Residuals: charmed (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	1.880	1.874	-6.4	high
2^1S_0	2.580	2.583	+2.7	high
1^3S_1	2.040	2.038	-1.9	high
2^3S_1	2.640	2.645	+5.0	high
1^3D_1	2.820	2.816	-3.5	high
1^3P_0	2.400	2.395	-5.1	high
1^1P_1	2.440	2.456	+15.7	high
1^3P_1	2.490	2.465	-24.8	high
1^3P_2	2.500	2.502	+2.0	high
1^3D_3	2.830	2.833	+2.9	high
1^3F_4	3.110	3.113	+3.0	medium
1^1S_0	1.980	1.974	-5.8	high
2^1S_0	2.670	2.675	+4.9	high
1^3S_1	2.130	2.125	-5.3	high
2^3S_1	2.730	2.735	+4.5	high
1^3D_1	2.900	2.899	-1.5	high
1^3P_0	2.480	2.481	+0.7	high
1^1P_1	2.530	2.547	+17.4	high
1^3P_1	2.570	2.554	-15.5	high
1^3P_2	2.590	2.591	+1.1	high
1^3D_3	2.920	2.916	-3.9	high
1^3F_4	3.190	3.190	-0.2	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	2.014	-140.9	+0.0	+0.0	+0.0	+0.0	+0.0	-140.9	1.874
2^1S_0	2.627	-44.4	+0.0	+0.0	+0.0	+0.0	+0.0	-44.4	2.583
1^3S_1	2.003	+35.3	+0.0	+0.0	+0.0	+0.0	+0.0	+35.3	2.038
2^3S_1	2.629	+16.2	+0.0	+0.0	+0.0	+0.0	+0.0	+16.2	2.645
1^3D_1	2.836	+1.6	-70.4	+54.1	-16.3	-4.9	+0.0	-19.6	2.816
1^3P_0	2.486	+7.7	-133.3	+58.0	-75.4	-23.6	+0.0	-91.3	2.395
1^1P_1	2.476	-18.8	+0.0	+0.0	+0.0	+0.0	+0.0	-18.8	2.456
1^3P_1	2.477	+6.3	-61.0	+30.3	-30.7	+11.1	+0.0	-13.3	2.465
1^3P_2	2.479	+4.6	+52.9	-32.4	+20.6	-2.0	+0.0	+23.2	2.502
1^3D_3	2.833	+1.0	+39.1	-39.0	+0.1	-1.2	+0.0	-0.1	2.833
1^3F_4	3.125	+0.3	+28.6	-40.3	-11.7	-0.7	+0.0	-12.1	3.113
1^1S_0	2.104	-130.1	+0.0	+0.0	+0.0	+0.0	+0.0	-130.1	1.974
2^1S_0	2.718	-43.2	+0.0	+0.0	+0.0	+0.0	+0.0	-43.2	2.675
1^3S_1	2.093	+32.1	+0.0	+0.0	+0.0	+0.0	+0.0	+32.1	2.125
2^3S_1	2.719	+15.2	+0.0	+0.0	+0.0	+0.0	+0.0	+15.2	2.735
1^3D_1	2.917	+1.2	-63.7	+48.7	-15.0	-5.0	+0.0	-18.8	2.899
1^3P_0	2.576	+6.2	-124.9	+49.4	-75.6	-25.5	+0.0	-94.8	2.481
1^1P_1	2.565	-14.7	+0.0	+0.0	+0.0	+0.0	+0.0	-14.7	2.547
1^3P_1	2.566	+5.0	-55.9	+25.3	-30.6	+11.7	+0.0	-13.9	2.554
1^3P_2	2.567	+3.7	+48.1	-25.9	+22.3	-2.1	+0.0	+23.9	2.591
1^3D_3	2.915	+0.8	+35.5	-33.6	+1.9	-1.2	+0.0	+1.5	2.916
1^3F_4	3.201	+0.3	+26.1	-36.4	-10.4	-0.7	+0.0	-10.8	3.190

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	1.628000	0.220000	disabled
2^1S_0	1.628000	0.220000	disabled
1^3S_1	1.628000	0.220000	disabled
2^3S_1	1.628000	0.220000	disabled
1^3D_1	1.628000	0.220000	unequal_mass_equal_share_LdotS
1^3P_0	1.628000	0.220000	unequal_mass_equal_share_LdotS
1^1P_1	1.628000	0.220000	unequal_mass_same_j_mixed
1^3P_1	1.628000	0.220000	unequal_mass_same_j_mixed
1^3P_2	1.628000	0.220000	unequal_mass_equal_share_LdotS
1^3D_3	1.628000	0.220000	unequal_mass_equal_share_LdotS
1^3F_4	1.628000	0.220000	unequal_mass_equal_share_LdotS
1^1S_0	1.628000	0.419000	disabled
2^1S_0	1.628000	0.419000	disabled
1^3S_1	1.628000	0.419000	disabled
2^3S_1	1.628000	0.419000	disabled
1^3D_1	1.628000	0.419000	unequal_mass_equal_share_LdotS
1^3P_0	1.628000	0.419000	unequal_mass_equal_share_LdotS
1^1P_1	1.628000	0.419000	unequal_mass_same_j_mixed
1^3P_1	1.628000	0.419000	unequal_mass_same_j_mixed
1^3P_2	1.628000	0.419000	unequal_mass_equal_share_LdotS
1^3D_3	1.628000	0.419000	unequal_mass_equal_share_LdotS
1^3F_4	1.628000	0.419000	unequal_mass_equal_share_LdotS

Same-J Antisymmetric Spin-Orbit Mixing

Rows below use the mixed eigenvalues from the (^1L_J, ^3L_J) mass block. Components are ordered as singlet/triplet in the unmixed basis.

state	unmixed GeV	mixed GeV	offdiag MeV	theta deg	singlet component	triplet component
1^1P_1	2.457	2.456	+3.7	-25.79	+0.900	-0.435
1^3P_1	2.463	2.465	+3.7	-25.79	+0.435	+0.900
1^1P_1	2.550	2.547	+3.5	-39.56	+0.771	-0.637
1^3P_1	2.552	2.554	+3.5	-39.56	+0.637	+0.771

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	2.645	2.645	+3.4	+1.000	-0.020
1^3D_1	2.816	2.816	+3.4	+0.020	+1.000
2^3S_1	2.735	2.735	+2.8	+1.000	-0.017
1^3D_1	2.898	2.899	+2.8	+0.017	+1.000

Mean absolute residual: 6.1 MeV. Max absolute residual: 24.8 MeV.

Spin-Averaged Diagnostics

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

multiplet	states	reference GeV	baseline GeV	residual MeV
1D	4	2.870	2.869	-1.1
1F	2	3.150	3.151	+1.4
1P	8	2.518	2.517	-0.4
1S	4	2.046	2.042	-4.2
2S	4	2.670	2.675	+4.5

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.