Calculation record
Finite benchmarks for Gaussian contact, confinement, and integrated stress.
The mathematical domains and compactness proof are stated in the notes.
These checks test explicit examples; all conditions remain active with -O.
Research context
- Confining oscillator domain
The harmonic spatial operator has a closed energy form, compact resolvent, and an explicit eigenbasis whose Gaussian tails justify specified boundary limits.
- Fibre-integrated stress
Integrating a conserved stress tensor over ordinary spatial fibres yields a lower-depth balance law with explicit metric, boundary-flux, and sampling terms.
- Gaussian contact profiles
Normalized Gaussian spatial densities give an exact contact overlap, force, and covariance rule under marginalization onto shared coordinates.
- Interaction operator tools
Self-contained tools for spatial projection, localized profiles, interaction operators, and conservation laws.
- 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.