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The science
The model
For three particles with resonant (very large scattering length) interactions, the hyperradial equation in the universal regime is -F'' - (s0^2 + 1/4) F / R^2 = E F. Substituting F = sqrt(R) u(x), x = ln(R/R0) turns it into u'' = (kappa^2 e^(2x) - s0^2) u with E = -kappa^2 in units hbar^2/(m R0^2). A hard core at R0 stands in for short-range physics.
Why a ladder
Inside the turning point u oscillates like sin(s0 x): it is log-periodic with period pi/s0. Each extra node therefore costs a fixed factor exp(pi/s0) in size and exp(2 pi/s0) in energy: 22.7 and 515 for identical bosons, s0 = 1.00624. This is discrete scale invariance.
Honest simplifications
No three-body parameter physics beyond a hard wall, no finite scattering length, no recombination, and one Jacobi-hyperradius convention for the mass scale. Absolute energies shown (kHz) depend on the chosen R0 and mass and are illustrative; the ratios are the universal result. The deepest state feels the cutoff most, so the check uses n >= 2.
Try this
Change s0 and watch the rung spacing follow 2 pi / s0; switch to the 0.4137 preset to see how few states fit; raise the number of states to see the 1/R^2 scaling of binding energy against size in the last graph.