This page contains information on the interval verifications for Sphere Packings IV. This was adapted from Sphere Packings IV, Appendix 1 on May 6, 1998.

%ALLOCATED:
% allocated 5/6/98: 
%5/98:{247814184, 909431001, 471064815, 812894433, 404793781, 747727191, 
%5/98: 474496219, 649551700, 74657942, 897129160,
%5/98: 760840103, 675901554, 712696695, 424011442, 140881233, 601456709, 
%5/98: 292977281, 927286061, 340409511, 727498658, 484314425, 440223030, 
%5/98: 115756648, 329882546, 427688691, 564506426, 562103670, 288224597, 
%5/98: 979916330, 749968927, 695180203, 690626704, 807023313, 590577214, 
%5/98: 949210508, 671961774, 173606284, 568664009, 645264496, 910154674,
%5/98: 877743345, 612259047, 357477295, 193776341, 898647773, 275286804, 
%5/98: 627654828, 995177961, 735892048, 53502142, 134398524, 371491817, 
%5/98: 832922998, 724796759, 431940343, 980721294, 989564937, 263355808, 
%5/98: 445132132, 806767374, 511038592, 4591018, 193728878, 2724096, 213514168, 
%5/98: 750768322, 371464244, 657011065, 953023504, 887276655,
%5/98: 246315515, 784421604, 258632246, 404164527, 163088471,
%5/98: 62532125,  370631902, 654422246, 366536370}
%5/11/98: 343330051, 49446087,
%5/12/98: 799187442,
%5/15/98: 844634710, 328845176, 233273785,  966955550.


% RETIRED
% retired 5/6/98:  refno{597997492},  refno{279477953} 
% retired 5/6/98:  refno{357223197}  refno{19971603}
% retired 5/10/98:$\dih<1.63$, if $y_6\in[2.51,3.02]$.  \refno{614013885}
% ret. 5/10/98: $\dih<1.51$, if $y_5,y_6\in[2.51,3.02]$.  \refno{734934433}
%\refno{247814184-5/11/98-A1}
%\refno{909431001-5/11/98-A1}
%\refno{471064815-5/11/98-A1}
%\refno{122573656-5/11/98-A11}


Let octavor0(Q)=0.5( vor0(Q)+ vor0(hat Q)), and octavor(Q) = 0.5( vor(Q)+ vor(hat Q)). We let taunu, tauV, tau0, and tauGamma be f- sol zeta pt, where f=nu, vor, vor0, and Gamma, respectively.

Edge lengths whose bounds are not specified are assumed to be between 2 and 2.51.