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0.72 ], "theta_after_bps": [ 0.1774, 0.1847, 0.1195, 0.0785, 0.1125, -0.1887, 0.2109, 0.1057, 0.1103, 0.049, 0.0502, -0.067, 0.0045, 0.0516, 0.0435, 0.057, 0.0375, -0.0137, 0.0823, 0.0131, 0.0379, 0.0305 ] }, { "gen": 3, "seeds": [ 200768, 201023 ], "sigma_bps": 0.2313, "median_pair_se": 0.01115, "max_abs_pair_t": 2.23, "t": [ 0.52, -1.19, 1.02, -0.5, -0.56, 1.42, -0.48, 0.92, 0.38, 0.72, 1.77, -0.23, -0.17, 0.51, 0.96, 0.35, 0.87, -0.25, 0.0, 1.04, 0.91, 1.01 ], "theta_after_bps": [ 0.1983, 0.137, 0.1604, 0.0586, 0.0902, -0.1319, 0.1916, 0.1427, 0.1253, 0.0777, 0.121, -0.0763, -0.0022, 0.072, 0.0819, 0.071, 0.0723, -0.0238, 0.0825, 0.0549, 0.0745, 0.0708 ] }, { "gen": 4, "seeds": [ 201024, 201279 ], "sigma_bps": 0.2121, "median_pair_se": 0.0114, "max_abs_pair_t": 2.16, "t": [ -0.35, -1.72, 1.02, -0.53, -0.98, -2.15, -0.06, -0.54, -0.05, 0.42, -0.88, -0.32, -0.12, 1.3, 0.86, 0.49, -1.14, 1.83, 1.58, 0.1, 0.7, 0.41 ], "theta_after_bps": [ 0.1843, 0.0683, 0.2011, 0.0374, 0.0511, -0.2178, 0.189, 0.1212, 0.1234, 0.0946, 0.0857, -0.0889, -0.0071, 0.1242, 0.1162, 0.0906, 0.0268, 0.0492, 0.1457, 0.0589, 0.1025, 0.0872 ] }, { "gen": 5, "seeds": [ 201280, 201535 ], "sigma_bps": 0.1945, "median_pair_se": 0.01004, "max_abs_pair_t": 2.97, "t": [ 0.05, 2.85, 3.39, 0.27, 1.32, -0.68, 1.11, 2.35, 3.23, 0.39, 0.99, -0.88, -0.34, 1.76, -1.01, 1.16, 0.11, 1.12, -0.31, -1.08, -1.83, 1.17 ], "theta_after_bps": [ 0.1861, 0.1823, 0.3211, 0.0481, 0.1038, -0.245, 0.2333, 0.2153, 0.2434, 0.1101, 0.1252, -0.124, -0.0208, 0.1947, 0.076, 0.137, 0.0311, 0.0939, 0.1333, 0.0156, 0.0293, 0.1342 ] }, { "gen": 6, "seeds": [ 201536, 201791 ], "sigma_bps": 0.1784, "median_pair_se": 0.0112, "max_abs_pair_t": 1.65, "t": [ -0.8, 0.29, -1.23, -0.15, -1.38, -0.6, -0.08, -0.58, 1.01, -0.21, 0.36, -1.29, -1.32, 0.43, 0.24, -0.73, 0.55, 0.04, 0.36, -1.66, -2.26, -0.14 ], "theta_after_bps": [ 0.154, 0.1938, 0.2718, 0.0423, 0.0484, -0.2688, 0.2302, 0.1922, 0.2838, 0.1017, 0.1397, -0.1756, -0.0735, 0.2117, 0.0855, 0.108, 0.053, 0.0956, 0.1476, -0.0509, -0.0611, 0.1285 ] }, { "gen": 7, "seeds": [ 201792, 202047 ], "sigma_bps": 0.1636, "median_pair_se": 0.01156, "max_abs_pair_t": 3.06, "t": [ -1.23, 2.39, 1.11, -0.23, 1.51, -1.7, 0.37, 2.46, 0.05, -0.96, 0.34, -1.5, -1.46, 1.88, 0.94, -0.72, -1.68, 0.6, -1.03, 1.51, 0.41, -0.81 ], "theta_after_bps": [ 0.105, 0.2895, 0.3163, 0.0333, 0.1089, -0.3369, 0.245, 0.2906, 0.2859, 0.0633, 0.1532, -0.2357, -0.1318, 0.2868, 0.123, 0.0792, -0.0142, 0.1196, 0.1066, 0.0096, -0.0448, 0.0962 ] }, { "gen": 8, "seeds": [ 202048, 202303 ], "sigma_bps": 0.15, "median_pair_se": 0.00906, "max_abs_pair_t": 2.13, "t": [ 0.9, -1.16, -0.31, -0.76, -0.15, 0.38, 0.75, -0.17, -1.4, 1.23, 0.92, 1.65, 1.16, -0.24, -1.41, 0.48, 0.8, -0.23, 0.74, -0.49, 0.12, -1.04 ], "theta_after_bps": [ 0.141, 0.2429, 0.3038, 0.0027, 0.1029, -0.3216, 0.275, 0.284, 0.2298, 0.1127, 0.1901, -0.1698, -0.0852, 0.2772, 0.0667, 0.0985, 0.0178, 0.1104, 0.1361, -0.0099, -0.0401, 0.0546 ] } ], "theta_order": "for level 1 then level 2: 6 row-band offsets then 5 column-band offsets (same order as bands)" }, "limitations": [ "Replica only (engine-faithful LEAN/QLX5 replica via the harness overlay); no engine run, no Solidity, no gas measurement, and seeds 10000..12047 were never run.", "TRAIN used 101376 simulations on seeds [200000, 202303]; VALID is one pass over 300000..304095 and CHOOSE was scored at most once for the kept correction only.", "ES evaluations use unquantised integer-millibps deltas (the raw C++ interface); only the candidates are rounded to the 0.5 bps lattice with qpl.apply(quantize=True) and checked with qpl.encode.", "The band parameterisation (6 row bands + 5 column bands per level, additive) cannot express corrections finer than a band or row-column interactions; level-knot index 2 carries about 1.2% of table 1 visit weight on the profile seeds, so its offsets are weakly determined.", "Mirrored differences cancel even-order effects; at a one-sided (kinked) optimum the finite-sigma gradient can point at a direction in which both signs lose. VALID is the guard against that.", "Pooled per-band gradients are inverse-variance averages over generations while theta moved, and are finite-difference slopes at sigma 0.3..0.15 bps, not exact derivatives.", "The best VALID candidate is selected among up to 4 candidates, so its VALID gain is selection-biased upward; the CHOOSE figure is the unbiased one.", "Band offsets were applied to every stored node of the band, including nodes with zero visit weight on the profile seeds." ] }