Calculation record
Finite checks of the stated spatial and resonance benchmarks; no fitted data.
Research context
- Chiral pseudoscalar mass term
A specified leading chiral action makes pseudoscalar mass squared proportional to light-quark masses, with the response scale left as matched input.
- Coulomb exponential profiles
Normalized exponential profiles give exact Coulomb integrals, a two-particle variational bound, and finite-range contact estimates.
- Cyclic resonance spectrum
A nearest-neighbour amplitude ring has exact Fourier resonances, paired levels, and a calculable response to alternating couplings.
- Dipole dispersion response
Second-order dipole coupling yields an attractive inverse-sixth-power energy with a coefficient fixed by the specified excitation response.
- Oscillator rotation branching
Harmonic-polynomial decomposition gives exact angular multiplicities for a flat oscillator shell and its restriction to an observer-selected spatial three-plane.
- Radial confinement bounds
The radial spatial measure fixes the centrifugal term, while a Hardy bound gives an explicit sufficient condition excluding levels below a saturating threshold.
- Resonance and profile tools
Tools for Coulomb profiles, angular functions, cyclic and quartic resonance, dispersion response, radial bounds, and pseudoscalar symmetry protection.
- Resonant quartet dynamics
A conservative quartic amplitude interaction has exact action invariants and a detuning-controlled exchange law under specified pump preparation.
- Zonal hybrid geometry
Spherical-harmonic addition gives exact directed-state overlaps and conditional trigonal, tetrahedral, and octahedral orthogonality.
- 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.