{
  "id": "EXT-03",
  "uri": "https://cosmological-constant.org/claims/#EXT-03",
  "record_type": "Scientific claim",
  "status": "Derived",
  "dependencies": [],
  "downstream_claims": [],
  "source_status": "Derived here",
  "technical_statement": "Let V_loc = span{E_4, C^2, j_1, j_2, D} be the standard parity-even local four-derivative anomaly basis, and let rho_dS = rho_S4 (+) rho_hor be the paired evaluation into the closed-sphere and spherical-horizon response spaces. Then Im(Pi_dS^univ o rho_dS |_V_loc) = span{e_A^dS}, where e_A^dS is the unit-normalised generator of the Euler/Wess-Zumino quotient line, and the transmitted coordinate is a_dS(Q) = a(Q); a QFT Q has projected local response 4 a(Q) e_A^dS. The C^2 and j_1 sectors vanish by conformal flatness; the trivial sector is removed by finite-counterterm invariance; and the nonzero j_2 sector belongs to the full auxiliary codimension-one boundary problem rather than to the common no-boundary response.",
  "public_statement": "Within the protected local anomaly-response sector studied in Paper II, the closed-sphere and static-patch descriptions of de Sitter share one convention-independent matter coefficient: the type-A Euler coefficient a. For the minimal Standard Model free-field census, a_SM = 1991/720.",
  "qualifier": "The public wording is a gloss; the exact theorem is restricted to the parity-even fixed-point local four-derivative logarithmic anomaly sector of exact round de Sitter. Established in the standalone theorem paper, not in the cosmological-constant manuscript.",
  "source_in_paper": "The Universal Local de Sitter Anomaly Channel Is Uniquely Type A, version 2.0: Sec. 2 (channel and theorem), Sec. 3 (closed-S4 extraction), Sec. 4 (static-patch realisation and j_2 test), Sec. 5 (Standard Model coordinate), Sec. 6 (application). doi:10.5281/zenodo.21809544",
  "external_foundations": "Deser & Schwimmer 1993; Duff 1994; Wess & Zumino 1971; Herzog, Huang & Jensen 2016; Law 2021; Anninos, Denef, Law & Sun 2022",
  "limits_open_issues": "The theorem does not establish the proton endpoint rule; the two-part paired-cap matching hypothesis or its fixed plane; the one-cap Einstein curvature-charge coordinate; the suppressed compact thimble; the exact Planck-boundary unit; the global-source action or source-charge convention; the asymptotic trace-average branch; the full static-patch edge theory; or the numerical cosmological result.",
  "relations": "extends EXT-01 (non-dependency): cross-realisation extension and observer-centred boundary-sector stress test; not required for the downstream numerical derivation.",
  "version_history": "v1.5 (2026-08-05): added at the Zenodo deposit of the standalone theorem paper, version 2.0, doi:10.5281/zenodo.21809544; public wording follows the plain-language gloss with the exact theorem in the technical statement.; v1.6 (2026-08-08): public statement shortened; the exact theorem remains in the technical statement and qualifier",
  "register_version": "v1.6"
}