Residuals: b_flavored (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	5.310	5.310	-0.1	high
2^1S_0	5.900	5.905	+4.6	high
1^3S_1	5.370	5.369	-0.6	high
2^3S_1	5.930	5.934	+3.6	high
1^3P_2	5.800	5.797	-3.1	high
1^3D_3	6.110	6.105	-4.6	medium
1^3F_4	6.360	6.364	+4.1	medium
1^1S_0	5.390	5.391	+0.8	high
2^1S_0	5.980	5.985	+4.9	high
1^3S_1	5.450	5.447	-2.6	high
2^3S_1	6.010	6.013	+3.5	high
1^3P_2	5.880	5.876	-4.4	high
1^3D_3	6.180	6.178	-1.5	medium
1^3F_4	6.430	6.431	+1.3	medium
1^1S_0	6.270	6.265	-4.8	high
2^1S_0	6.850	6.856	+5.7	high
1^3S_1	6.340	6.333	-6.9	high
2^3S_1	6.890	6.889	-1.1	high
1^3P_2	6.770	6.766	-3.6	high
1^3D_3	7.040	7.045	+4.8	medium
1^3F_4	7.270	7.271	+0.7	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	5.358	-48.0	+0.0	+0.0	+0.0	+0.0	+0.0	-48.0	5.310
2^1S_0	5.926	-21.7	+0.0	+0.0	+0.0	+0.0	+0.0	-21.7	5.905
1^3S_1	5.356	+13.8	+0.0	+0.0	+0.0	+0.0	+0.0	+13.8	5.369
2^3S_1	5.926	+7.2	+0.0	+0.0	+0.0	+0.0	+0.0	+7.2	5.934
1^3P_2	5.788	+2.1	+34.3	-26.6	+7.7	-0.8	+0.0	+9.0	5.797
1^3D_3	6.111	+0.5	+25.5	-30.7	-5.3	-0.5	+0.0	-5.3	6.105
1^3F_4	6.376	+0.2	+18.7	-30.6	-11.9	-0.3	+0.0	-12.0	6.364
1^1S_0	5.437	-46.0	+0.0	+0.0	+0.0	+0.0	+0.0	-46.0	5.391
2^1S_0	6.006	-21.6	+0.0	+0.0	+0.0	+0.0	+0.0	-21.6	5.985
1^3S_1	5.434	+13.0	+0.0	+0.0	+0.0	+0.0	+0.0	+13.0	5.447
2^3S_1	6.006	+7.1	+0.0	+0.0	+0.0	+0.0	+0.0	+7.1	6.013
1^3P_2	5.865	+1.7	+30.2	-20.9	+9.3	-0.9	+0.0	+10.2	5.876
1^3D_3	6.182	+0.4	+22.5	-26.2	-3.7	-0.5	+0.0	-3.8	6.178
1^3F_4	6.442	+0.1	+16.7	-27.7	-11.0	-0.3	+0.0	-11.2	6.431
1^1S_0	6.324	-58.8	+0.0	+0.0	+0.0	+0.0	+0.0	-58.8	6.265
2^1S_0	6.882	-26.5	+0.0	+0.0	+0.0	+0.0	+0.0	-26.5	6.856
1^3S_1	6.318	+14.6	+0.0	+0.0	+0.0	+0.0	+0.0	+14.6	6.333
2^3S_1	6.881	+7.7	+0.0	+0.0	+0.0	+0.0	+0.0	+7.7	6.889
1^3P_2	6.752	+1.2	+20.9	-6.6	+14.4	-1.0	+0.0	+14.5	6.766
1^3D_3	7.039	+0.3	+14.7	-9.2	+5.6	-0.5	+0.0	+5.4	7.045
1^3F_4	7.270	+0.1	+11.0	-10.6	+0.4	-0.3	+0.0	+0.2	7.271

Fine-Structure Mass Convention (audit note)

Unequal-mass diagonal fine structure still uses the symmetric L·S contraction. Same-J ^1L_J/^3L_J rows are then corrected by the antisymmetric spin-orbit block when both partner rows are present; other unequal-mass rows remain under the symmetric convention.

state	m1 GeV	m2 GeV	convention
1^1S_0	4.977000	0.220000	disabled
2^1S_0	4.977000	0.220000	disabled
1^3S_1	4.977000	0.220000	disabled
2^3S_1	4.977000	0.220000	disabled
1^3P_2	4.977000	0.220000	unequal_mass_equal_share_LdotS
1^3D_3	4.977000	0.220000	unequal_mass_equal_share_LdotS
1^3F_4	4.977000	0.220000	unequal_mass_equal_share_LdotS
1^1S_0	4.977000	0.419000	disabled
2^1S_0	4.977000	0.419000	disabled
1^3S_1	4.977000	0.419000	disabled
2^3S_1	4.977000	0.419000	disabled
1^3P_2	4.977000	0.419000	unequal_mass_equal_share_LdotS
1^3D_3	4.977000	0.419000	unequal_mass_equal_share_LdotS
1^3F_4	4.977000	0.419000	unequal_mass_equal_share_LdotS
1^1S_0	4.977000	1.628000	disabled
2^1S_0	4.977000	1.628000	disabled
1^3S_1	4.977000	1.628000	disabled
2^3S_1	4.977000	1.628000	disabled
1^3P_2	4.977000	1.628000	unequal_mass_equal_share_LdotS
1^3D_3	4.977000	1.628000	unequal_mass_equal_share_LdotS
1^3F_4	4.977000	1.628000	unequal_mass_equal_share_LdotS

Mean absolute residual: 3.2 MeV. Max absolute residual: 6.9 MeV.

Spin-Averaged Diagnostics

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

multiplet	states	reference GeV	baseline GeV	residual MeV
1D	3	6.443	6.443	-0.5
1F	3	6.687	6.689	+2.0
1P	3	6.150	6.146	-3.7
1S	6	5.704	5.701	-2.9
2S	6	6.268	6.271	+2.8

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.