{
  "id": "SAD-05",
  "uri": "https://cosmological-constant.org/claims/#SAD-05",
  "record_type": "Scientific claim",
  "status": "Derived",
  "dependencies": [
    "SAD-02",
    "SAD-04"
  ],
  "downstream_claims": [],
  "source_status": "Derived here",
  "technical_statement": "On the declared sub-Planckian domain z=e^{2 sigma_0}>=1, the reduced damped zero-mode integral is finite: the Planck boundary removes the small-radius endpoint and the damped thimble controls infinity. Extension to z=0 reproduces the divergent R1 reading; there is no separate anomaly-integrability test passed by a_SM>0.",
  "public_statement": "The declared Planck boundary, not the sign of the anomaly coefficient, makes the reduced thimble integral finite.",
  "qualifier": "Domain-regulated finiteness conditional on the selected contour and measure.",
  "source_in_paper": "CC Paper I v1.0, Sec. 9, Eq. (26) and Appendix C",
  "external_foundations": "GHP1978; MazurMottola1990; AntoniadisMazurMottola1997",
  "limits_open_issues": "Does not determine contour inclusion, orientation, Stokes data, boundary unit or full metric/ghost stability.",
  "relations": "",
  "version_history": "v1.2; v1.3 (2026-08-01): corrected in the paired-cap revision: finiteness is regulated by the declared domain, not by the sign of a_SM.; v1.4b (2026-08-04): SM-01 removed (finiteness is regulated by the declared domain, not by the sign of a_SM); SAD-04 added for the boundary",
  "register_version": "v1.6"
}