Aspect lift — residue

Tried to promote the compact γ (aspect ≤ 4) to a global lower bound on β_3^{rad}. Did not certify.

Replay: python3 aspect_try.py writes certs/aspect_try.json.

For a probability-constrained critical point the first variation is V(r)=(Q/2)(r²+D) on the support, with V(r)=∫ g(r,u) m(du) and g=(r³+u³)/(2 max). A one-point measure satisfies it with Q=1. The power-law n=3.5 quadrature is only approximately critical (max relative error about 2×10^{-3} on 64 atoms).

Geometric chains with ratio t0 (the minimizer of f) stay at Q ≥ 0.9379 through 24 atoms, both for equal m-mass and equal D-mass. That is above compact γ=0.9019 and above the power-law 0.9207. So the pairs that saturate f=fmin do not, by themselves, beat the compact number. A search is not a lower bound.

The two-window lift in lift_global.py uses fmin on every cross term and therefore returns essentially fmin once p12 is maximised.