The Hoyle Resonance and Bound Carbon-12

This working paper examines how the Eigenraum hypothesis, developed in the book project Raum ohne Zeit, can be formulated and tested for the Hoyle resonance and bound carbon-12. The hypothesis describes the Eigenraum as the relational spatial extent of a shared field configuration. An equilateral three-alpha cluster model uses the measured charge radii of helium-4 and carbon-12 to calculate electromagnetic transition strengths for bound carbon-12. The calculated electric quadrupole strength agrees with the electron-scattering result, while the electric octupole strength is about 40% below the experimental reference value. Under the adopted band assignments, the measured excitation energy of the first 3⁻ state exceeds the upper bound of a common rigid oblate rotor by 0.763 MeV. For the Hoyle resonance, the study proposes a natural-orbital definition of the spatial extent of the collective alpha mode. A simplified Gaussian calculation illustrates how to evaluate this quantity and underestimates the monopole transition matrix element inferred from electron scattering. The retrospective proxy test explores a proposed spatial stability bound. An independent test requires a full resonance wave function and a physical rule for assigning the energy that sets the bound. This record contains the complete English and German editions of the same working paper, version 1.0.