FILTRATION (17 simplices): 4 1 0 14 3 13 01 2 23 02 04 12 24 124 024 123 012

step  simplex   boundary                 reduction (add earlier reduced columns until low is new)      result
  1   4         {}                                                                                      R=0: positive
  2   1         {}                                                                                      R=0: positive
  3   0         {}                                                                                      R=0: positive
  4   14        {4,1}                                                                                   low=1: PAIR (1,14)
  5   3         {}                                                                                      R=0: positive
  6   13        {1,3}                                                                                   low=3: PAIR (3,13)
  7   01        {1,0}                                                                                   low=0: PAIR (0,01)
  8   2         {}                                                                                      R=0: positive
  9   23        {3,2}                                                                                   low=2: PAIR (2,23)
 10   02        {0,2}                   +R(23)={3,2} -> {0,3} +R(13)={1,3} -> {1,0} +R(01)={1,0} -> {}  R=0: positive
 11   04        {4,0}                   +R(01)={1,0} -> {4,1} +R(14)={4,1} -> {}                        R=0: positive
 12   12        {1,2}                   +R(23)={3,2} -> {1,3} +R(13)={1,3} -> {}                        R=0: positive
 13   24        {4,2}                   +R(23)={3,2} -> {4,3} +R(13)={1,3} -> {4,1} +R(14)={4,1} -> {}  R=0: positive
 14   124       {14,12,24}                                                                              low=24: PAIR (24,124)
 15   024       {02,04,24}              +R(124)={14,12,24} -> {14,02,04,12}                             low=12: PAIR (12,024)
 16   123       {13,23,12}              +R(024)={14,02,04,12} -> {14,13,23,02,04}                       low=04: PAIR (04,123)
 17   012       {01,02,12}              +R(024)={14,02,04,12} -> {14,01,04} +R(123)={14,13,23,02,04} -> {13,01,23,02}  low=02: PAIR (02,012)

P (reduction = rank formula): (1,14) (3,13) (0,01) (2,23) (24,124) (12,024) (04,123) (02,012)
V_P (face pairs): (1,14) (3,13) (0,01) (2,23) (24,124) (02,012)
non-incident pairs: (12,024) (04,123)
essential: ['4']
closed V-path in V_P: None  => V_P is a gradient (acyclic)

critical cells of V_P (orig order): ['4', '04', '12', '024', '123']
   Morse boundary of 4    = []
   Morse boundary of 04   = []
   Morse boundary of 12   = []
   Morse boundary of 024  = ['04']
   Morse boundary of 123  = ['12']
column reduction of the Morse boundary in the ORIGINAL order gives pairs: [('04', '024'), ('12', '123')]
non-incident pairs of P                                          : [('04', '123'), ('12', '024')]

C3a (V_P-pairs consecutive) complete search: NONE (nodes 122)
C3b (any f, any tie-breaking) complete search: NONE (nodes 2907)
