Exact Sturm count and index check for the reduced witnesses (Lck, ZAP-70 constant; no CD8)

== level 2, MM intermediates collapsed: 12 receptor states (3 free), deg_L B = 3, deg_L U = 2, deg p = 4
   minors interpolated at L = 1..4 and checked at 1/3, 7/2, 1000; equal to direct solve at L1, L3: True
   p squarefree: True ; Sturm: roots in (0, L_tot): 3 ; roots in (0, oo): 3 ; roots in bracket (99/10000, 11/125): 1
   p(L1) = p(L3) = 0 exactly; p'(L1) > 0: True ; p'(L3) > 0: True ; g(bracket) = (+, -)
   => exactly three positive steady states in this class, all nondegenerate; g' > 0 at L1 and L3, g' < 0 at the middle root: True
   L1: det(-K|_V) > 0: True ; det(-J|_S) == det(-K|_V) * g'(L) exactly: True ; g'(L1) = 831.791
   L3: det(-K|_V) > 0: True ; det(-J|_S) == det(-K|_V) * g'(L) exactly: True ; g'(L3) = 1.07198

== level 2, MM intermediates kept: 18 receptor states (3 free), deg_L B = 3, deg_L U = 2, deg p = 4
   minors interpolated at L = 1..4 and checked at 1/3, 7/2, 1000; equal to direct solve at L1, L3: True
   p squarefree: True ; Sturm: roots in (0, L_tot): 3 ; roots in (0, oo): 3 ; roots in bracket (99/10000, 11/125): 1
   p(L1) = p(L3) = 0 exactly; p'(L1) > 0: True ; p'(L3) > 0: True ; g(bracket) = (+, -)
   => exactly three positive steady states in this class, all nondegenerate; g' > 0 at L1 and L3, g' < 0 at the middle root: True
   L1: det(-K|_V) > 0: True ; det(-J|_S) == det(-K|_V) * g'(L) exactly: True ; g'(L1) = 831.617
   L3: det(-K|_V) > 0: True ; det(-J|_S) == det(-K|_V) * g'(L) exactly: True ; g'(L3) = 1.07197

== level 3, MM intermediates collapsed: 17 receptor states (4 free), deg_L B = 4, deg_L U = 3, deg p = 5
   minors interpolated at L = 1..5 and checked at 1/3, 7/2, 1000; equal to direct solve at L1, L3: True
   p squarefree: True ; Sturm: roots in (0, L_tot): 3 ; roots in (0, oo): 3 ; roots in bracket (99/10000, 11/125): 1
   p(L1) = p(L3) = 0 exactly; p'(L1) > 0: True ; p'(L3) > 0: True ; g(bracket) = (+, -)
   => exactly three positive steady states in this class, all nondegenerate; g' > 0 at L1 and L3, g' < 0 at the middle root: True
   L1: det(-K|_V) > 0: True ; det(-J|_S) == det(-K|_V) * g'(L) exactly: True ; g'(L1) = 831.823
   L3: det(-K|_V) > 0: True ; det(-J|_S) == det(-K|_V) * g'(L) exactly: True ; g'(L3) = 1.07201

== level 3, MM intermediates kept: 26 receptor states (4 free), deg_L B = 4, deg_L U = 3, deg p = 5
   minors interpolated at L = 1..5 and checked at 1/3, 7/2, 1000; equal to direct solve at L1, L3: True
   p squarefree: True ; Sturm: roots in (0, L_tot): 3 ; roots in (0, oo): 3 ; roots in bracket (99/10000, 11/125): 1
   p(L1) = p(L3) = 0 exactly; p'(L1) > 0: True ; p'(L3) > 0: True ; g(bracket) = (+, -)
   => exactly three positive steady states in this class, all nondegenerate; g' > 0 at L1 and L3, g' < 0 at the middle root: True
   L1: det(-K|_V) > 0: True ; det(-J|_S) == det(-K|_V) * g'(L) exactly: True ; g'(L1) = 831.653
   L3: det(-K|_V) > 0: True ; det(-J|_S) == det(-K|_V) * g'(L) exactly: True ; g'(L3) = 1.07201
