Calculation record
Checks for exact mode counting, evaluation, and spectral bounds.
Research context
- Round-sphere Dirac counts
The round-sphere Dirac spectrum has a dimension-dependent spinor multiplicity, giving two times the simplex count on S3 and four times it on S5.
- Simplex band level moments
Uniform counting over a cumulative oscillator band gives exact mean and variance of the excitation level, without selecting a physical occupation or mass correction.
- Simplex heat trace
The tower with one eigenvalue per simplex index has an explicit heat-trace bound and convergence domain, distinct from the spatial dimension of a sector operator.
- Weighted mode evaluation
A weighted coefficient norm bounds point evaluation exactly when the corresponding inverse-weighted evaluation sum is finite; counts alone do not establish that condition.
- Normalized oscillator modes
Explicit normalized modes and density overlaps supply calculational inputs without identifying them with mixing amplitudes.
- 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.