Residuals: charmonium (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	2.970	2.967	-2.9	high
2^1S_0	3.620	3.626	+5.8	high
3^1S_0	4.060	4.064	+3.6	high
1^3S_1	3.100	3.091	-8.6	high
2^3S_1	3.680	3.679	-0.9	high
1^3D_1	3.820	3.818	-1.7	high
3^3S_1	4.100	4.100	+0.0	high
2^3D_1	4.190	4.194	+4.1	high
4^3S_1	4.450	4.449	-1.2	medium
3^3D_1	4.520	4.520	-0.5	medium
1^1P_1	3.520	3.515	-4.9	high
2^1P_1	3.960	3.956	-3.8	high
1^3P_0	3.440	3.443	+2.9	high
2^3P_0	3.920	3.916	-3.5	high
1^3P_1	3.510	3.508	-1.8	high
2^3P_1	3.950	3.953	+3.2	high
1^3P_2	3.550	3.548	-1.8	high
2^3P_2	3.980	3.980	-0.5	high
1^3F_2	4.090	4.091	+1.4	medium
1^1D_2	3.840	3.837	-3.4	high
2^1D_2	4.210	4.208	-2.5	high
1^3D_2	3.840	3.837	-2.6	high
2^3D_2	4.210	4.208	-1.8	high
1^3D_3	3.850	3.848	-2.3	high
2^3D_3	4.220	4.217	-3.4	high
1^1F_3	4.090	4.094	+3.8	medium
1^3F_3	4.100	4.096	-3.9	medium
1^3F_4	4.090	4.095	+4.8	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	3.078	-111.4	+0.0	+0.0	+0.0	+0.0	+0.0	-111.4	2.967
2^1S_0	3.667	-41.0	+0.0	+0.0	+0.0	+0.0	+0.0	-41.0	3.626
3^1S_0	4.091	-27.1	+0.0	+0.0	+0.0	+0.0	+0.0	-27.1	4.064
1^3S_1	3.066	+25.6	+0.0	+0.0	+0.0	+0.0	+0.0	+25.6	3.091
2^3S_1	3.666	+12.7	+0.0	+0.0	+0.0	+0.0	+0.0	+12.7	3.679
1^3D_1	3.841	+0.7	-42.4	+23.2	-19.3	-3.9	+0.0	-22.4	3.818
3^3S_1	4.091	+9.0	+0.0	+0.0	+0.0	+0.0	+0.0	+9.0	4.100
2^3D_1	4.210	+0.6	-31.2	+17.2	-14.0	-2.7	+0.0	-16.2	4.194
4^3S_1	4.442	+7.2	+0.0	+0.0	+0.0	+0.0	+0.0	+7.2	4.449
3^3D_1	4.533	+0.5	-25.5	+13.8	-11.7	-2.2	+0.0	-13.3	4.520
1^1P_1	3.523	-8.2	+0.0	+0.0	+0.0	+0.0	+0.0	-8.2	3.515
2^1P_1	3.963	-6.4	+0.0	+0.0	+0.0	+0.0	+0.0	-6.4	3.956
1^3P_0	3.535	+3.7	-94.6	+22.8	-71.8	-23.8	+0.0	-91.9	3.443
2^3P_0	3.964	+2.5	-52.4	+14.7	-37.8	-12.4	+0.0	-47.8	3.916
1^3P_1	3.524	+2.8	-39.8	+11.1	-28.7	+10.2	+0.0	-15.6	3.508
2^3P_1	3.963	+2.2	-24.9	+7.3	-17.6	+6.0	+0.0	-9.4	3.953
1^3P_2	3.525	+2.2	+33.6	-10.7	+22.9	-1.8	+0.0	+23.3	3.548
2^3P_2	3.963	+1.8	+22.9	-7.2	+15.7	-1.1	+0.0	+16.3	3.980
1^3F_2	4.095	+0.2	-26.1	+23.6	-2.5	-1.5	+0.0	-3.7	4.091
1^1D_2	3.838	-1.9	+0.0	+0.0	+0.0	+0.0	+0.0	-1.9	3.837
2^1D_2	4.209	-1.6	+0.0	+0.0	+0.0	+0.0	+0.0	-1.6	4.208
1^3D_2	3.839	+0.6	-13.0	+7.6	-5.4	+3.6	+0.0	-1.2	3.837
2^3D_2	4.209	+0.5	-9.8	+5.7	-4.1	+2.6	+0.0	-1.0	4.208
1^3D_3	3.839	+0.6	+24.0	-15.0	+9.0	-1.0	+0.0	+8.6	3.848
2^3D_3	4.210	+0.5	+18.6	-11.3	+7.3	-0.7	+0.0	+7.0	4.217
1^1F_3	4.094	-0.7	+0.0	+0.0	+0.0	+0.0	+0.0	-0.7	4.094
1^3F_3	4.094	+0.2	-6.2	+5.9	-0.4	+1.8	+0.0	+1.6	4.096
1^3F_4	4.095	+0.2	+17.8	-17.4	+0.4	-0.6	+0.0	+0.0	4.095

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	3.679	3.679	+1.1	+1.000	-0.008
1^3D_1	3.818	3.818	+1.1	+0.008	+1.000
3^3S_1	4.100	4.100	+0.7	+1.000	-0.007
2^3D_1	4.194	4.194	+0.7	+0.007	+1.000
4^3S_1	4.449	4.449	+0.5	+1.000	-0.007
3^3D_1	4.519	4.520	+0.5	+0.007	+1.000
2^3P_2	3.980	3.980	+0.1	+1.000	-0.001
1^3F_2	4.091	4.091	+0.1	+0.001	+1.000

Mean absolute residual: 2.9 MeV. Max absolute residual: 8.6 MeV.

Spin-Averaged Diagnostics

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

multiplet	states	reference GeV	baseline GeV	residual MeV
1D	4	3.841	3.838	-2.6
2D	4	4.211	4.209	-1.6
3D	1	4.520	4.520	-0.5
1F	4	4.093	4.094	+1.7
1P	4	3.523	3.521	-2.2
2P	4	3.962	3.962	-0.6
1S	2	3.068	3.060	-7.2
2S	2	3.665	3.666	+0.8
3S	2	4.090	4.091	+0.9
4S	1	4.450	4.449	-1.2

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.