version_history": "v1.2; v1.3 (2026-08-01): source citation updated to the paired-cap revision.",
  "register_version": "v1.6"
}