Calculation record
Finite independent benchmarks for the spectral analysis notes.
No empirical V2 significance or physical rate is inferred by these checks.
All conditions remain active under Python -O. No output files are written.
Research context
- Bounded spectral perturbations
A bounded self-adjoint perturbation preserves compact resolvent, bounds every ordered eigenvalue shift, and preserves isolated spectral-cluster rank under an explicit gap condition.
- Continuum mode memory
Eliminating a coupled continuum produces an exact memory kernel, with exponential decay available only under additional weak-coupling and spectral assumptions.
- Fixed-null calibration
A specified null model permits exact combination of independent match probabilities, explicit treatment of probability floors, and honest finite-simulation uncertainty.
- Gaussian mode geometry
Normalized positive Gaussian profiles have an exact parameter-space metric determined by their mean and covariance, with zero Berry curvature for this real family.
- Isotropic projection fractions
An isotropically prepared spatial direction has a beta-distributed squared projection onto a fixed subspace, with explicit moments and observer-relative momentum bookkeeping.
- Simplex spectral zeta
Explicit analytic continuation of the one-eigenvalue-per-index simplex tower gives its value and derivative at zero, including the normalization dependence of its zeta determinant.
- Spectral analysis tools
Exact tools for recurrence, continuum response, spectral robustness, Gaussian profile geometry, simplex regularization, and statistical calibration.
- Spectral survival recurrence
Pure-point spectral evolution has a positive mean return weight and arbitrarily accurate recurrences, while an integrable continuous spectral density permits decay of the return amplitude.
- 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.