R = 4.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
M0 <= [348.41120457649094528661630450571098660276359846610104712097176387104257138258333385947042 +/- 4.73e-87]
HEAD (i <= 16, from s0_head.log) <= [43.537789114875634000000000000000000000000000000000000000000000000000000000000000000000000 +/- 1.75e-89]
TAIL (i >  16, Cauchy at R)      <= [1.0608695005189784648314414532101655416680269416606388311955284825086977453232259603612667 +/- 4.11e-89]
S_0 = HEAD + TAIL                <= [44.598658615394612464831441453210165541668026941660638831195528482508697745323225960361267 +/- 2.73e-88]