== (1) Theorem 3 (C6): Stein-Chen identity and consistency
   max |E[F(N)(N_i - s)] - s(1-q)Delta_i(f)| over 18 random cases: 1.0023e-51 (truncation K = 60)
   implied lower bounds R_ID >= R(q) sqrt((1-q)s/q) at exactly known q: q=0.2599: 0.849939, q=0.2700: 0.845564, q=0.2929: 0.832555, q=0.3500: 0.853243, q=0.4500: 0.850519, q=0.5000: 0.832555
   all below sqrt(2/e) = 0.857764: True (Theorem 3 does not contradict C5)
== (2) Theorem 5 / Proposition 5.1 (C8)
   k=1: q_k* = 0.39346934, argmax_j = 1, M = 0.97703883, B = 0.97703883, |B-M| = 1.34e-51
   k=2: q_k* = 0.22119922, argmax_j = 2, M = 0.91427397, B = 0.91427397, |B-M| = 0.0
   k=3: q_k* = 0.15351828, argmax_j = 3, M = 0.89477662, B = 0.89477662, |B-M| = 0.0
   k=4: q_k* = 0.1175031, argmax_j = 4, M = 0.88528033, B = 0.88528033, |B-M| = 0.0
   k=5: q_k* = 0.095162582, argmax_j = 5, M = 0.87966151, B = 0.87966151, |B-M| = 1.34e-51
   E_1 = 0.030279424 (= sqrt(2/(e ln2)) - 1 = 0.030279424), E_2 = 0.010304475, E_3 = 0.0051799962, E_5 = 0.0020787711
   E_k strictly decreasing for k = 1..2000: True; 16 k^2 E_k at k = 10, 100, 2000: 0.908546, 0.990093, 0.9995
   sup of B/M - 1 on (0, q0] (grid of 2e5 points, from q = 2.93e-06): 0.030279 at q = 0.292893
   sup of B/M - 1 on (0, 1/4] (grid of 2e5 points, from q = 2.50e-06): 0.010304 at q = 0.183504
   sup of B/M - 1 on (0, 1/10] (grid of 2e5 points, from q = 1.00e-06): 0.002079 at q = 0.087129
   min of B/M - 1 on (0, 1/2] (grid): 2.220e-16 (>= 0 up to rounding: B >= M, consistent with M <= R <= B)
== (3) Proposition 7 (C10): ladder strategy
   end pieces: (0, 1/200]: L >= (99/100)^3 = 0.970299;  [49/100, 1/2): L >= 0.9997999
   certified L(q) > 0.962 on [1/200, 49/100] (20000 arb intervals); smallest certified lower bound 0.962190 on [0.21115, 0.21117]
   minimum of L: q = 0.21132487, L = 0.96225045
   q=0.2, eps=1.0e-6: ladder steps [24, 27], E|M| = 0.9886230641 >= sqrt(1-eps^2) L(q) = 0.9623618425: True; admissible: True; max |y^2 + r - c| on all paths: 2.67e-51
   q=0.2, eps=0.001: ladder steps [11, 13], E|M| = 0.9746467854 >= sqrt(1-eps^2) L(q) = 0.9623613614: True; admissible: True; max |y^2 + r - c| on all paths: 2.67e-51
   q=0.21, eps=1.0e-9: ladder steps [35, 38], E|M| = 0.9907015338 >= sqrt(1-eps^2) L(q) = 0.9622519693: True; admissible: True; max |y^2 + r - c| on all paths: 2.67e-51
   q=0.05, eps=1.0e-6: ladder steps [116, 144], E|M| = 0.9997646083 >= sqrt(1-eps^2) L(q) = 0.9846188569: True; admissible: True; max |y^2 + r - c| on all paths: 2.67e-50
   q=0.3, eps=1.0e-6: ladder steps [13, 14], E|M| = 0.9855263845 >= sqrt(1-eps^2) L(q) = 0.9687076876: True; admissible: True; max |y^2 + r - c| on all paths: 2.67e-51
   q=0.45, eps=1.0e-6: ladder steps [4, 5], E|M| = 0.9981891853 >= sqrt(1-eps^2) L(q) = 0.9959376865: True; admissible: True; max |y^2 + r - c| on all paths: 2.67e-51
== (4) Proposition 6(a) (C9): jumps above the compensator
   200 random Kolmogorov measures (those with all atoms >= m_K kept): max |enumeration - 2 m e^(-v)| = 2.66e-15; all <= sqrt(2/e)
== (5) F4: two-to-one merge counterexample
   split E|W + Z_pair| = 0.7837058 (probability mass enumerated 1.000000000000)  [RQ-B: 0.783706]
   Gaussian merge E|W + G(0.328)| = 0.7707013
   E|W| = 0.6290726; for |c| >= C: E|W + Z_c| <= E|W| + 2 w/|c| < split iff |c| > 4.242
   best single atom of variance 0.328 on |c| in [0.05, 8] (2400-point grid + local refinement): 0.7752794 at c = -0.5626  [RQ-B: 0.775279 at -0.5626]
   small |c| (values approach the Gaussian merge): -0.05: 0.770993, -0.03: 0.770883, -0.02: 0.770824, -0.01: 0.770764, 0.01: 0.770636, 0.02: 0.770569, 0.03: 0.770500, 0.05: 0.770355
   for |c| <= 0.05, d_W(Z_c, G) <= |c| (zero-bias bound) gives E|W + Z_c| <= 0.820701 < split: False
   excess split - best merged = 0.00843  [RQ-B: +8.4e-3]
done in 7s
