Residuals: bottomonium (GI-style)

Model: with GI momentum-sandwiched smeared contact hyperfine (every L), fixed-sector L·S (vector+Thomas) and OGE-tensor diagonalization with GI momentum-factor sandwiches and smeared-G/S derivative kernels; GI Table II b, c, masses, ε factors, and Fig. 2 α_s(r); closed-form GI G̃(r), S̃(r), plus central Coulomb momentum sandwich A(p)G̃A(p) in the solver's native p² representation, see the GIModel package (src/ at the repository root) for the computation and GIPaper (GIPaper/src/) for the comparison layer.

Numerics: OscillatorSolver — nbasis = 24:8:80 adaptive, ΔE ≤ 0.1 MeV, beta in [0.25, 2.35] GeV (22 bracket points, refined to 0.002 GeV), 6 levels/channel.

state	reference GeV	baseline GeV	residual MeV	confidence
1^1S_0	9.400	9.393	-6.7	high
2^1S_0	9.980	9.975	-5.4	high
3^1S_0	10.340	10.332	-7.6	high
1^3S_1	9.460	9.459	-1.2	high
2^3S_1	10.000	10.004	+4.1	high
1^3D_1	10.140	10.137	-2.8	high
3^3S_1	10.350	10.354	+3.5	high
2^3D_1	10.440	10.441	+0.8	high
4^3S_1	10.630	10.633	+2.8	medium
3^3D_1	10.700	10.698	-1.7	medium
5^3S_1	10.880	10.875	-5.5	medium
6^3S_1	11.100	11.092	-7.7	medium
1^1P_1	9.880	9.881	+0.5	high
2^1P_1	10.250	10.250	-0.4	high
1^3P_0	9.850	9.845	-5.2	high
2^3P_0	10.230	10.225	-4.9	high
1^3P_1	9.880	9.875	-5.2	high
2^3P_1	10.250	10.246	-4.4	high
1^3P_2	9.900	9.896	-4.3	high
2^3P_2	10.260	10.261	+0.6	high
1^3F_2	10.350	10.350	-0.3	medium
1^1D_2	10.150	10.148	-2.3	high
2^1D_2	10.450	10.450	-0.5	high
1^3D_2	10.150	10.147	-3.2	high
2^3D_2	10.450	10.449	-1.3	high
1^3D_3	10.160	10.155	-5.4	high
2^3D_3	10.450	10.455	+5.2	high
1^1F_3	10.350	10.354	+4.3	medium
1^3F_3	10.350	10.354	+4.3	medium
1^3F_4	10.360	10.358	-2.3	medium

Contribution Breakdown (diagnostic)

The central, contact, spin-orbit, and tensor columns are operator contributions in the same fully diagonalized fixed-sector eigenstate. They are not differences from a separate central-only solve.

state	central contribution GeV	contact MeV	L·S(vec) MeV	L·S(Thomas) MeV	L·S total MeV	tensor MeV	annihilation MeV	spin + annihilation MeV	predicted GeV
1^1S_0	9.452	-58.7	+0.0	+0.0	+0.0	+0.0	+0.0	-58.7	9.393
2^1S_0	9.999	-24.6	+0.0	+0.0	+0.0	+0.0	+0.0	-24.6	9.975
3^1S_0	10.350	-17.3	+0.0	+0.0	+0.0	+0.0	+0.0	-17.3	10.332
1^3S_1	9.445	+13.6	+0.0	+0.0	+0.0	+0.0	+0.0	+13.6	9.459
2^3S_1	9.998	+6.5	+0.0	+0.0	+0.0	+0.0	+0.0	+6.5	10.004
1^3D_1	10.149	+0.3	-15.4	+4.8	-10.6	-1.4	+0.0	-11.8	10.137
3^3S_1	10.349	+4.8	+0.0	+0.0	+0.0	+0.0	+0.0	+4.8	10.354
2^3D_1	10.450	+0.2	-12.5	+3.7	-8.7	-1.2	+0.0	-9.7	10.441
4^3S_1	10.629	+4.0	+0.0	+0.0	+0.0	+0.0	+0.0	+4.0	10.633
3^3D_1	10.707	+0.2	-10.8	+3.1	-7.7	-1.0	+0.0	-8.5	10.698
5^3S_1	10.871	+3.5	+0.0	+0.0	+0.0	+0.0	+0.0	+3.5	10.875
6^3S_1	11.089	+3.2	+0.0	+0.0	+0.0	+0.0	+0.0	+3.2	11.092
1^1P_1	9.883	-2.6	+0.0	+0.0	+0.0	+0.0	+0.0	-2.6	9.881
2^1P_1	10.252	-2.0	+0.0	+0.0	+0.0	+0.0	+0.0	-2.0	10.250
1^3P_0	9.888	+1.1	-38.7	+4.8	-33.8	-10.5	+0.0	-43.2	9.845
2^3P_0	10.254	+0.8	-26.1	+3.3	-22.8	-7.0	+0.0	-28.9	10.225
1^3P_1	9.883	+0.9	-16.3	+2.3	-14.0	+4.5	+0.0	-8.6	9.875
2^3P_1	10.252	+0.7	-11.5	+1.6	-9.9	+3.1	+0.0	-6.1	10.246
1^3P_2	9.884	+0.8	+14.2	-2.2	+12.0	-0.8	+0.0	+12.0	9.896
2^3P_2	10.252	+0.6	+10.3	-1.6	+8.7	-0.6	+0.0	+8.7	10.261
1^3F_2	10.355	+0.1	-9.5	+4.9	-4.6	-0.5	+0.0	-5.1	10.350
1^1D_2	10.148	-0.7	+0.0	+0.0	+0.0	+0.0	+0.0	-0.7	10.148
2^1D_2	10.450	-0.6	+0.0	+0.0	+0.0	+0.0	+0.0	-0.6	10.450
1^3D_2	10.148	+0.2	-4.8	+1.6	-3.3	+1.4	+0.0	-1.7	10.147
2^3D_2	10.450	+0.2	-3.9	+1.2	-2.7	+1.1	+0.0	-1.4	10.449
1^3D_3	10.149	+0.2	+9.2	-3.1	+6.1	-0.4	+0.0	+6.0	10.155
2^3D_3	10.450	+0.2	+7.5	-2.4	+5.1	-0.3	+0.0	+5.0	10.455
1^1F_3	10.355	-0.3	+0.0	+0.0	+0.0	+0.0	+0.0	-0.3	10.354
1^3F_3	10.355	+0.1	-2.3	+1.2	-1.1	+0.7	+0.0	-0.3	10.354
1^3F_4	10.355	+0.1	+6.7	-3.6	+3.2	-0.2	+0.0	+3.0	10.358

Same-J Tensor Mixing

Rows below use the mixed eigenvalues from triplet L=J-1 / L=J+1 tensor blocks. Components are ordered as lower-L/higher-L in the unmixed basis.

state	unmixed GeV	mixed GeV	offdiag MeV	lower-L component	higher-L component
2^3S_1	10.004	10.004	+0.2	+1.000	-0.001
1^3D_1	10.137	10.137	+0.2	+0.001	+1.000
3^3S_1	10.354	10.354	+0.0	+1.000	-0.000
2^3D_1	10.441	10.441	+0.0	+0.000	+1.000
4^3S_1	10.633	10.633	-0.0	+1.000	+0.001
3^3D_1	10.698	10.698	-0.0	-0.001	+1.000
2^3P_2	10.261	10.261	-0.0	+1.000	+0.000
1^3F_2	10.350	10.350	-0.0	-0.000	+1.000

Mean absolute residual: 3.5 MeV. Max absolute residual: 7.7 MeV.

Spin-Averaged Diagnostics

Weighted by 2J+1 within each available (n, L) group.

multiplet	states	reference GeV	baseline GeV	residual MeV
1D	4	10.152	10.148	-3.7
2D	4	10.448	10.450	+1.5
3D	1	10.700	10.698	-1.7
1F	4	10.353	10.355	+1.4
1P	4	9.886	9.882	-3.4
2P	4	10.252	10.251	-1.3
1S	2	9.445	9.442	-2.6
2S	2	9.995	9.997	+1.7
3S	2	10.348	10.348	+0.7
4S	1	10.630	10.633	+2.8
5S	1	10.880	10.875	-5.5
6S	1	11.100	11.092	-7.7

The spin-independent central path is the current GI reproduction candidate. Remaining heavy-quarkonium residuals should be read mainly as spin-dependent/operator-ordering and extraction-audit targets.