== B12 N=3 - [copy]: status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.250004, 0.0s
  eps = 0.25000000
  tf: [0.0] at [(1, 1, 1)]
  R0 -0.25  Ra [-0.25, -0.125, -0.0]
  pair (0,1) law P+(++)=1/12 P-(++)=7/20  coef -0.250000
  pair (0,2) law P+(++)=1/12 P-(++)=7/20  coef -0.250000
  pair (1,2) law P+(++)=1/6 P-(++)=3/10  coef 0.000000
  copy (0, 1, 2) pair laws [(0, 1, '1/12'), (0, 2, '1/12'), (1, 2, '1/6')]  coef 0.125000
  rho_+: {'++-': 0.08333, '+-+': 0.08333, '+--': 0.25, '-++': 0.16667, '-+-': 0.16667, '--+': 0.16667, '---': 0.08333}
  rho_-: {'+++': 0.2, '++-': 0.15, '+-+': 0.15, '+--': 0.05, '-++': 0.1, '-+-': 0.1, '--+': 0.1, '---': 0.15}
  max R 0.25  vertices at max: ['+--', '-++', '--+']
== B12 N=4 - [copy]: status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.0833403333333333, 0.0s
  eps = 0.08333333
  tf: [0.0] at [(1, 1, 1)]
  R0 -0.25  Ra [-0.125, -0.125, -0.0, -0.125]
  pair (0,1) law P+(++)=1/12 P-(++)=7/20  coef -0.125000
  pair (0,2) law P+(++)=1/12 P-(++)=7/20  coef -0.020833
  pair (0,3) law P+(++)=1/12 P-(++)=7/20  coef -0.145833
  pair (1,2) law P+(++)=1/6 P-(++)=3/10  coef 0.062500
  pair (1,3) law P+(++)=1/6 P-(++)=3/10  coef -0.062500
  pair (2,3) law P+(++)=1/12 P-(++)=7/20  coef -0.208333
  copy (0, 1, 2) pair laws [(0, 1, '1/12'), (0, 2, '1/12'), (1, 2, '1/6')]  coef 0.125000
  rho_+: {'++--': 0.08333, '+-+-': 0.08333, '+--+': 0.08333, '+---': 0.16667, '-++-': 0.16667, '-+-+': 0.16667, '--++': 0.08333, '--+-': 0.08333, '---+': 0.08333}
  rho_-: {'++++': 0.2, '++--': 0.15, '+-++': 0.1, '+-+-': 0.05, '+--+': 0.05, '-+++': 0.05, '-++-': 0.05, '-+-+': 0.05, '-+--': 0.05, '--+-': 0.1, '---+': 0.1, '----': 0.05}
  max R 0.08333333  vertices at max: ['+++-', '+-+-', '+--+', '+---', '-++-', '-+-+', '--+-', '---+']
== B12 N=5 - [copy]: status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.05000795, 0.6s
  eps = 0.05000000
  tf: [0.0] at [(1, 1, 1)]
  R0 -0.25  Ra [-0.0625, -0.0625, -0.15625, -0.09375, -0.0]
  pair (0,1) law P+(++)=1/12 P-(++)=7/20  coef -0.012500
  pair (0,2) law P+(++)=1/12 P-(++)=7/20  coef -0.156250
  pair (0,3) law P+(++)=1/12 P-(++)=7/20  coef -0.093750
  pair (0,4) law P+(++)=1/6 P-(++)=3/10  coef 0.050000
  pair (1,2) law P+(++)=1/6 P-(++)=3/10  coef -0.106250
  pair (1,3) law P+(++)=1/6 P-(++)=3/10  coef -0.043750
  pair (1,4) law P+(++)=1/12 P-(++)=7/20  coef -0.050000
  pair (2,3) law P+(++)=1/12 P-(++)=7/20  coef -0.187500
  pair (2,4) law P+(++)=1/6 P-(++)=3/10  coef 0.050000
  pair (3,4) law P+(++)=1/6 P-(++)=3/10  coef 0.050000
  copy (0, 1, 2) pair laws [(0, 1, '1/12'), (0, 2, '1/12'), (1, 2, '1/6')]  coef 0.031250
  copy (0, 1, 3) pair laws [(0, 1, '1/12'), (0, 3, '1/12'), (1, 3, '1/6')]  coef 0.093750
  rho_+: {'++---': 0.08333, '+-+-+': 0.08333, '+--+-': 0.08333, '+---+': 0.08333, '+----': 0.08333, '-++--': 0.16667, '-+-++': 0.08333, '-+-+-': 0.08333, '--++-': 0.08333, '--+-+': 0.08333, '---++': 0.08333}
  rho_-: {'++++-': 0.15, '+++--': 0.05, '++-++': 0.05, '++--+': 0.1, '+-+++': 0.1, '+-+-+': 0.05, '+--+-': 0.05, '-++-+': 0.1, '-+-++': 0.1, '--+++': 0.05, '--++-': 0.05, '-----': 0.15}
  max R 0.05  vertices at max: ['++-++', '++-+-', '++---', '+-+-+', '+--++', '+---+', '+----', '-++--', '-+-+-', '-+---', '--+++', '--+-+', '--+--', '---++', '---+-']
== B12 N=6 - [copy]: run with the same model and penalty by an earlier variant of this script (time limit 2400 s; finished in about 4 minutes, i.e. optimal)
  tf: [np.float64(0.0)] free [(1, 1, 1)]
  R0 -0.25  Ra [np.float64(-0.06534), np.float64(-0.04545), np.float64(-0.04545), np.float64(-0.11648), np.float64(-0.00568), np.float64(-0.09659)]
  pair (0,1) law P+(++)=0.0833 P-(++)=0.3500  coef -0.03125
  pair (0,2) law P+(++)=0.0833 P-(++)=0.3500  coef -0.04545
  pair (0,3) law P+(++)=0.0833 P-(++)=0.3500  coef -0.13068
  pair (0,4) law P+(++)=0.1667 P-(++)=0.3000  coef -0.01989
  pair (0,5) law P+(++)=0.0833 P-(++)=0.3500  coef -0.05682
  pair (1,2) law P+(++)=0.1667 P-(++)=0.3000  coef 0.04545
  pair (1,3) law P+(++)=0.0833 P-(++)=0.3500  coef -0.07670
  pair (1,4) law P+(++)=0.0833 P-(++)=0.3500  coef -0.00000
  pair (2,5) law P+(++)=0.0833 P-(++)=0.3500  coef -0.09091
  pair (3,4) law P+(++)=0.1667 P-(++)=0.3000  coef -0.02557
  pair (3,5) law P+(++)=0.0833 P-(++)=0.3500  coef -0.06250
  pair (4,5) law P+(++)=0.0833 P-(++)=0.3500  coef -0.00568
  copy (0, 1, 2) placement ((0, 1, (0, 0, (Fraction(1, 12), Fraction(7, 20)))), (0, 2, (0, 0, (Fraction(1, 12), Fraction(7, 20)))), (1, 2, (0, 0, (Fraction(1, 6), Fraction(3, 10)))))  coef -0.04545
  copy (0, 1, 4) placement ((0, 1, (0, 0, (Fraction(1, 12), Fraction(7, 20)))), (0, 4, (0, 0, (Fraction(1, 6), Fraction(3, 10)))), (1, 4, (0, 0, (Fraction(1, 12), Fraction(7, 20)))))  coef 0.05398
  copy (0, 4, 5) placement ((0, 4, (0, 0, (Fraction(1, 6), Fraction(3, 10)))), (0, 5, (0, 0, (Fraction(1, 12), Fraction(7, 20)))), (4, 5, (0, 0, (Fraction(1, 12), Fraction(7, 20)))))  coef 0.03409
  copy (1, 3, 4) placement ((1, 3, (0, 0, (Fraction(1, 12), Fraction(7, 20)))), (1, 4, (0, 0, (Fraction(1, 12), Fraction(7, 20)))), (3, 4, (0, 0, (Fraction(1, 6), Fraction(3, 10)))))  coef 0.05398
  copy (3, 4, 5) placement ((3, 4, (0, 0, (Fraction(1, 6), Fraction(3, 10)))), (3, 5, (0, 0, (Fraction(1, 12), Fraction(7, 20)))), (4, 5, (0, 0, (Fraction(1, 12), Fraction(7, 20)))))  coef 0.02841
  rho_+: {'++---+': np.float64(0.0833), '+-++--': np.float64(0.0833), '+---+-': np.float64(0.1667), '+-----': np.float64(0.0833), '-+++--': np.float64(0.0833), '-++-++': np.float64(0.0833), '-+---+': np.float64(0.1667), '--+++-': np.float64(0.1667), '---+-+': np.float64(0.0833)}
  rho_-: {'++++++': np.float64(0.05), '++++--': np.float64(0.0833), '+++-++': np.float64(0.05), '+++--+': np.float64(0.0167), '++-++-': np.float64(0.0833), '++-+-+': np.float64(0.05), '++--+-': np.float64(0.0167), '+-++-+': np.float64(0.05), '+-+-++': np.float64(0.1), '+--+-+': np.float64(0.0333), '+-----': np.float64(0.0167), '-++-+-': np.float64(0.0833), '-++---': np.float64(0.0167), '-+-+++': np.float64(0.0667), '-+-+-+': np.float64(0.0167), '-+----': np.float64(0.0167), '--++++': np.float64(0.0833), '--++--': np.float64(0.0167), '---++-': np.float64(0.0167), '-----+': np.float64(0.0333), '------': np.float64(0.1)}
  max R 0.022727  #vertices at max 26

== B12 N=7 - [copy]: status 1 (Time limit reached. (HiGHS Status 13: Time limit reached)), dual bound 8.061078398221664e-06, 240.0s
  eps = 0.00000000
  tf: [0.0] at [(1, 1, 1)]
  R0 -0.25  Ra [-0.0625, -0.0625, -0.0, -0.0625, -0.0625, -0.0625, -0.0625]
  pair (0,1) law P+(++)=1/12 P-(++)=7/20  coef -0.031250
  pair (0,2) law P+(++)=1/12 P-(++)=7/20  coef -0.000000
  pair (0,3) law P+(++)=1/12 P-(++)=7/20  coef -0.031250
  pair (0,4) law P+(++)=1/12 P-(++)=7/20  coef -0.062500
  pair (1,2) law P+(++)=1/6 P-(++)=3/10  coef -0.000000
  pair (1,3) law P+(++)=1/12 P-(++)=7/20  coef -0.062500
  pair (1,5) law P+(++)=1/6 P-(++)=3/10  coef -0.000000
  pair (1,6) law P+(++)=1/12 P-(++)=7/20  coef -0.031250
  pair (2,3) law P+(++)=1/6 P-(++)=3/10  coef -0.000000
  pair (2,4) law P+(++)=1/12 P-(++)=7/20  coef -0.062500
  pair (2,5) law P+(++)=1/12 P-(++)=7/20  coef -0.062500
  pair (2,6) law P+(++)=1/12 P-(++)=7/20  coef -0.000000
  pair (3,4) law P+(++)=1/6 P-(++)=3/10  coef -0.000000
  pair (3,6) law P+(++)=1/12 P-(++)=7/20  coef -0.031250
  pair (4,5) law P+(++)=1/12 P-(++)=7/20  coef -0.062500
  pair (5,6) law P+(++)=1/12 P-(++)=7/20  coef -0.062500
  copy (0, 1, 2) pair laws [(0, 1, '1/12'), (0, 2, '1/12'), (1, 2, '1/6')]  coef 0.031250
  copy (0, 2, 3) pair laws [(0, 2, '1/12'), (0, 3, '1/12'), (2, 3, '1/6')]  coef 0.031250
  copy (1, 2, 6) pair laws [(1, 2, '1/6'), (1, 6, '1/12'), (2, 6, '1/12')]  coef 0.031250
  copy (2, 3, 6) pair laws [(2, 3, '1/6'), (2, 6, '1/12'), (3, 6, '1/12')]  coef 0.031250
  rho_+: {'++---+-': 0.08333, '+-+---+': 0.08333, '+--+-+-': 0.08333, '+---+-+': 0.08333, '+----++': 0.08333, '-++-+--': 0.08333, '-++----': 0.08333, '-+-+++-': 0.08333, '-+--+-+': 0.08333, '--++-+-': 0.08333, '--++---': 0.08333, '---++-+': 0.08333}
  rho_-: {'+++++++': 0.05, '+++++--': 0.025, '++++-+-': 0.025, '+++-+++': 0.05, '+++-+--': 0.05, '++-++++': 0.075, '++-++-+': 0.075, '+-++--+': 0.075, '+-++---': 0.025, '+-+--+-': 0.05, '+---+-+': 0.025, '+-----+': 0.025, '-++-+++': 0.1, '-+-+---': 0.1, '--+++++': 0.075, '--++---': 0.025, '----+--': 0.025, '-----+-': 0.125}
  max R 0.0  vertices at max: ['+++--+-', '+++---+', '+++----', '++---+-', '+-++-+-', '+-++--+', '+-++---', '+-+--+-', '+-+---+', '+-+----', '+--+-+-', '+---+-+', '+----++', '+----+-', '+-----+', '-++-+-+', '-++-+--', '-++--+-', '-++---+', '-++----', '-+-+++-', '-+-++--', '-+-+-+-', '-+--++-', '-+--+-+', '-+--+--', '-+---+-', '--+++-+', '--+++--', '--++-+-', '--++--+', '--++---', '--+-+-+', '--+-+--', '--+--+-', '--+---+', '--+----', '---+++-', '---++-+', '---++--', '---+-+-', '----+-+']

== rerun with the valid coefficient cap (eps <= 1/4, cap 1/4 + |mu| = 1/2):
== B12 N=3 - [copy] (coefficient cap 0.5, eps <= 0.25): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.250004, 0.0s
  eps = 0.25000000
  tf: [0.0] at [(1, 1, 1)]
  R0 -0.25  Ra [-0.25, -0.125, 0.0]
  pair (0,1) law P+(++)=1/12 P-(++)=7/20  coef -0.361111
  pair (0,2) law P+(++)=1/12 P-(++)=7/20  coef -0.138889
  pair (1,2) law P+(++)=1/6 P-(++)=3/10  coef 0.000000
  copy (0, 1, 2) pair laws [(0, 1, '1/12'), (0, 2, '1/12'), (1, 2, '1/6')]  coef 0.125000
  rho_+: {'++-': 0.08333, '+-+': 0.08333, '+--': 0.25, '-++': 0.16667, '-+-': 0.16667, '--+': 0.16667, '---': 0.08333}
  rho_-: {'+++': 0.2, '++-': 0.15, '+-+': 0.15, '+--': 0.05, '-++': 0.1, '-+-': 0.1, '--+': 0.1, '---': 0.15}
  max R 0.25  vertices at max: ['+--', '-++']
== B12 N=4 - [copy] (coefficient cap 0.5, eps <= 0.25): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.08333983333333334, 0.1s
  eps = 0.08333333
  tf: [0.0] at [(1, 1, 1)]
  R0 -0.25  Ra [-0.1875, -0.1875, -0.09375, 0.09375]
  pair (0,1) law P+(++)=1/12 P-(++)=7/20  coef -0.187500
  pair (0,2) law P+(++)=1/12 P-(++)=7/20  coef -0.177083
  pair (0,3) law P+(++)=1/12 P-(++)=7/20  coef 0.010417
  pair (1,2) law P+(++)=1/6 P-(++)=3/10  coef -0.093750
  pair (1,3) law P+(++)=1/6 P-(++)=3/10  coef 0.093750
  pair (2,3) law P+(++)=1/12 P-(++)=7/20  coef -0.145833
  copy (0, 1, 2) pair laws [(0, 1, '1/12'), (0, 2, '1/12'), (1, 2, '1/6')]  coef -0.031250
  copy (0, 1, 3) pair laws [(0, 1, '1/12'), (0, 3, '1/12'), (1, 3, '1/6')]  coef 0.156250
  rho_+: {'++--': 0.08333, '+-+-': 0.08333, '+--+': 0.08333, '+---': 0.16667, '-++-': 0.16667, '-+-+': 0.16667, '--++': 0.08333, '--+-': 0.08333, '---+': 0.08333}
  rho_-: {'++++': 0.2, '++--': 0.15, '+-++': 0.15, '+---': 0.05, '-++-': 0.1, '-+-+': 0.1, '--+-': 0.1, '---+': 0.1, '----': 0.05}
  max R 0.08333333  vertices at max: ['++-+', '+-+-', '+--+', '+---', '-++-', '-+-+', '--++', '--+-', '---+']
== B12 N=5 - [copy] (coefficient cap 0.5, eps <= 0.25): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.05000889999999998, 1.0s
  eps = 0.05000000
  tf: [0.0] at [(1, 1, 1)]
  R0 -0.25  Ra [-0.0625, -0.16875, -0.0125, -0.18125, 0.05]
  pair (0,1) law P+(++)=1/12 P-(++)=7/20  coef -0.118750
  pair (0,2) law P+(++)=1/12 P-(++)=7/20  coef -0.012500
  pair (0,3) law P+(++)=1/12 P-(++)=7/20  coef -0.131250
  pair (0,4) law P+(++)=1/6 P-(++)=3/10  coef 0.050000
  pair (1,2) law P+(++)=1/6 P-(++)=3/10  coef -0.068750
  pair (1,3) law P+(++)=1/12 P-(++)=7/20  coef -0.237500
  pair (1,4) law P+(++)=1/6 P-(++)=3/10  coef 0.050000
  pair (2,3) law P+(++)=1/6 P-(++)=3/10  coef -0.081250
  pair (2,4) law P+(++)=1/6 P-(++)=3/10  coef -0.000000
  pair (3,4) law P+(++)=1/6 P-(++)=3/10  coef 0.050000
  copy (0, 1, 2) pair laws [(0, 1, '1/12'), (0, 2, '1/12'), (1, 2, '1/6')]  coef 0.068750
  copy (0, 2, 3) pair laws [(0, 2, '1/12'), (0, 3, '1/12'), (2, 3, '1/6')]  coef 0.056250
  rho_+: {'++--+': 0.08333, '+-+-+': 0.08333, '+--+-': 0.08333, '+----': 0.16667, '-++--': 0.16667, '-+-+-': 0.08333, '-+--+': 0.08333, '--+++': 0.08333, '--++-': 0.08333, '---++': 0.08333}
  rho_-: {'+++++': 0.0875, '+++--': 0.1125, '++-++': 0.125, '++-+-': 0.025, '+-++-': 0.1125, '+-+-+': 0.0375, '+---+': 0.05, '-++++': 0.0875, '-++--': 0.0125, '-+-+-': 0.025, '-+---': 0.075, '--++-': 0.0125, '--+-+': 0.0875, '---+-': 0.075, '----+': 0.075}
  max R 0.05  vertices at max: ['+++-+', '++--+', '+-+-+', '+-+--', '+--++', '+---+', '+----', '-++-+', '-++--', '-+--+', '-+---', '--+++', '--++-', '--+--', '---++', '---+-']
== B12 N=6 - [copy] (coefficient cap 0.5, eps <= 0.25): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.02274204336124402, 73.8s
  eps = 0.02272727
  tf: [0.0] at [(1, 1, 1)]
  R0 -0.25  Ra [-0.065341, -0.045455, -0.045455, -0.116477, -0.096591, -0.005682]
  pair (0,1) law P+(++)=1/12 P-(++)=7/20  coef -0.045455
  pair (0,2) law P+(++)=1/12 P-(++)=7/20  coef -0.011364
  pair (0,3) law P+(++)=1/12 P-(++)=7/20  coef -0.130682
  pair (0,4) law P+(++)=1/12 P-(++)=7/20  coef -0.076705
  pair (0,5) law P+(++)=1/6 P-(++)=3/10  coef -0.019886
  pair (1,2) law P+(++)=1/6 P-(++)=3/10  coef 0.045455
  pair (1,4) law P+(++)=1/12 P-(++)=7/20  coef -0.090909
  pair (2,3) law P+(++)=1/12 P-(++)=7/20  coef -0.056818
  pair (2,5) law P+(++)=1/12 P-(++)=7/20  coef -0.000000
  pair (3,4) law P+(++)=1/12 P-(++)=7/20  coef -0.082386
  pair (3,5) law P+(++)=1/6 P-(++)=3/10  coef -0.025568
  pair (4,5) law P+(++)=1/12 P-(++)=7/20  coef -0.005682
  copy (0, 1, 2) pair laws [(0, 1, '1/12'), (0, 2, '1/12'), (1, 2, '1/6')]  coef -0.045455
  copy (0, 2, 5) pair laws [(0, 2, '1/12'), (0, 5, '1/6'), (2, 5, '1/12')]  coef 0.034091
  copy (0, 4, 5) pair laws [(0, 4, '1/12'), (0, 5, '1/6'), (4, 5, '1/12')]  coef 0.053977
  copy (2, 3, 5) pair laws [(2, 3, '1/12'), (2, 5, '1/12'), (3, 5, '1/6')]  coef 0.034091
  copy (3, 4, 5) pair laws [(3, 4, '1/12'), (3, 5, '1/6'), (4, 5, '1/12')]  coef 0.048295
  rho_+: {'++----': 0.08333, '+-+-+-': 0.08333, '+--+--': 0.08333, '+----+': 0.16667, '-+++--': 0.08333, '-++-+-': 0.08333, '-+-+-+': 0.16667, '--+-++': 0.08333, '--+-+-': 0.08333, '---++-': 0.08333}
  rho_-: {'+++++-': 0.05, '+++-++': 0.075, '+++--+': 0.075, '++-++-': 0.1, '++--++': 0.05, '+-++++': 0.05, '+-++--': 0.1, '+--+++': 0.025, '+--+-+': 0.025, '-+++++': 0.075, '-+++-+': 0.025, '-+----': 0.1, '--++++': 0.05, '--+---': 0.05, '---+-+': 0.05, '----++': 0.025, '----+-': 0.05, '-----+': 0.025}
  max R 0.02272727  vertices at max: ['+++--+', '+++---', '++-+--', '++---+', '++----', '+-+-++', '+-+-+-', '+-+--+', '+-+---', '+--+--', '+---++', '+---+-', '+----+', '+-----', '-+++-+', '-+++--', '-++-+-', '-++--+', '-+-+-+', '-+-+--', '--+-+-', '---++-', '---+-+', '---+--', '----++', '----+-']
