proposition,case,quantity,theory,simulation,rel_error
P1-P2,"single model, phi=0",tau,0.9589566551591868,0.9588458450583444,0.00011555277315851961
P1-P2,"single model, phi=0",lam,0.019179133103183737,0.019175752481317396,0.0001762656241109893
P1-P2,"single model, phi=0",mse,0.04104334484081318,0.04129126465884099,0.006040438930827145
P1-P2,"single model, phi=0",rhobar,0.3787878787878788,0.37947533265704547,0.0018148782146000552
P1-P2,"single model, phi=0",sync,0.6236590070768526,0.6237815836734695,0.0001965442577208661
P1-P2,"single model, phi=0.1",tau,0.9516558812333461,0.9516118476031707,4.6270538588263265e-05
P1-P2,"single model, phi=0.1",lam,0.01903311762466692,0.019018044989802807,0.0007919162357605526
P1-P2,"single model, phi=0.1",mse,0.0483441187666539,0.04828641424547546,0.001193620292407563
P1-P2,"single model, phi=0.1",rhobar,0.3818800247371676,0.3817584348587759,0.00031839811070336966
P1-P2,"single model, phi=0.1",sync,0.6248831487706711,0.6249644571428571,0.00013011772256295257
P1-P2,"single model, phi=0.2",tau,0.9269558769002596,0.926803288755423,0.00016461209064977988
P1-P2,"single model, phi=0.2",lam,0.018539117538005193,0.01853558630569371,0.000190474670881426
P1-P2,"single model, phi=0.2",mse,0.0730441230997404,0.07321495387982196,0.0023387340806090497
P1-P2,"single model, phi=0.2",rhobar,0.39270253555967843,0.3927190039434333,4.1936026034011325e-05
P1-P2,"single model, phi=0.2",sync,0.6291676446990355,0.6290899428571428,0.0001234994242748715
P1-P2,"single model, phi=0.5",tau,0.7795447458684129,0.7814543864299311,0.0024496869123155607
P1-P2,"single model, phi=0.5",lam,0.015590894917368259,0.015603423881791543,0.000803607778109422
P1-P2,"single model, phi=0.5",mse,0.22045525413158706,0.21987004006908134,0.00265457071917377
P1-P2,"single model, phi=0.5",rhobar,0.471552257266543,0.47343561787020266,0.003993959470318295
P1-P2,"single model, phi=0.5",sync,0.6603832578914052,0.6608069224489797,0.0006415434560337463
P1-P2,"single model, phi=1",tau,0.49436424757761516,0.49184955889597654,0.005086712265218604
P1-P2,"single model, phi=1",lam,0.009887284951552304,0.009859406617159425,0.0028196147404957062
P1-P2,"single model, phi=1",mse,0.5056357524223849,0.5068518891714339,0.002405163683981475
P1-P2,"single model, phi=1",rhobar,0.7575757575757576,0.7571975042536527,0.000499294385178386
P1-P2,"single model, phi=1",sync,0.773616364569609,0.7735689387755101,6.130402130941514e-05
P1(i),tau strictly decreasing over phi grid (1=yes),monotone,1.0,1.0,0.0
P1(i),Omega(phi=1/N) / Omega(phi=0),ratio,1.0,1.0,0.0
P1(ii),"N->inf limit, phi=0.2",tau_inf,0.9615384615384615,0.9615383284021541,1.3846175960452457e-07
P1(ii),"bound tau(N=50)<=tau_inf, phi=0.2 (1=yes)",bound,1.0,1.0,0.0
P1(ii),"N->inf limit, phi=0.5",tau_inf,0.8,0.7999999270398466,9.120019184294392e-08
P1(ii),"bound tau(N=50)<=tau_inf, phi=0.5 (1=yes)",bound,1.0,1.0,0.0
P1(iii),"phi=0, N=1e7",tau->1,1.0,0.9999998359997768,1.640002231795279e-07
P2(ii),phi=0.5,rho_same,0.7575757575757576,0.7570963864431715,0.0006327698950136717
P2(ii),phi=0.5,rho_cross,0.3787878787878788,0.3779700431514435,0.0021590860801891454
P2(iv),"phi=0.5, same-model pair",S(rho1)=1/2+asin(rho1)/pi,0.773616364569609,0.7733414666666667,0.00035534137530203864
P2 placebo,sigma_eta=0: Omega(phi=1)/Omega(phi=0),ratio,1.0,1.0,0.0
P3,"Phi=1, G=1 (50)",tau,0.49436424757761516,0.49341141461729443,0.0019273905121367655
P3,"Phi=1, G=1 (50)",rhobar,0.7575757575757576,0.7569853104346328,0.0007793902262846997
P3,"Phi=1, G=1 (50)",sync,0.773616364569609,0.7736320367346939,2.025831639902203e-05
P3,"Phi=1, G=2 uniform (25,25)",tau,0.6566850538481743,0.6574905050550102,0.0012265410977696156
P3,"Phi=1, G=2 uniform (25,25)",rhobar,0.5643166357452072,0.5660294353951645,0.0030351748317599446
P3,"Phi=1, G=2 uniform (25,25)",sync,0.6971075087059577,0.6976120734693878,0.0007237976311095928
P3,"Phi=1, G=5 uniform (10x5)",tau,0.8177952240758913,0.8172375337609343,0.0006819437171294251
P3,"Phi=1, G=5 uniform (10x5)",rhobar,0.4483611626468769,0.44833526158669923,5.776829559631221e-05
P3,"Phi=1, G=5 uniform (10x5)",sync,0.6512021951877671,0.6512468040816326,6.85023702240756e-05
P3,"Phi=1, G=3 skewed (30,10,10)",tau,0.6836204539239814,0.6831971941831166,0.000619144348936982
P3,"Phi=1, G=3 skewed (30,10,10)",rhobar,0.5411255411255411,0.5400367440856554,0.0020120969297088404
P3,"Phi=1, G=3 skewed (30,10,10)",sync,0.6879264460023196,0.6872304367346939,0.0010117495433855585
P3,"Phi=0.6, G=1 (30)",tau,0.719010641357492,0.7188837757769287,0.00017644464944743162
P3,"Phi=0.6, G=1 (30)",rhobar,0.5132962275819418,0.513237234068623,0.00011493073618862985
P3,"Phi=0.6, G=1 (30)",sync,0.6769091707579539,0.6769316775510205,3.324935462373573e-05
P3,"Phi=0.6, G=2 uniform (15,15)",tau,0.8259002312520647,0.8253527513594462,0.0006628886539824756
P3,"Phi=0.6, G=2 uniform (15,15)",rhobar,0.44372294372294374,0.44365069827898973,0.0001628165614963565
P3,"Phi=0.6, G=2 uniform (15,15)",sync,0.6493659826470395,0.6495021346938776,0.00020966920115393528
P3,"Phi=0.6, G=3 uniform (10,10,10)",tau,0.8689607229753215,0.8685960391342109,0.00041967816435001736
P3,"Phi=0.6, G=3 uniform (10,10,10)",rhobar,0.4205318491032777,0.4195118784420024,0.002425430234238455
P3,"Phi=0.6, G=3 uniform (10,10,10)",sync,0.6401849199434013,0.6396935102040816,0.0007676059276172269
P3(iii),simulated tau decreasing in H within each Phi (1=yes),ordering,1.0,1.0,0.0
P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=1, G=1 (50) (1=yes)",bounds,1.0,1.0,0.0
P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=1, G=2 uniform (25,25) (1=yes)",bounds,1.0,1.0,0.0
P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=1, G=5 uniform (10x5) (1=yes)",bounds,1.0,1.0,0.0
P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=1, G=3 skewed (30,10,10) (1=yes)",bounds,1.0,1.0,0.0
P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=0.6, G=1 (30) (1=yes)",bounds,1.0,1.0,0.0
P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=0.6, G=2 uniform (15,15) (1=yes)",bounds,1.0,1.0,0.0
P3(ii),"Phi^2/G <= H <= Phi^2 for Phi=0.6, G=3 uniform (10,10,10) (1=yes)",bounds,1.0,1.0,0.0
P4(i),lambda*gamma=0.3,variance amplification 1/(1-lg)^2,2.0408163265306127,2.040816326530612,4.3520742565306126e-16
P4(iii),lambda*gamma=0.3,Var(P1-v)=sv^2[(1-tau)+tau(kappa-1)^2],0.24330132497937995,0.24370288120040037,0.0016504481471872538
P4(i),lambda*gamma=0.3,max|dP - kappa*lam*Y| (abs),0.0,8.881784197001252e-16,8.881784197001252e-16
P4(i),lambda*gamma=0.6,variance amplification 1/(1-lg)^2,6.249999999999999,6.249999999999997,2.8421709430404013e-16
P4(iii),lambda*gamma=0.6,Var(P1-v)=sv^2[(1-tau)+tau(kappa-1)^2],2.1586948461253246,2.160366856281589,0.00077454678657593
P4(i),lambda*gamma=0.6,max|dP - kappa*lam*Y| (abs),0.0,3.552713678800501e-15,3.552713678800501e-15
P4(ii),lambda*gamma=1.0: |dP| after 60 rounds >= 50 * |lam*Y| (1=yes),divergence,1.0,1.0,0.0
P4(ii),lambda*gamma=1.2: |dP| after 60 rounds >= 50 * |lam*Y| (1=yes),divergence,1.0,1.0,0.0
P5(ii),"a=0.60, b=0.0, dP0=-1.0",fixed point (dP0+lam*b/m)/(1-a),-2.5,-2.5,0.0
P5(ii),"a=0.60, b=5.0, dP0=-1.0",fixed point (dP0+lam*b/m)/(1-a),-2.25,-2.25,0.0
P5(ii),"a=0.60, b=0",multiplier 1/(1-a),2.5,2.5,0.0
P5(i),"a=0.60, b=5, dP0=-0.1 (inside buffer)",dP = dP0,-0.1,-0.1,0.0
P5(iii),a=1.00: cascade below -1e3 (1=yes),no finite fixed point,1.0,1.0,0.0
P5(iii),a=1.20: cascade below -1e3 (1=yes),no finite fixed point,1.0,1.0,0.0
P5(iv),phi_L=0,sd(X_net),10.788883167408942,10.758877785651544,0.00278113881592846
P5(iv),phi_L=0,E|X| = sigX*sqrt(2/pi),8.60828330758151,8.575270770976026,0.0038349732955942407
P5(iv),"phi_L=0, threshold m/lambda=10.789",P(X>=m/lambda)=2*Phibar,0.31731050786291415,0.31466,0.008353041570433076
P5(iv),phi_L=0.5,sd(X_net),11.679041056525145,11.63964211855805,0.0033734737104192366
P5(iv),phi_L=0.5,E|X| = sigX*sqrt(2/pi),9.318526543984198,9.282062585089383,0.003913060581273512
P5(iv),"phi_L=0.5, threshold m/lambda=10.789",P(X>=m/lambda)=2*Phibar,0.35560003994636147,0.352595,0.008450617572525456
P5(iv),phi_L=1,sd(X_net),14.366627996854378,14.356194803386284,0.0007262103167408725
P5(iv),phi_L=1,E|X| = sigX*sqrt(2/pi),11.462910669488306,11.450867751700944,0.001050598590061189
P5(iv),"phi_L=1, threshold m/lambda=10.789",P(X>=m/lambda)=2*Phibar,0.45267169342522484,0.4527,6.253223955967488e-05