# part B: sharpness family of (ii) 2026-10-17 06:59
{'d': 1, 'n': 2, 'L': 1, 'N': 2, 'graph': 'P2^1', 'TP_brute': 2, 'TP_formula_2hyp': 2, 'TP_far_brute': 2, 'TS': 2, 'TS_lower_bound_N_minus_1_L': 1, 'TS_to_far_corner': 1, 'TP_plus_N': 4, 'bound_2d_plus_1_n_d': 6, 'TS_plus_N': 4, 'bound_n_2d_minus_1': 2, 'ineq_TP': True, 'ineq_TS': True, 'box_path_length_2d_n1_L': 2}
#   (1,2) took 0.0 s
{'d': 1, 'n': 5, 'L': 1, 'N': 5, 'graph': 'P5^1', 'TP_brute': 8, 'TP_formula_2hyp': 8, 'TP_far_brute': 8, 'TS': 8, 'TS_lower_bound_N_minus_1_L': 4, 'TS_to_far_corner': 4, 'TP_plus_N': 13, 'bound_2d_plus_1_n_d': 15, 'TS_plus_N': 13, 'bound_n_2d_minus_1': 5, 'ineq_TP': True, 'ineq_TS': True, 'box_path_length_2d_n1_L': 8}
#   (1,5) took 0.0 s
{'d': 2, 'n': 2, 'L': 2, 'N': 4, 'graph': 'P3^2', 'TP_brute': 8, 'TP_formula_2hyp': 8, 'TP_far_brute': 8, 'TS': 8, 'TS_lower_bound_N_minus_1_L': 6, 'TS_to_far_corner': 8, 'TP_plus_N': 12, 'bound_2d_plus_1_n_d': 20, 'TS_plus_N': 12, 'bound_n_2d_minus_1': 8, 'ineq_TP': True, 'ineq_TS': True, 'box_path_length_2d_n1_L': 8}
#   (2,2) took 0.0 s
{'d': 2, 'n': 3, 'L': 3, 'N': 9, 'graph': 'P7^2', 'TP_brute': 24, 'TP_formula_2hyp': 24, 'TP_far_brute': 24, 'TS': 30, 'TS_lower_bound_N_minus_1_L': 24, 'TS_to_far_corner': 24, 'TP_plus_N': 33, 'bound_2d_plus_1_n_d': 45, 'TS_plus_N': 39, 'bound_n_2d_minus_1': 27, 'ineq_TP': True, 'ineq_TS': True, 'box_path_length_2d_n1_L': 24}
#   (2,3) took 1.0 s
{'d': 3, 'n': 2, 'L': 4, 'N': 8, 'graph': 'P5^3', 'TP_brute': 24, 'TP_formula_2hyp': 24, 'TP_far_brute': 24, 'TS': 32, 'TS_lower_bound_N_minus_1_L': 28, 'TS_to_far_corner': 28, 'TP_plus_N': 32, 'bound_2d_plus_1_n_d': 56, 'TS_plus_N': 40, 'bound_n_2d_minus_1': 32, 'ineq_TP': True, 'ineq_TS': True, 'box_path_length_2d_n1_L': 24}
#   (3,2) took 52.1 s
{'d': 2, 'n': 4, 'L': 4, 'N': 16, 'graph': 'P13^2', 'TP_brute': None, 'TP_formula_2hyp': 48, 'TP_far_brute': None, 'TS': 64, 'TS_lower_bound_N_minus_1_L': 60, 'TS_to_far_corner': 64, 'TP_plus_N': 64, 'bound_2d_plus_1_n_d': 80, 'TS_plus_N': 80, 'bound_n_2d_minus_1': 64, 'ineq_TP': True, 'ineq_TS': True, 'box_path_length_2d_n1_L': 48}
#   (2,4) took 1.1 s
# negative control: wrong spacing L' = n^(d-2) for d = 2 (L' = 1): TS-inequality must fail
{'d': 2, 'n': 3, 'L': 1, 'N': 9, 'graph': 'P3^2', 'TP_brute': None, 'TP_formula_2hyp': 8, 'TP_far_brute': None, 'TS': 10, 'TS_lower_bound_N_minus_1_L': 8, 'TS_to_far_corner': 8, 'TP_plus_N': 17, 'bound_2d_plus_1_n_d': 45, 'TS_plus_N': 19, 'bound_n_2d_minus_1': 27, 'ineq_TP': True, 'ineq_TS': False, 'box_path_length_2d_n1_L': 8}
NC_B n=3: TS+N = 19 vs n^(2d-1) = 27: inequality holds? False (expected False)
{'d': 2, 'n': 4, 'L': 1, 'N': 16, 'graph': 'P4^2', 'TP_brute': None, 'TP_formula_2hyp': 12, 'TP_far_brute': None, 'TS': 16, 'TS_lower_bound_N_minus_1_L': 15, 'TS_to_far_corner': 16, 'TP_plus_N': 28, 'bound_2d_plus_1_n_d': 80, 'TS_plus_N': 32, 'bound_n_2d_minus_1': 64, 'ineq_TP': True, 'ineq_TS': False, 'box_path_length_2d_n1_L': 12}
NC_B n=4: TS+N = 32 vs n^(2d-1) = 64: inequality holds? False (expected False)
# done in 55.3 s
