Calculation record
Check the analytic localization boundaries of smooth and root self-mass.
The nonexistence proofs concern the stated flat radial ansatz. Numerical
initial-value tails are illustrations, not failed-shooting existence tests.
All coordinates are ordinary spatial coordinates; no topology is selected.
Research context
- Massless radial scalar contact
Regular flat radial scalar Dirac fields have no finite-norm stationary state for cubic or smooth saturating contact; the homogeneous root is also excluded under the stated virial hypotheses.
- Positive current matrices and spatial localization
A scalar Dirac identity and spatial virial exclude localized flat-space stationary fields in the positive-current cone of the convex hierarchy, retaining all spinor and coefficient components.
Interpret numerical checks within the assumptions and limitations documented in these notes.