Residuals: isoscalar (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	0.520	0.520	+0.0	medium
1^1S_0	0.960	0.960	+0.0	medium
2^1S_0	1.440	1.440	-0.0	medium
2^1S_0	1.630	1.630	-0.0	medium
1^3S_1	0.780	0.780	-0.1	medium
1^3S_1	1.020	1.020	+0.4	medium
2^3S_1	1.460	1.457	-3.4	medium
1^3D_1	1.660	1.664	+4.3	medium
2^3S_1	1.690	1.690	-0.4	medium
1^3D_1	1.880	1.879	-1.4	medium
1^1P_1	1.220	1.218	-1.5	medium
1^1P_1	1.470	1.473	+3.1	medium
2^1P_1	1.780	1.777	-3.1	medium
2^1P_1	2.010	2.008	-2.0	medium
1^3P_0	1.090	1.087	-3.1	medium
1^3P_0	1.360	1.355	-5.5	medium
2^3P_0	1.780	1.778	-1.8	medium
2^3P_0	1.990	1.986	-4.4	medium
1^3P_1	1.240	1.238	-2.5	medium
1^3P_1	1.480	1.480	-0.0	medium
2^3P_1	1.820	1.818	-2.0	medium
2^3P_1	2.030	2.027	-2.7	medium
1^3P_2	1.280	1.276	-4.4	medium
1^3P_2	1.530	1.532	+1.6	medium
2^3P_2	1.820	1.815	-4.6	medium
2^3P_2	2.040	2.042	+2.5	medium
1^3F_2	2.050	2.054	+4.4	medium
1^3F_2	2.240	2.243	+2.6	medium
1^1D_2	1.680	1.680	+0.5	medium
1^1D_2	1.890	1.893	+3.0	medium
1^3D_2	1.700	1.696	-4.3	medium
1^3D_2	1.910	1.904	-5.5	medium
1^3D_3	1.680	1.683	+3.1	medium
1^3D_3	1.900	1.897	-3.0	medium
1^3G_3	2.370	2.370	+0.3	medium
1^3G_3	2.540	2.542	+1.8	medium
1^1F_3	2.030	2.033	+2.8	medium
1^1F_3	2.220	2.223	+2.8	medium
1^3F_3	2.050	2.046	-4.0	medium
1^3F_3	2.230	2.234	+4.1	medium
1^3F_4	2.010	2.008	-2.4	medium
1^3F_4	2.200	2.202	+2.4	medium
1^1G_4	2.330	2.333	+3.2	medium
1^1G_4	2.510	2.507	-3.0	medium
1^3G_4	2.340	2.344	+4.3	medium
1^3G_4	2.520	2.517	-2.9	medium
1^3G_5	2.300	2.296	-3.6	medium
1^3G_5	2.470	2.475	+4.7	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	0.764	-614.5	+0.0	+0.0	+0.0	+0.0	+370.9	-243.5	0.520
1^1S_0	0.995	-339.8	+0.0	+0.0	+0.0	+0.0	+304.8	-35.0	0.960
2^1S_0	1.397	-104.8	+0.0	+0.0	+0.0	+0.0	+148.0	+43.2	1.440
2^1S_0	1.653	-76.0	+0.0	+0.0	+0.0	+0.0	+52.7	-23.3	1.630
1^3S_1	0.667	+104.1	+0.0	+0.0	+0.0	+0.0	+8.7	+112.8	0.780
1^3S_1	0.949	+67.9	+0.0	+0.0	+0.0	+0.0	+3.3	+71.2	1.020
2^3S_1	1.411	+44.2	+0.0	+0.0	+0.0	+0.0	+0.9	+45.1	1.457
1^3D_1	1.700	+3.1	-127.5	+98.6	-29.0	-9.4	+0.0	-35.2	1.664
2^3S_1	1.660	+29.3	+0.0	+0.0	+0.0	+0.0	+0.6	+29.9	1.690
1^3D_1	1.906	+2.0	-101.8	+81.1	-20.7	-8.3	+0.0	-27.0	1.879
1^1P_1	1.262	-43.2	+0.0	+0.0	+0.0	+0.0	+0.0	-43.2	1.218
1^1P_1	1.500	-26.5	+0.0	+0.0	+0.0	+0.0	+0.0	-26.5	1.473
2^1P_1	1.810	-32.7	+0.0	+0.0	+0.0	+0.0	+0.0	-32.7	1.777
2^1P_1	2.028	-20.1	+0.0	+0.0	+0.0	+0.0	+0.0	-20.1	2.008
1^3P_0	1.284	+18.0	-267.6	+106.6	-161.0	-53.9	+0.0	-196.9	1.087
1^3P_0	1.519	+11.5	-211.6	+82.1	-129.4	-46.8	+0.0	-164.7	1.355
2^3P_0	1.807	+10.3	-109.7	+91.6	-18.1	-20.9	+0.0	-28.7	1.778
2^3P_0	2.025	+6.6	-88.8	+60.8	-28.0	-18.2	+0.0	-39.6	1.986
1^3P_1	1.261	+13.9	-120.8	+57.6	-63.1	+25.4	+0.0	-23.9	1.238
1^3P_1	1.500	+8.9	-93.8	+42.9	-50.9	+21.6	+0.0	-20.4	1.480
2^3P_1	1.807	+9.4	-53.9	+45.4	-8.5	+10.3	+0.0	+11.2	1.818
2^3P_1	2.027	+6.2	-44.4	+29.7	-14.7	+9.2	+0.0	+0.6	2.027
1^3P_2	1.268	+8.6	+99.7	-65.2	+34.5	-4.5	-30.9	+7.7	1.276
1^3P_2	1.504	+6.1	+78.2	-44.9	+33.2	-3.8	-7.8	+27.7	1.532
2^3P_2	1.808	+8.2	+53.5	-44.5	+9.1	-2.1	-7.8	+7.4	1.815
2^3P_2	2.028	+5.4	+43.9	-29.0	+14.9	-1.9	-3.7	+14.8	2.042
1^3F_2	2.041	+0.7	-74.9	+90.9	+16.0	-3.4	+0.0	+13.3	2.054
1^3F_2	2.228	+0.5	-60.7	+78.1	+17.3	-3.1	+0.0	+14.7	2.243
1^1D_2	1.687	-6.8	+0.0	+0.0	+0.0	+0.0	+0.0	-6.8	1.680
1^1D_2	1.898	-4.6	+0.0	+0.0	+0.0	+0.0	+0.0	-4.6	1.893
1^3D_2	1.688	+2.4	-38.7	+35.2	-3.5	+8.8	+0.0	+7.7	1.696
1^3D_2	1.898	+1.6	-30.9	+27.9	-2.9	+7.8	+0.0	+6.4	1.904
1^3D_3	1.693	+1.6	+68.0	-77.1	-9.1	-2.3	+0.0	-9.8	1.683
1^3D_3	1.901	+1.2	+55.0	-57.8	-2.8	-2.0	+0.0	-3.6	1.897
1^3G_3	2.338	+0.2	-50.2	+84.1	+33.9	-1.7	+0.0	+32.4	2.370
1^3G_3	2.510	+0.1	-41.3	+74.7	+33.5	-1.6	+0.0	+32.1	2.542
1^1F_3	2.034	-1.6	+0.0	+0.0	+0.0	+0.0	+0.0	-1.6	2.033
1^1F_3	2.224	-1.2	+0.0	+0.0	+0.0	+0.0	+0.0	-1.2	2.223
1^3F_3	2.035	+0.6	-17.4	+24.1	+6.7	+4.1	+0.0	+11.3	2.046
1^3F_3	2.224	+0.4	-14.2	+20.1	+5.9	+3.7	+0.0	+10.0	2.234
1^3F_4	2.038	+0.4	+47.6	-77.4	-29.8	-1.3	+0.0	-30.6	2.008
1^3F_4	2.226	+0.3	+39.3	-61.9	-22.7	-1.2	+0.0	-23.5	2.202
1^1G_4	2.334	-0.4	+0.0	+0.0	+0.0	+0.0	+0.0	-0.4	2.333
1^1G_4	2.507	-0.3	+0.0	+0.0	+0.0	+0.0	+0.0	-0.3	2.507
1^3G_4	2.334	+0.1	-9.5	+17.6	+8.2	+2.2	+0.0	+10.6	2.344
1^3G_4	2.507	+0.1	-7.8	+15.3	+7.5	+2.1	+0.0	+9.7	2.517
1^3G_5	2.336	+0.1	+35.4	-74.7	-39.3	-0.8	+0.0	-40.0	2.296
1^3G_5	2.509	+0.1	+29.5	-62.8	-33.3	-0.7	+0.0	-33.9	2.475

Isoscalar Annihilation Mixing

Rows below use the selected isoscalar annihilation scheme. calibrated_p1 is the Fig. 5/Table III pseudoscalar control; p1/p2 are the paper Eq. (18a,b) formula modes; general_eq16 is the literal Eq. (16) block (^3S_1, ^3P_2); ideal assigns the heavier row to the s sbar channel prediction per the Table III ideal-mixing prescription.

state	scheme	unmixed GeV	mixed GeV	shift MeV
1^1S_0	calibrated_p1	0.149	0.520	+370.9
1^1S_0	calibrated_p1	0.655	0.960	+304.8
2^1S_0	calibrated_p1	1.292	1.440	+148.0
2^1S_0	calibrated_p1	1.577	1.630	+52.7
1^3S_1	general_eq16	0.771	0.780	+8.7
1^3S_1	general_eq16	1.017	1.020	+3.3
2^3S_1	general_eq16	1.456	1.457	+0.9
1^3D_1	ideal	1.664	1.664	+0.0
2^3S_1	general_eq16	1.689	1.690	+0.6
1^3D_1	ideal	1.879	1.879	+0.0
1^1P_1	ideal	1.218	1.218	+0.0
1^1P_1	ideal	1.473	1.473	+0.0
2^1P_1	ideal	1.777	1.777	+0.0
2^1P_1	ideal	2.008	2.008	+0.0
1^3P_0	ideal	1.087	1.087	+0.0
1^3P_0	ideal	1.355	1.355	+0.0
2^3P_0	ideal	1.778	1.778	+0.0
2^3P_0	ideal	1.986	1.986	+0.0
1^3P_1	ideal	1.238	1.238	+0.0
1^3P_1	ideal	1.480	1.480	+0.0
2^3P_1	ideal	1.818	1.818	+0.0
2^3P_1	ideal	2.027	2.027	+0.0
1^3P_2	general_eq16	1.307	1.276	-30.9
1^3P_2	general_eq16	1.539	1.532	-7.8
2^3P_2	general_eq16	1.823	1.815	-7.8
2^3P_2	general_eq16	2.046	2.042	-3.7
1^3F_2	ideal	2.054	2.054	+0.0
1^3F_2	ideal	2.243	2.243	+0.0
1^1D_2	ideal	1.680	1.680	+0.0
1^1D_2	ideal	1.893	1.893	+0.0
1^3D_2	ideal	1.696	1.696	+0.0
1^3D_2	ideal	1.904	1.904	+0.0
1^3D_3	ideal	1.683	1.683	+0.0
1^3D_3	ideal	1.897	1.897	+0.0
1^3G_3	ideal	2.370	2.370	+0.0
1^3G_3	ideal	2.542	2.542	+0.0
1^1F_3	ideal	2.033	2.033	+0.0
1^1F_3	ideal	2.223	2.223	+0.0
1^3F_3	ideal	2.046	2.046	+0.0
1^3F_3	ideal	2.234	2.234	+0.0
1^3F_4	ideal	2.008	2.008	+0.0
1^3F_4	ideal	2.202	2.202	+0.0
1^1G_4	ideal	2.333	2.333	+0.0
1^1G_4	ideal	2.507	2.507	+0.0
1^3G_4	ideal	2.344	2.344	+0.0
1^3G_4	ideal	2.517	2.517	+0.0
1^3G_5	ideal	2.296	2.296	+0.0
1^3G_5	ideal	2.475	2.475	+0.0

Mean absolute residual: 2.6 MeV. Max absolute residual: 5.5 MeV.

Spin-Averaged Diagnostics

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

multiplet	states	reference GeV	baseline GeV	residual MeV
1D	8	1.789	1.789	-0.5
1F	8	2.126	2.127	+1.3
1G	8	2.419	2.419	+0.6
1P	8	1.364	1.363	-1.0
2P	8	1.916	1.914	-1.9
1S	4	0.860	0.860	+0.1
2S	4	1.565	1.564	-1.4

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.