Containment-Coupling at L1/L2: A Unified, Falsifiable Pathway from Lissajous to Quasi-Halo and Halo Orbits

This package turns recent analytical results on L1/L2 bifurcations into a compact, falsifiable workflow for mission design. Building on Lindstedt–Poincare series for the CRTBP, it treats Lissajous, quasi-halo, and halo orbits within one coupling-led model where the bifurcation condition Δ(η,Ax,Az,…)=0 marks the format switch from planar to 3-D motion. The materials include a Switch Detection Table (measurable onset at a fixed phase), an Aspect Ratio Table r=Az/Ax with near-threshold scaling |r|~=k*sqrt(sigma), and a Triangle Distances card linking planar points to the mirrored north/south halo branches. A minimal analytic recipe provides fast seeds for continuation into enriched models; falsifiable tests (mirror symmetry, scaling law, disable-coupling) support verification on simulation or flight-like data.