Calculation record
Finite checks for the standalone interaction operator tools.
Verifies specified mathematical models, not empirical particle assignments.
All conditions remain active under python -O. No files are overwritten.
Research context
- Angular kernel parity
The dot-square angular integral has an exact finite spectrum, while its density-sourced Hartree potential acts by multiplication and preserves parity.
- Anomaly-free charge family
The one-family anomaly equations admit a hypercharge and B-minus-L family when a right-handed neutrino is included; selecting observed charges needs additional conditions.
- Colour singlet criterion
Vanishing mean colour charge is weaker than the singlet condition; the positive total quadratic Casimir distinguishes them exactly.
- Dirac heat curvature
The untwisted spatial Dirac heat kernel has local relative coefficient minus scalar curvature over twelve, with an explicit round-sphere spectral benchmark.
- Green function marginal
Full flat-fibre integration of a normalized Laplace Green function gives the lower-dimensional Green function, while restriction to a slice does not.
- Interaction operator tools
Self-contained tools for spatial projection, localized profiles, interaction operators, and conservation laws.
- Projected bilocal variation
Varying an exchange-symmetric interaction between projected densities retains the channel projector and one kernel convolution in each mean-field term.
- Diagnostic catalog
Reproduction commands and scope descriptions for every local finite diagnostic and helper.
Interpret numerical checks within the assumptions and limitations documented in these notes.