joint statistics against exact enumeration (chains scaled by 1, seed 2027) ring 8, fixed T = 1.5, 4 sweeps: 200000 chains, 2930 bins; exact law: chi2 3030.0 (p 0.095), G 3066.8 (p 0.037), TV 0.0436, cell |z| 1.91 (p 1.000), pair |z| 2.61 (p 1.000); same as the reference 200000/200000; 3.7 s control, the same marginals with independent cells: chi2 244079.4 on 3247 bins (p 0.00e0), cell |z| 1.91 (p 1.000), pair |z| 86.9 (p 0.00e0) [PASS] ring 8, fixed T = 1.5, 4 sweeps: the joint law is the exact law (every p at least 0.001) [PASS] ring 8, fixed T = 1.5, 4 sweeps: every chain's final state is the reference's [PASS] ring 8, fixed T = 1.5, 4 sweeps: the independent-cells control is rejected (chi-square p below 1e-6) ring 8, the job's anneal from T = 2.5, 10 sweeps: 200000 chains, 45 bins; exact law: chi2 38.5 (p 0.708), G 38.6 (p 0.702), TV 0.0022, cell |z| 1.20 (p 1.000), pair |z| 2.35 (p 1.000); same as the reference 200000/200000; 6.2 s control, the same marginals with independent cells: chi2 1933336.3 on 181 bins (p 0.00e0), cell |z| 1.20 (p 1.000), pair |z| 390.3 (p 0.00e0) [PASS] ring 8, the job's anneal from T = 2.5, 10 sweeps: the joint law is the exact law (every p at least 0.001) [PASS] ring 8, the job's anneal from T = 2.5, 10 sweeps: every chain's final state is the reference's [PASS] ring 8, the job's anneal from T = 2.5, 10 sweeps: the independent-cells control is rejected (chi-square p below 1e-6) dense 6, fixed T = 4, 2 sweeps: 200000 chains, 729 bins; exact law: chi2 682.6 (p 0.884), G 685.3 (p 0.870), TV 0.0219, cell |z| 1.73 (p 1.000), pair |z| 3.58 (p 0.047); same as the reference 200000/200000; 2.1 s control, the same marginals with independent cells: chi2 91995.4 on 729 bins (p 0.00e0), cell |z| 1.73 (p 1.000), pair |z| 54.5 (p 0.00e0) [PASS] dense 6, fixed T = 4, 2 sweeps: the joint law is the exact law (every p at least 0.001) [PASS] dense 6, fixed T = 4, 2 sweeps: every chain's final state is the reference's [PASS] dense 6, fixed T = 4, 2 sweeps: the independent-cells control is rejected (chi-square p below 1e-6) sparse 10, the job's anneal from T = 1.5, 8 sweeps: 400000 chains, 190 bins; exact law: chi2 196.1 (p 0.346), G 207.7 (p 0.167), TV 0.0048, cell |z| 1.45 (p 1.000), pair |z| 3.04 (p 0.773); same as the reference 400000/400000; 12.4 s control, the same marginals with independent cells: chi2 14139391.3 on 1531 bins (p 0.00e0), cell |z| 1.45 (p 1.000), pair |z| 373.6 (p 0.00e0) [PASS] sparse 10, the job's anneal from T = 1.5, 8 sweeps: the joint law is the exact law (every p at least 0.001) [PASS] sparse 10, the job's anneal from T = 1.5, 8 sweeps: every chain's final state is the reference's [PASS] sparse 10, the job's anneal from T = 1.5, 8 sweeps: the independent-cells control is rejected (chi-square p below 1e-6) [PASS] the engine still answers with its ID at the end: no other session replaced it 13 checks, 0 failed