==================================================================================================== 0. FAST FITTER VALIDATION against the verbatim Nelder-Mead fit (nll, parameter, tau) opus15 M0: nll NM 52.5502 fast 52.5502 (d +1.4e-14) params [] vs [] tau 7.085 vs 7.085 opus15 M1: nll NM 46.4111 fast 46.4111 (d +1.4e-14) params [5.7053] vs [5.7053] tau 4.160 vs 4.160 opus15 M2: nll NM 36.5779 fast 36.5779 (d +0.0e+00) params [0.5392] vs [0.5392] tau 0.980 vs 0.980 opus15 M3: nll NM 42.6947 fast 42.6947 (d +1.4e-14) params [7.3286] vs [7.3286] tau 2.639 vs 2.639 opus15 M5: nll NM 39.5771 fast 39.5771 (d +2.1e-14) params [2.4956] vs [2.4956] tau 1.887 vs 1.887 weaker6 M0: nll NM 25.2424 fast 25.2424 (d +3.6e-15) params [] vs [] tau 15.327 vs 15.327 weaker6 M1: nll NM 24.3390 fast 24.3390 (d +7.1e-15) params [8.1201] vs [8.1201] tau 12.927 vs 12.927 weaker6 M2: nll NM 23.6965 fast 23.6965 (d +7.1e-15) params [0.3834] vs [0.3834] tau 11.455 vs 11.455 weaker6 M3: nll NM 24.3390 fast 24.3390 (d +7.1e-15) params [8.1201] vs [8.1201] tau 12.927 vs 12.927 weaker6 M5: nll NM 24.1950 fast 24.1950 (d +3.6e-15) params [2.4542] vs [2.4542] tau 12.610 vs 12.610 all21 M0: nll NM 79.8262 fast 79.8262 (d +2.8e-14) params [] vs [] tau 9.667 vs 9.667 all21 M1: nll NM 74.4852 fast 74.4852 (d +1.4e-14) params [6.3857] vs [6.3857] tau 6.733 vs 6.733 all21 M2: nll NM 69.9025 fast 69.9025 (d +1.4e-14) params [0.4529] vs [0.4529] tau 4.411 vs 4.411 all21 M3: nll NM 72.9048 fast 72.9048 (d +1.4e-14) params [7.7262] vs [7.7262] tau 5.724 vs 5.724 all21 M5: nll NM 71.4132 fast 71.4132 (d +1.4e-14) params [2.4729] vs [2.4729] tau 4.939 vs 4.939 Observed (fast fitter): BF law:constant 9.82, law:capped 5.58, law:zero 186.18, law:smooth cap 3.05; MAE gap constant-law 1.862; Opus-15 AIC gap constant-law 19.67; k weak 0.3834, k Opus 0.5392 ==================================================================================================== 1. CONTROL-SCORE STANDARD ERROR PER ROW: se_m = sqrt(m (100 - m) / n_eff) opus15: id, m, tasks x repeats = n_eff, se_m, s (row SE), h, worst-case Cov(h noise, Delta noise) L003 m 97.70 87 x 1 = 87 se_m 1.61 (tasks only 1.61) s 2.35 h 2.3 cov 2.58 L004 m 92.00 87 x 1 = 87 se_m 2.91 (tasks only 2.91) s 2.64 h 8.0 cov 7.67 L010 m 100.00 30 x 1 = 30 se_m 0.00 (tasks only 0.00) s 0.84 h 0.0 cov 0.00 L011 m 90.00 16 x 1 = 16 se_m 7.50 (tasks only 7.50) s 10.61 h 10.0 cov 56.25 L012 m 89.00 15 x 2 = 30 se_m 5.71 (tasks only 8.08) s 4.03 h 11.0 cov 23.03 L016 m 95.00 60 x 1 = 60 se_m 2.81 (tasks only 2.81) s 4.28 h 5.0 cov 7.92 L057 m 74.20 66 x 1 = 66 se_m 5.39 (tasks only 5.39) s 6.59 h 25.8 cov 29.01 L099 m 89.00 120 x 1 = 120 se_m 2.86 (tasks only 2.86) s 4.46 h 11.0 cov 8.16 L124 m 83.30 112 x 3 = 336 se_m 2.03 (tasks only 3.52) s 2.73 h 16.7 cov 4.14 L126 m 84.40 173 x 3 = 519 se_m 1.59 (tasks only 2.76) s 2.19 h 15.6 cov 2.54 L136 m 90.30 224 x 3 = 672 se_m 1.14 (tasks only 1.98) s 1.18 h 9.7 cov 1.30 L147 m 86.90 61 x 3 = 183 se_m 2.49 (tasks only 4.32) s 3.62 h 13.1 cov 6.22 L163 m 89.90 417 x 1 = 417 se_m 1.48 (tasks only 1.48) s 1.35 h 10.1 cov 1.99 L166 m 80.70 212 x 1 = 212 se_m 2.71 (tasks only 2.71) s 2.78 h 19.3 cov 7.35 L174 m 84.90 417 x 1 = 417 se_m 1.75 (tasks only 1.75) s 1.71 h 15.1 cov 3.00 opus15 [primary]: mean se_m 2.799 (rms 3.384); Var(e_m) 11.454; Var(h_obs) 43.15 (sd 6.57); expected spurious slope Var(e_m)/Var(h_obs) 0.2655 (worst-case cov 0.2490); through-origin weighted analogue 0.0293; se_m > s on ['L004', 'L012', 'L163', 'L174'] opus15 [tasks_only]: mean se_m 3.311 (rms 3.940); Var(e_m) 15.523; Var(h_obs) 43.15 (sd 6.57); expected spurious slope Var(e_m)/Var(h_obs) 0.3598 (worst-case cov 0.2938); through-origin weighted analogue 0.0388; se_m > s on ['L004', 'L012', 'L124', 'L126', 'L136', 'L147', 'L163', 'L174'] weaker6: id, m, tasks x repeats = n_eff, se_m, s (row SE), h, worst-case Cov(h noise, Delta noise) L001 m 66.60 417 x 2 = 834 se_m 1.63 (tasks only 2.31) s 3.13 h 33.4 cov 2.67 L002 m 80.10 168 x 2 = 336 se_m 2.18 (tasks only 3.08) s 4.05 h 19.9 cov 4.74 L006 m 63.10 65 x 1 = 65 se_m 5.99 (tasks only 5.99) s 5.89 h 36.9 cov 35.24 L007 m 72.40 58 x 1 = 58 se_m 5.87 (tasks only 5.87) s 5.28 h 27.6 cov 30.98 L054 m 90.90 66 x 1 = 66 se_m 3.54 (tasks only 3.54) s 4.12 h 9.1 cov 12.53 L058 m 78.60 84 x 1 = 84 se_m 4.47 (tasks only 4.47) s 4.92 h 21.4 cov 20.02 weaker6 [primary]: mean se_m 3.947 (rms 4.286); Var(e_m) 18.374; Var(h_obs) 102.05 (sd 10.10); expected spurious slope Var(e_m)/Var(h_obs) 0.1801 (worst-case cov 0.1734); through-origin weighted analogue 0.0248; se_m > s on ['L006', 'L007'] weaker6 [tasks_only]: mean se_m 4.210 (rms 4.428); Var(e_m) 19.609; Var(h_obs) 102.05 (sd 10.10); expected spurious slope Var(e_m)/Var(h_obs) 0.1922 (worst-case cov 0.1855); through-origin weighted analogue 0.0267; se_m > s on ['L006', 'L007'] ==================================================================================================== 2. ERRORS-IN-VARIABLES CORRECTION OF k model: h_obs = h - e_m, Delta_obs = k h - e_m + e_t + eta; Var(e_m) = se_m^2, Cov(h noise, Delta noise) = cov opus15 [primary ] k naive 0.5392 -> method of moments 0.5246 (tau 0.91); SIMEX quadratic 0.5562, linear 0.5326; SIMEX means by lambda {'0.0': 0.53917, '0.5': 0.53292, '1.0': 0.53509, '1.5': 0.53769, '2.0': 0.54305} opus15 [tasks_only] k naive 0.5392 -> method of moments 0.5250 (tau 0.92); SIMEX quadratic 0.5631, linear 0.5349; SIMEX means by lambda {'0.0': 0.53917, '0.5': 0.52952, '1.0': 0.53153, '1.5': 0.53115, '2.0': 0.5368} weaker6 [primary ] k naive 0.3834 -> method of moments 0.3680 (tau 11.45); SIMEX quadratic 0.3773, linear 0.3948; SIMEX means by lambda {'0.0': 0.38336, '0.5': 0.38804, '1.0': 0.38086, '1.5': 0.37577, '2.0': 0.37067} weaker6 [tasks_only] k naive 0.3834 -> method of moments 0.3668 (tau 11.45); SIMEX quadratic 0.3639, linear 0.3918; SIMEX means by lambda {'0.0': 0.38336, '0.5': 0.38118, '1.0': 0.3828, '1.5': 0.38233, '2.0': 0.36725} Corrected weak-to-Opus forecast (law with corrected weak k; tau re-profiled on the weak rows at that k; other models as fitted) [primary k_mom ] k 0.3680 tau_w 11.45: BF vs zero 177.21, constant 9.34, capped 5.31, smooth cap 2.91; MAE 3.403 RMSE 3.993 [primary k_simex_quadratic] k 0.3773 tau_w 11.45: BF vs zero 183.03, constant 9.65, capped 5.48, smooth cap 3.0; MAE 3.343 RMSE 3.913 [tasks_only k_mom ] k 0.3668 tau_w 11.45: BF vs zero 176.38, constant 9.3, capped 5.28, smooth cap 2.89; MAE 3.411 RMSE 4.004 [tasks_only k_simex_quadratic] k 0.3639 tau_w 11.45: BF vs zero 174.29, constant 9.19, capped 5.22, smooth cap 2.86; MAE 3.43 RMSE 4.029 [uncorrected ] k 0.3834: BF vs zero 186.18, constant 9.82, capped 5.58; MAE 3.304 ==================================================================================================== 3. PARAMETRIC BOOTSTRAP OF COUPLING-ONLY NULLS (4000 datasets each) each population simulated with true h = observed h, control noise e_m ~ N(0, se_m^2) in both h and Delta (h kept >= 0), remaining Delta noise so Var(Delta noise) = s^2 (worst-case coupling, see header). true lift: 'constant' = the constant c fitted on that population (weak 8.12, Opus 5.71: the two populations differ); 'common' = one constant for both (the all-21 constant fit); 'zero' = 0. 'tau0' = no between-row spread (the primary specification); 'taufit' = the null model's own fitted tau (standard parametric bootstrap). 'nocoupling' = the same null with se_m = 0, to separate coupling from the rest of the null. Bayes factors and MAE: models fitted on the simulated weak set, scored on the simulated Opus set (own tau). (15 configurations in 686 s) [constant_tau0] true lift weak 8.120 / Opus 5.705; spread tau weak 0.00 / Opus 0.00; n_eff primary; coupled True BF law:constant observed 9.82 (log10 0.99) null log10 median -2.76 95th 16.28 99th 32.52 null >= observed 1194/4000 (null BF > 1: 0.35) BF law:capped observed 5.58 (log10 0.75) null log10 median 1.43 95th 15.26 99th 20.79 null >= observed 2184/4000 (null BF > 1: 0.61) BF law:zero observed 186.18 (log10 2.27) null log10 median -2.98 95th 4.54 99th 5.50 null >= observed 1269/4000 (null BF > 1: 0.40) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -0.95 95th 8.91 99th 12.36 null >= observed 1220/4000 (null BF > 1: 0.36) MAE constant - law observed 1.862 null median 0.069 95th 2.897 99th 4.383 null >= observed 573/4000 MAE capped - law observed 0.717 null median 0.114 95th 1.976 99th 2.694 null >= observed 1209/4000 MAE zero - law observed 3.015 null median 2.571 95th 3.765 99th 4.250 null >= observed 1077/4000 Opus-15 AIC constant - law observed 19.67 null median -11.574 95th -3.450 99th -0.104 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.3001 95th 0.3852 99th 0.4173 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.4248 95th 0.4871 99th 0.5083 null >= observed 2/4000 [constant_taufit] true lift weak 8.120 / Opus 5.705; spread tau weak 12.93 / Opus 4.16; n_eff primary; coupled True BF law:constant observed 9.82 (log10 0.99) null log10 median 0.28 95th 5.35 99th 22.50 null >= observed 1183/4000 (null BF > 1: 0.61) BF law:capped observed 5.58 (log10 0.75) null log10 median 0.11 95th 2.49 99th 15.75 null >= observed 961/4000 (null BF > 1: 0.56) BF law:zero observed 186.18 (log10 2.27) null log10 median 1.32 95th 3.81 99th 4.87 null >= observed 1006/4000 (null BF > 1: 0.90) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -0.09 95th 0.89 99th 3.92 null >= observed 599/4000 (null BF > 1: 0.42) MAE constant - law observed 1.862 null median 0.516 95th 6.952 99th 10.370 null >= observed 1273/4000 MAE capped - law observed 0.717 null median 0.347 95th 2.807 99th 3.590 null >= observed 1646/4000 MAE zero - law observed 3.015 null median 1.416 95th 3.451 99th 4.221 null >= observed 354/4000 Opus-15 AIC constant - law observed 19.67 null median -2.540 95th 5.191 99th 9.494 null >= observed 2/4000 k weak (fitted on null data) observed 0.3834 null mean 0.305 95th 0.6458 99th 0.7811 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.4175 95th 0.5757 99th 0.6346 null >= observed 413/4000 [common_tau0] true lift weak 6.386 / Opus 6.386; spread tau weak 0.00 / Opus 0.00; n_eff primary; coupled True BF law:constant observed 9.82 (log10 0.99) null log10 median -15.13 95th 0.31 99th 7.97 null >= observed 163/4000 (null BF > 1: 0.06) BF law:capped observed 5.58 (log10 0.75) null log10 median -5.05 95th 9.64 99th 14.71 null >= observed 809/4000 (null BF > 1: 0.23) BF law:zero observed 186.18 (log10 2.27) null log10 median -9.79 95th 3.41 99th 7.61 null >= observed 552/4000 (null BF > 1: 0.27) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -5.50 95th 7.92 99th 11.86 null >= observed 615/4000 (null BF > 1: 0.17) MAE constant - law observed 1.862 null median -1.419 95th 0.667 99th 1.824 null >= observed 36/4000 MAE capped - law observed 0.717 null median -1.109 95th 0.489 99th 1.345 null >= observed 148/4000 MAE zero - law observed 3.015 null median 2.301 95th 3.458 99th 3.960 null >= observed 623/4000 Opus-15 AIC constant - law observed 19.67 null median -13.455 95th -4.982 99th -0.569 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.2396 95th 0.33 99th 0.3644 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.4707 95th 0.5317 99th 0.5589 null >= observed 122/4000 [common_taufit] true lift weak 6.386 / Opus 6.386; spread tau weak 12.93 / Opus 4.16; n_eff primary; coupled True BF law:constant observed 9.82 (log10 0.99) null log10 median 0.06 95th 3.33 99th 15.27 null >= observed 762/4000 (null BF > 1: 0.53) BF law:capped observed 5.58 (log10 0.75) null log10 median -0.01 95th 1.94 99th 14.38 null >= observed 719/4000 (null BF > 1: 0.50) BF law:zero observed 186.18 (log10 2.27) null log10 median 1.05 95th 3.43 99th 4.51 null >= observed 718/4000 (null BF > 1: 0.85) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -0.18 95th 0.68 99th 2.77 null >= observed 378/4000 (null BF > 1: 0.34) MAE constant - law observed 1.862 null median -0.044 95th 5.086 99th 8.688 null >= observed 831/4000 MAE capped - law observed 0.717 null median -0.024 95th 2.648 99th 4.271 null >= observed 1229/4000 MAE zero - law observed 3.015 null median 1.481 95th 3.573 99th 4.471 null >= observed 432/4000 Opus-15 AIC constant - law observed 19.67 null median -3.414 95th 4.723 99th 8.834 null >= observed 2/4000 k weak (fitted on null data) observed 0.3834 null mean 0.2419 95th 0.5771 99th 0.7124 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.4651 95th 0.6238 99th 0.6861 null >= observed 895/4000 [zero_tau0] true lift weak 0.000 / Opus 0.000; spread tau weak 0.00 / Opus 0.00; n_eff primary; coupled True BF law:constant observed 9.82 (log10 0.99) null log10 median 0.73 95th 8.76 99th 16.34 null >= observed 1737/4000 (null BF > 1: 0.83) BF law:capped observed 5.58 (log10 0.75) null log10 median 0.58 95th 6.76 99th 12.63 null >= observed 1814/4000 (null BF > 1: 0.83) BF law:zero observed 186.18 (log10 2.27) null log10 median -0.01 95th 1.07 99th 1.87 null >= observed 20/4000 (null BF > 1: 0.47) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median 0.11 95th 3.40 99th 6.49 null >= observed 1218/4000 (null BF > 1: 0.65) MAE constant - law observed 1.862 null median 0.195 95th 1.440 99th 2.200 null >= observed 90/4000 MAE capped - law observed 0.717 null median 0.162 95th 1.275 99th 1.948 null >= observed 625/4000 MAE zero - law observed 3.015 null median -0.025 95th 0.263 99th 0.467 null >= observed 0/4000 Opus-15 AIC constant - law observed 19.67 null median 0.060 95th 2.714 99th 4.609 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.0151 95th 0.1185 99th 0.1595 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.022 95th 0.0989 99th 0.128 null >= observed 0/4000 [zero_taufit] true lift weak 0.000 / Opus 0.000; spread tau weak 15.33 / Opus 7.08; n_eff primary; coupled True BF law:constant observed 9.82 (log10 0.99) null log10 median 0.28 95th 4.00 99th 13.95 null >= observed 858/4000 (null BF > 1: 0.83) BF law:capped observed 5.58 (log10 0.75) null log10 median 0.24 95th 3.13 99th 11.84 null >= observed 967/4000 (null BF > 1: 0.81) BF law:zero observed 186.18 (log10 2.27) null log10 median 0.07 95th 0.98 99th 1.77 null >= observed 10/4000 (null BF > 1: 0.69) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median 0.10 95th 1.08 99th 3.12 null >= observed 766/4000 (null BF > 1: 0.72) MAE constant - law observed 1.862 null median 0.685 95th 5.397 99th 8.526 null >= observed 1070/4000 MAE capped - law observed 0.717 null median 0.619 95th 4.119 99th 6.690 null >= observed 1888/4000 MAE zero - law observed 3.015 null median -0.188 95th 0.605 99th 1.192 null >= observed 0/4000 Opus-15 AIC constant - law observed 19.67 null median 0.005 95th 2.225 99th 3.839 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.02 95th 0.4161 99th 0.5842 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.0349 95th 0.2847 99th 0.3848 null >= observed 0/4000 [constant_tau0_nocoupling] true lift weak 8.120 / Opus 5.705; spread tau weak 0.00 / Opus 0.00; n_eff primary; coupled False BF law:constant observed 9.82 (log10 0.99) null log10 median -2.11 95th 18.62 99th 32.34 null >= observed 1301/4000 (null BF > 1: 0.37) BF law:capped observed 5.58 (log10 0.75) null log10 median 1.70 95th 18.16 99th 23.58 null >= observed 2181/4000 (null BF > 1: 0.59) BF law:zero observed 186.18 (log10 2.27) null log10 median 0.63 95th 4.08 99th 4.84 null >= observed 1379/4000 (null BF > 1: 0.52) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -0.83 95th 9.98 99th 14.04 null >= observed 1410/4000 (null BF > 1: 0.39) MAE constant - law observed 1.862 null median -0.330 95th 2.609 99th 3.796 null >= observed 455/4000 MAE capped - law observed 0.717 null median -0.086 95th 2.173 99th 2.943 null >= observed 1106/4000 MAE zero - law observed 3.015 null median 2.141 95th 3.280 99th 3.731 null >= observed 402/4000 Opus-15 AIC constant - law observed 19.67 null median -14.389 95th -7.030 99th -3.745 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.2906 95th 0.4036 99th 0.449 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.4057 95th 0.5031 99th 0.5431 null >= observed 50/4000 [constant_taufit_nocoupling] true lift weak 8.120 / Opus 5.705; spread tau weak 12.93 / Opus 4.16; n_eff primary; coupled False BF law:constant observed 9.82 (log10 0.99) null log10 median 0.03 95th 4.68 99th 31.42 null >= observed 896/4000 (null BF > 1: 0.52) BF law:capped observed 5.58 (log10 0.75) null log10 median -0.04 95th 2.20 99th 18.36 null >= observed 734/4000 (null BF > 1: 0.48) BF law:zero observed 186.18 (log10 2.27) null log10 median 1.05 95th 3.24 99th 4.24 null >= observed 701/4000 (null BF > 1: 0.89) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -0.19 95th 0.77 99th 5.05 null >= observed 377/4000 (null BF > 1: 0.33) MAE constant - law observed 1.862 null median 0.168 95th 6.428 99th 9.729 null >= observed 1147/4000 MAE capped - law observed 0.717 null median 0.186 95th 2.759 99th 3.678 null >= observed 1541/4000 MAE zero - law observed 3.015 null median 1.089 95th 2.946 99th 3.748 null >= observed 184/4000 Opus-15 AIC constant - law observed 19.67 null median -4.137 95th 2.592 99th 5.778 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.2868 95th 0.6341 99th 0.7722 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.3964 95th 0.5686 99th 0.6459 null >= observed 351/4000 [common_tau0_nocoupling] true lift weak 6.386 / Opus 6.386; spread tau weak 0.00 / Opus 0.00; n_eff primary; coupled False BF law:constant observed 9.82 (log10 0.99) null log10 median -12.75 95th 0.32 99th 7.65 null >= observed 176/4000 (null BF > 1: 0.06) BF law:capped observed 5.58 (log10 0.75) null log10 median -3.29 95th 11.71 99th 16.86 null >= observed 1038/4000 (null BF > 1: 0.28) BF law:zero observed 186.18 (log10 2.27) null log10 median -7.18 95th 3.19 99th 7.36 null >= observed 543/4000 (null BF > 1: 0.38) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -3.87 95th 9.93 99th 13.65 null >= observed 842/4000 (null BF > 1: 0.22) MAE constant - law observed 1.862 null median -1.707 95th 0.162 99th 1.448 null >= observed 20/4000 MAE capped - law observed 0.717 null median -1.259 95th 0.429 99th 1.528 null >= observed 139/4000 MAE zero - law observed 3.015 null median 1.953 95th 3.112 99th 3.538 null >= observed 263/4000 Opus-15 AIC constant - law observed 19.67 null median -16.085 95th -8.366 99th -5.170 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.2269 95th 0.3359 99th 0.3841 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.4526 95th 0.5531 99th 0.5889 null >= observed 294/4000 [common_taufit_nocoupling] true lift weak 6.386 / Opus 6.386; spread tau weak 12.93 / Opus 4.16; n_eff primary; coupled False BF law:constant observed 9.82 (log10 0.99) null log10 median -0.12 95th 2.86 99th 12.22 null >= observed 611/4000 (null BF > 1: 0.44) BF law:capped observed 5.58 (log10 0.75) null log10 median -0.14 95th 1.85 99th 9.22 null >= observed 578/4000 (null BF > 1: 0.41) BF law:zero observed 186.18 (log10 2.27) null log10 median 0.82 95th 2.93 99th 4.01 null >= observed 514/4000 (null BF > 1: 0.82) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -0.27 95th 0.49 99th 2.72 null >= observed 204/4000 (null BF > 1: 0.26) MAE constant - law observed 1.862 null median -0.295 95th 4.606 99th 7.830 null >= observed 734/4000 MAE capped - law observed 0.717 null median -0.177 95th 2.531 99th 3.798 null >= observed 1154/4000 MAE zero - law observed 3.015 null median 1.180 95th 3.173 99th 4.106 null >= observed 268/4000 Opus-15 AIC constant - law observed 19.67 null median -5.131 95th 2.310 99th 6.158 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.2249 95th 0.566 99th 0.7042 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.4458 95th 0.6266 99th 0.7035 null >= observed 760/4000 [zero_tau0_nocoupling] true lift weak 0.000 / Opus 0.000; spread tau weak 0.00 / Opus 0.00; n_eff primary; coupled False BF law:constant observed 9.82 (log10 0.99) null log10 median 0.66 95th 7.95 99th 14.80 null >= observed 1714/4000 (null BF > 1: 0.82) BF law:capped observed 5.58 (log10 0.75) null log10 median 0.53 95th 6.40 99th 12.05 null >= observed 1759/4000 (null BF > 1: 0.82) BF law:zero observed 186.18 (log10 2.27) null log10 median -0.03 95th 0.78 99th 1.39 null >= observed 4/4000 (null BF > 1: 0.42) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median 0.11 95th 3.07 99th 5.89 null >= observed 1181/4000 (null BF > 1: 0.63) MAE constant - law observed 1.862 null median 0.174 95th 1.307 99th 2.047 null >= observed 61/4000 MAE capped - law observed 0.717 null median 0.151 95th 1.182 99th 1.898 null >= observed 581/4000 MAE zero - law observed 3.015 null median -0.032 95th 0.183 99th 0.347 null >= observed 0/4000 Opus-15 AIC constant - law observed 19.67 null median 0.005 95th 1.853 99th 3.135 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.0013 95th 0.1088 99th 0.1574 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.0001 95th 0.0835 99th 0.1147 null >= observed 0/4000 [zero_taufit_nocoupling] true lift weak 0.000 / Opus 0.000; spread tau weak 15.33 / Opus 7.08; n_eff primary; coupled False BF law:constant observed 9.82 (log10 0.99) null log10 median 0.26 95th 4.32 99th 19.30 null >= observed 906/4000 (null BF > 1: 0.82) BF law:capped observed 5.58 (log10 0.75) null log10 median 0.23 95th 3.49 99th 17.19 null >= observed 1017/4000 (null BF > 1: 0.82) BF law:zero observed 186.18 (log10 2.27) null log10 median 0.06 95th 0.96 99th 1.58 null >= observed 9/4000 (null BF > 1: 0.69) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median 0.10 95th 1.19 99th 3.33 null >= observed 767/4000 (null BF > 1: 0.73) MAE constant - law observed 1.862 null median 0.684 95th 5.445 99th 7.762 null >= observed 1130/4000 MAE capped - law observed 0.717 null median 0.607 95th 4.540 99th 7.067 null >= observed 1895/4000 MAE zero - law observed 3.015 null median -0.201 95th 0.538 99th 1.051 null >= observed 0/4000 Opus-15 AIC constant - law observed 19.67 null median 0.002 95th 1.776 99th 3.360 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean -0.0086 95th 0.3973 99th 0.5462 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.005 95th 0.2671 99th 0.3856 null >= observed 1/4000 [constant_taufit_tasks_only] true lift weak 8.120 / Opus 5.705; spread tau weak 12.93 / Opus 4.16; n_eff tasks_only; coupled True BF law:constant observed 9.82 (log10 0.99) null log10 median 0.29 95th 5.05 99th 21.29 null >= observed 1145/4000 (null BF > 1: 0.63) BF law:capped observed 5.58 (log10 0.75) null log10 median 0.12 95th 2.38 99th 18.67 null >= observed 938/4000 (null BF > 1: 0.57) BF law:zero observed 186.18 (log10 2.27) null log10 median 1.34 95th 3.68 99th 4.67 null >= observed 973/4000 (null BF > 1: 0.89) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -0.08 95th 0.93 99th 5.27 null >= observed 585/4000 (null BF > 1: 0.43) MAE constant - law observed 1.862 null median 0.525 95th 7.036 99th 10.664 null >= observed 1270/4000 MAE capped - law observed 0.717 null median 0.408 95th 2.827 99th 3.844 null >= observed 1660/4000 MAE zero - law observed 3.015 null median 1.456 95th 3.457 99th 4.268 null >= observed 380/4000 Opus-15 AIC constant - law observed 19.67 null median -2.249 95th 5.755 99th 9.699 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.3011 95th 0.6312 99th 0.7578 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.4199 95th 0.5739 99th 0.6283 null >= observed 426/4000 [common_taufit_tasks_only] true lift weak 6.386 / Opus 6.386; spread tau weak 12.93 / Opus 4.16; n_eff tasks_only; coupled True BF law:constant observed 9.82 (log10 0.99) null log10 median 0.09 95th 3.63 99th 16.48 null >= observed 814/4000 (null BF > 1: 0.54) BF law:capped observed 5.58 (log10 0.75) null log10 median 0.01 95th 2.13 99th 12.78 null >= observed 762/4000 (null BF > 1: 0.51) BF law:zero observed 186.18 (log10 2.27) null log10 median 1.03 95th 3.55 99th 4.67 null >= observed 800/4000 (null BF > 1: 0.85) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median -0.18 95th 0.71 99th 2.38 null >= observed 385/4000 (null BF > 1: 0.36) MAE constant - law observed 1.862 null median 0.084 95th 5.435 99th 8.083 null >= observed 892/4000 MAE capped - law observed 0.717 null median 0.025 95th 2.670 99th 4.183 null >= observed 1302/4000 MAE zero - law observed 3.015 null median 1.498 95th 3.618 99th 4.507 null >= observed 450/4000 Opus-15 AIC constant - law observed 19.67 null median -3.041 95th 6.033 99th 10.471 null >= observed 3/4000 k weak (fitted on null data) observed 0.3834 null mean 0.2414 95th 0.5764 99th 0.705 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.4658 95th 0.6145 99th 0.6702 null >= observed 892/4000 [zero_taufit_tasks_only] true lift weak 0.000 / Opus 0.000; spread tau weak 15.33 / Opus 7.08; n_eff tasks_only; coupled True BF law:constant observed 9.82 (log10 0.99) null log10 median 0.26 95th 3.83 99th 18.47 null >= observed 875/4000 (null BF > 1: 0.81) BF law:capped observed 5.58 (log10 0.75) null log10 median 0.22 95th 3.00 99th 13.96 null >= observed 978/4000 (null BF > 1: 0.80) BF law:zero observed 186.18 (log10 2.27) null log10 median 0.07 95th 0.99 99th 1.66 null >= observed 8/4000 (null BF > 1: 0.68) BF law:smooth cap observed 3.05 (log10 0.48) null log10 median 0.09 95th 1.06 99th 2.84 null >= observed 726/4000 (null BF > 1: 0.71) MAE constant - law observed 1.862 null median 0.663 95th 5.474 99th 7.912 null >= observed 1114/4000 MAE capped - law observed 0.717 null median 0.581 95th 4.291 99th 6.586 null >= observed 1843/4000 MAE zero - law observed 3.015 null median -0.186 95th 0.621 99th 1.201 null >= observed 0/4000 Opus-15 AIC constant - law observed 19.67 null median 0.019 95th 2.428 99th 4.552 null >= observed 0/4000 k weak (fitted on null data) observed 0.3834 null mean 0.0162 95th 0.4176 99th 0.5894 k Opus-15 (fitted on null data) observed 0.5392 null mean 0.0448 95th 0.2957 99th 0.3827 null >= observed 1/4000 ==================================================================================================== 4. WHAT COUPLING ADDS: each coupled null against the same null with se_m = 0 (share of null datasets at or beyond the observed value; k = mean Opus-15 k fitted on null data) constant_tau0 BF law:constant 0.2985 vs 0.3252; BF law:capped 0.5460 vs 0.5453; BF law:zero 0.3172 vs 0.3448; MAE constant - law 0.1432 vs 0.1138; Opus-15 AIC constant - law 0.0000 vs 0.0000; k Opus-15 null mean 0.4248 vs 0.4057; k weak null mean 0.3001 vs 0.2906 constant_taufit BF law:constant 0.2958 vs 0.2240; BF law:capped 0.2402 vs 0.1835; BF law:zero 0.2515 vs 0.1752; MAE constant - law 0.3182 vs 0.2868; Opus-15 AIC constant - law 0.0005 vs 0.0000; k Opus-15 null mean 0.4175 vs 0.3964; k weak null mean 0.3050 vs 0.2868 common_tau0 BF law:constant 0.0408 vs 0.0440; BF law:capped 0.2023 vs 0.2595; BF law:zero 0.1380 vs 0.1358; MAE constant - law 0.0090 vs 0.0050; Opus-15 AIC constant - law 0.0000 vs 0.0000; k Opus-15 null mean 0.4707 vs 0.4526; k weak null mean 0.2396 vs 0.2269 common_taufit BF law:constant 0.1905 vs 0.1527; BF law:capped 0.1797 vs 0.1445; BF law:zero 0.1795 vs 0.1285; MAE constant - law 0.2077 vs 0.1835; Opus-15 AIC constant - law 0.0005 vs 0.0000; k Opus-15 null mean 0.4651 vs 0.4458; k weak null mean 0.2419 vs 0.2249 zero_tau0 BF law:constant 0.4343 vs 0.4285; BF law:capped 0.4535 vs 0.4397; BF law:zero 0.0050 vs 0.0010; MAE constant - law 0.0225 vs 0.0152; Opus-15 AIC constant - law 0.0000 vs 0.0000; k Opus-15 null mean 0.0220 vs 0.0001; k weak null mean 0.0151 vs 0.0013 zero_taufit BF law:constant 0.2145 vs 0.2265; BF law:capped 0.2417 vs 0.2542; BF law:zero 0.0025 vs 0.0022; MAE constant - law 0.2675 vs 0.2825; Opus-15 AIC constant - law 0.0000 vs 0.0000; k Opus-15 null mean 0.0349 vs 0.0050; k weak null mean 0.0200 vs -0.0086 wrote coupling.json (692 s)