r2_dynamics.py (verification run 2); numpy 2.5.4; N = 1000; floating point, NOT a proof
steady states (S): 0.973078759015, 0.976976484125, 0.980131721344, 0.982433429148, 0.983715309104
largest |right-hand side| at the five rounded states: 3.5e-18, 1.7e-18, 1.7e-18, 8.7e-19, 8.7e-19
[4] generic start S(0) = 0, all C_j(0) = 0.5/(N+1) S(0) = 0.000000000 -> S(T) = 0.973078759007: steady state 1 (largest difference of a coordinate 8.2e-12; |right-hand side| 3.5e-18); feasible all the time: True; 1775 steps, 47 s
      t=1e+02: S=0.001167057; t=1e+05: S=0.154784448; t=1e+07: S=0.970241166; t=1e+08: S=0.973075152; t=3e+08: S=0.973078759; t=1e+09: S=0.973078759; t=3e+09: S=0.973078759; t=6e+09: S=0.973078759
[5] generic start S(0) = 0.5, all C_j(0) = 0.1/(N+1) S(0) = 0.500000000 -> S(T) = 0.973078759235: steady state 1 (largest difference of a coordinate 2.2e-10; |right-hand side| 1.5e-17); feasible all the time: True; 1775 steps, 42 s
      t=1e+02: S=0.500720120; t=1e+05: S=0.747874649; t=1e+07: S=0.970811167; t=1e+08: S=0.973075555; t=3e+08: S=0.973078759; t=1e+09: S=0.973078759; t=3e+09: S=0.973078759; t=6e+09: S=0.973078759
[6] generic start S(0) = 0.975, all C_j(0) = 0.5/(N+1) S(0) = 0.975000000 -> S(T) = 0.983715309093: steady state 5 (largest difference of a coordinate 1.1e-11; |right-hand side| 1.7e-18); feasible all the time: True; 1775 steps, 30 s
      t=1e+02: S=0.975556445; t=1e+05: S=0.986699822; t=1e+07: S=0.984092569; t=1e+08: S=0.983716232; t=3e+08: S=0.983715309; t=1e+09: S=0.983715309; t=3e+09: S=0.983715309; t=6e+09: S=0.983715309
[7] generic start S(0) = 0.9785, all C_j(0) = 0.5/(N+1) S(0) = 0.978500000 -> S(T) = 0.983715309112: steady state 5 (largest difference of a coordinate 7.8e-12; |right-hand side| 4.7e-18); feasible all the time: True; 1775 steps, 38 s
      t=1e+02: S=0.978906689; t=1e+05: S=0.986896640; t=1e+07: S=0.984096139; t=1e+08: S=0.983716238; t=3e+08: S=0.983715309; t=1e+09: S=0.983715309; t=3e+09: S=0.983715309; t=6e+09: S=0.983715309
all trajectories of this call stay feasible and converge to one of the steady states 1, 3, 5; the saddle starts reach the two neighbours: True
