Scholarly record
Research summary
Paper VIII classifies the physical retained celestial Clebsch–Gordan operator on its dense radiative Bose-pair domain as injective, unbounded and closable, with a canonical closed realization on a proper dense source domain. On the exact retained image it establishes two strict interaction-continuity refinements, τret ⊊ τ3 ⊊ τ3,4, for the complete-action gravitational cubic and fixed-action-leg quartic families. The quartic obstruction excludes a physical Riesz vector from the genuine partial-adjoint range plus the entire admissible cubic span, with a seven-row complete-action packet certificate and exact bounds on five polarization moments. Native regulator tests establish compatible null-face quartic decay on a specified scalar-vacuum branch, a nonzero occupied-to-null-face defect, and selected mesh and radius-child transport obstructions. A stronger source-recovering carrier offers a distinct continuous topology. No continuum scattering operator, universal interacting celestial OPE, or regulator-uniform nonlinear action equivalence is constructed.
This catalog summary is provided for orientation. Please consult the complete manuscript for its original abstract and mathematical results.
Scientific context
This paper belongs to the Gaussian Physical States & Celestial Representation research program.