Calculation record
Checks for centred spatial dynamics and exact count identities.
Uses independent pair-energy finite differences for the centred scalar
functional, symbolic operator identities, and exact rational count sums.
Failures remain active under python -O.
Research context
- Centroid-relative self-binding
Centering the auxiliary scalar moment functional yields an explicit translation-covariant self-binding model with zero net self-force.
- Cylindrical barrier separation
A barrier continued cylindrically has no route around it through the added coordinates; a separated Hamiltonian reduces each transverse mode to a longitudinal crossing problem.
- Nested sector dynamics
Cylindrical function lifts require a projection, and exact inheritance of dynamics additionally requires an invariant domain and an intertwining operator relation.
- Simplex reciprocal sum
Reciprocal simplex counts have an exact telescoping sum and truncation remainder, providing a conditional trace check for the V2 count spectrum.
- 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.