files / problems / simon-ionization-excess / compute / q4 / work / lift_notes.md

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Lift — tighter compact γ at aspect 10

Same Newton Q=I/DQ=I/D as q3. The q3 bottleneck was the compact γ\gamma at R=12R=12 (φ=0.9055\varphi=0.9055, PP error ≈0.00597\approx 0.00597), not the cut 12/1312/13.

Raising φ\varphi and nn on the mid-radius Rayleigh:

67,108,86367{,}108{,}863 faces, copositive, 2323 residual skips, min⁡m⊤Mm>4⋅10−4\min m^\top Mm>4\cdot 10^{-4}. Stdlib rebuild of AA matches the stored matrix to 10−1510^{-15}.

Same §7 chain. Printed

Nc<1.1057Z+3.946 Z1/3(Z≥4).N_c<1.1057Z+3.946\,Z^{1/3}\qquad(Z\ge 4).

Not the withdrawn 1.11681.1168. The aspect-≤4\le 4 number 1.10871.1087 is not quoted as class-only; the unrestricted leading sits below it.

Finite ZZ and N0(Z)−ZN_0(Z)-Z stay residue.