Residuals: isovector (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	0.150	0.149	-0.9	high
2^1S_0	1.300	1.292	-8.0	high
1^3S_1	0.770	0.771	+1.2	high
2^3S_1	1.450	1.455	+5.2	high
1^3D_1	1.660	1.666	+5.9	high
3^1S_0	1.880	1.872	-7.5	high
3^3S_1	2.000	1.998	-1.9	high
2^3D_1	2.150	2.153	+3.5	high
1^1P_1	1.220	1.218	-1.5	high
2^1P_1	1.780	1.777	-3.1	high
1^3P_0	1.090	1.087	-3.1	high
2^3P_0	1.780	1.778	-1.8	high
1^3P_1	1.240	1.238	-2.5	high
2^3P_1	1.820	1.818	-2.0	high
1^3P_2	1.310	1.307	-3.4	high
2^3P_2	1.820	1.823	+3.2	high
1^3F_2	2.050	2.055	+4.6	high
1^1D_2	1.680	1.680	+0.5	high
2^1D_2	2.130	2.135	+4.9	high
1^3D_2	1.700	1.696	-4.3	high
2^3D_2	2.150	2.155	+4.7	high
1^3D_3	1.680	1.683	+3.1	high
2^3D_3	2.130	2.131	+1.0	high
1^3G_3	2.370	2.370	+0.3	high
1^1F_3	2.030	2.033	+2.8	high
1^3F_3	2.050	2.046	-4.0	high
1^3F_4	2.010	2.008	-2.4	high
1^1G_4	2.330	2.333	+3.2	high
1^3G_4	2.340	2.344	+4.3	high
1^3G_5	2.300	2.296	-3.6	high

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	0.764	-614.5	+0.0	+0.0	+0.0	+0.0	+0.0	-614.5	0.149
2^1S_0	1.397	-104.8	+0.0	+0.0	+0.0	+0.0	+0.0	-104.8	1.292
1^3S_1	0.667	+104.1	+0.0	+0.0	+0.0	+0.0	+0.0	+104.1	0.771
2^3S_1	1.411	+44.2	+0.0	+0.0	+0.0	+0.0	+0.0	+44.2	1.455
1^3D_1	1.700	+3.1	-127.5	+98.6	-29.0	-9.4	+0.0	-35.2	1.666
3^1S_0	1.949	-76.2	+0.0	+0.0	+0.0	+0.0	+0.0	-76.2	1.872
3^3S_1	1.962	+36.0	+0.0	+0.0	+0.0	+0.0	+0.0	+36.0	1.998
2^3D_1	2.145	+2.8	-75.2	+85.8	+10.6	-5.1	+0.0	+8.2	2.153
1^1P_1	1.262	-43.2	+0.0	+0.0	+0.0	+0.0	+0.0	-43.2	1.218
2^1P_1	1.810	-32.7	+0.0	+0.0	+0.0	+0.0	+0.0	-32.7	1.777
1^3P_0	1.284	+18.0	-267.6	+106.6	-161.0	-53.9	+0.0	-196.9	1.087
2^3P_0	1.807	+10.3	-109.7	+91.6	-18.1	-20.9	+0.0	-28.7	1.778
1^3P_1	1.261	+13.9	-120.8	+57.6	-63.1	+25.4	+0.0	-23.9	1.238
2^3P_1	1.807	+9.4	-53.9	+45.4	-8.5	+10.3	+0.0	+11.2	1.818
1^3P_2	1.268	+8.6	+99.7	-65.2	+34.5	-4.5	+0.0	+38.7	1.307
2^3P_2	1.808	+8.2	+53.5	-44.5	+9.1	-2.1	+0.0	+15.2	1.823
1^3F_2	2.041	+0.7	-74.9	+90.9	+16.0	-3.4	+0.0	+13.3	2.055
1^1D_2	1.687	-6.8	+0.0	+0.0	+0.0	+0.0	+0.0	-6.8	1.680
2^1D_2	2.142	-7.5	+0.0	+0.0	+0.0	+0.0	+0.0	-7.5	2.135
1^3D_2	1.688	+2.4	-38.7	+35.2	-3.5	+8.8	+0.0	+7.7	1.696
2^3D_2	2.142	+2.5	-24.1	+29.1	+5.0	+5.0	+0.0	+12.4	2.155
1^3D_3	1.693	+1.6	+68.0	-77.1	-9.1	-2.3	+0.0	-9.8	1.683
2^3D_3	2.144	+2.1	+46.1	-59.5	-13.3	-1.4	+0.0	-12.6	2.131
1^3G_3	2.338	+0.2	-50.2	+84.1	+33.9	-1.7	+0.0	+32.4	2.370
1^1F_3	2.034	-1.6	+0.0	+0.0	+0.0	+0.0	+0.0	-1.6	2.033
1^3F_3	2.035	+0.6	-17.4	+24.1	+6.7	+4.1	+0.0	+11.3	2.046
1^3F_4	2.038	+0.4	+47.6	-77.4	-29.8	-1.3	+0.0	-30.6	2.008
1^1G_4	2.334	-0.4	+0.0	+0.0	+0.0	+0.0	+0.0	-0.4	2.333
1^3G_4	2.334	+0.1	-9.5	+17.6	+8.2	+2.2	+0.0	+10.6	2.344
1^3G_5	2.336	+0.1	+35.4	-74.7	-39.3	-0.8	+0.0	-40.0	2.296

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	1.456	1.455	+9.6	+0.999	-0.045
1^3D_1	1.664	1.666	+9.6	+0.045	+0.998
3^3S_1	1.998	1.998	+2.1	+1.000	-0.013
2^3D_1	2.153	2.153	+2.1	+0.013	+1.000
2^3P_2	1.823	1.823	+1.4	+1.000	-0.006
1^3F_2	2.054	2.055	+1.4	+0.006	+1.000
2^3D_3	2.131	2.131	+0.3	+1.000	-0.001
1^3G_3	2.370	2.370	+0.3	+0.001	+1.000

Mean absolute residual: 3.3 MeV. Max absolute residual: 8.0 MeV.

Spin-Averaged Diagnostics

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

multiplet	states	reference GeV	baseline GeV	residual MeV
1D	4	1.682	1.683	+1.0
2D	4	2.138	2.141	+3.3
1F	4	2.032	2.032	-0.3
1G	4	2.331	2.332	+0.8
1P	4	1.252	1.249	-2.7
2P	4	1.807	1.807	-0.1
1S	2	0.615	0.616	+0.7
2S	2	1.412	1.414	+1.9
3S	2	1.970	1.967	-3.3

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.