Listing: Listing

# contact_space.py output   (python 3.13.5, exact QQ arithmetic via fractions.Fraction)
# M.3 coherent contact space, graph-contact map G, kernel/image (conditional on (S-bv) through M.2)
CHECK input present: graph_general_table.txt: True
# sha256(graph_general_table.txt) = 4cd29d3c9f691340b314aecbfe7d6aef3590b9cee21dcdb486fe9fbcdd679e49
CHECK input present: kernel_basis.json: True
# sha256(kernel_basis.json) = fcbe2876abd2a6b410813f732356f829c970c22c3a333f7e4ec34909c0e0793b
CHECK graph_general_table.txt: 3282 sector-resolved nonzero lines (M.1): True
CHECK d_N = 1,4,10,20,35 (M.2, conditional on (S-bv)): True
CHECK reconstruction available for all 255 labels: True
# dim D_{<=N} = {0: 1, 1: 5, 2: 15, 3: 35, 4: 70}  ; dim C_coh = 3321  ; dim C_reg = 3150  ; raw labelled slots = 14321
CHECK FORMAL N=0: exact rank 1 equals independent mod-p rank: True
CHECK FORMAL N=1: exact rank 4 equals independent mod-p rank: True
CHECK FORMAL N=2: exact rank 10 equals independent mod-p rank: True
CHECK FORMAL N=3: exact rank 20 equals independent mod-p rank: True
CHECK FORMAL N=4: exact rank 35 equals independent mod-p rank: True
# FORMAL                     dim U_N = [1, 4, 10, 20, 35] ; dim im G = 3321 ; dim ker G = 0 ; on C_reg: dim im = 3150, dim ker = 0  (0.1s)
CHECK TIME-ONLY N=0: exact rank 1 equals independent mod-p rank: True
CHECK TIME-ONLY N=1: exact rank 4 equals independent mod-p rank: True
CHECK TIME-ONLY N=2: exact rank 10 equals independent mod-p rank: True
CHECK TIME-ONLY N=3: exact rank 20 equals independent mod-p rank: True
CHECK TIME-ONLY N=4: exact rank 35 equals independent mod-p rank: True
# TIME-ONLY                  dim U_N = [1, 4, 10, 20, 35] ; dim im G = 3321 ; dim ker G = 0 ; on C_reg: dim im = 3150, dim ker = 0  (0.1s)
CHECK BACKGROUND N=0: exact rank 1 equals independent mod-p rank: True
CHECK BACKGROUND N=1: exact rank 4 equals independent mod-p rank: True
CHECK BACKGROUND N=2: exact rank 10 equals independent mod-p rank: True
CHECK BACKGROUND N=3: exact rank 20 equals independent mod-p rank: True
CHECK BACKGROUND N=4: exact rank 10 equals independent mod-p rank: True
# BACKGROUND                 dim U_N = [1, 4, 10, 20, 10] ; dim im G = 1571 ; dim ker G = 1750 ; on C_reg: dim im = 1400, dim ker = 1750  (0.0s)
CHECK TIME+BG N=0: exact rank 1 equals independent mod-p rank: True
CHECK TIME+BG N=1: exact rank 4 equals independent mod-p rank: True
CHECK TIME+BG N=2: exact rank 10 equals independent mod-p rank: True
CHECK TIME+BG N=3: exact rank 16 equals independent mod-p rank: True
CHECK TIME+BG N=4: exact rank 10 equals independent mod-p rank: True
# TIME+BG                    dim U_N = [1, 4, 10, 16, 10] ; dim im G = 1431 ; dim ker G = 1890 ; on C_reg: dim im = 1260, dim ker = 1890  (0.0s)
CHECK PLATEAU(J_3 only, formal) N=0: exact rank 0 equals independent mod-p rank: True
CHECK PLATEAU(J_3 only, formal) N=1: exact rank 0 equals independent mod-p rank: True
CHECK PLATEAU(J_3 only, formal) N=2: exact rank 10 equals independent mod-p rank: True
CHECK PLATEAU(J_3 only, formal) N=3: exact rank 20 equals independent mod-p rank: True
CHECK PLATEAU(J_3 only, formal) N=4: exact rank 35 equals independent mod-p rank: True
# PLATEAU(J_3 only, formal)  dim U_N = [0, 0, 10, 20, 35] ; dim im G = 3300 ; dim ker G = 21 ; on C_reg: dim im = 3150, dim ker = 0  (0.0s)
CHECK C_2 only, formal N=0: exact rank 1 equals independent mod-p rank: True
CHECK C_2 only, formal N=1: exact rank 4 equals independent mod-p rank: True
CHECK C_2 only, formal N=2: exact rank 10 equals independent mod-p rank: True
CHECK C_2 only, formal N=3: exact rank 0 equals independent mod-p rank: True
CHECK C_2 only, formal N=4: exact rank 0 equals independent mod-p rank: True
# C_2 only, formal           dim U_N = [1, 4, 10, 0, 0] ; dim im G = 171 ; dim ker G = 3150 ; on C_reg: dim im = 0, dim ker = 3150  (0.0s)
CHECK M_2 only, formal N=0: exact rank 0 equals independent mod-p rank: True
CHECK M_2 only, formal N=1: exact rank 4 equals independent mod-p rank: True
CHECK M_2 only, formal N=2: exact rank 10 equals independent mod-p rank: True
CHECK M_2 only, formal N=3: exact rank 20 equals independent mod-p rank: True
CHECK M_2 only, formal N=4: exact rank 0 equals independent mod-p rank: True
# M_2 only, formal           dim U_N = [0, 4, 10, 20, 0] ; dim im G = 870 ; dim ker G = 2451 ; on C_reg: dim im = 700, dim ker = 2450  (0.0s)
CHECK specialized visible ranks are bounded by the formal ones (specialization cannot raise rank): True
CHECK N=0: S^2 direction is graph-visible (U_0 = H_4): True
CHECK coefficient monomials of different N are disjoint (grading prep order 2-s, h order 2-N+s): True
CHECK every reduced coefficient monomial has prep order + h order = 4 - N: True
CHECK N=0: annihilator of U_N has dimension d_N - dim U_N = 0: True
CHECK N=1: annihilator of U_N has dimension d_N - dim U_N = 0: True
CHECK N=2: annihilator of U_N has dimension d_N - dim U_N = 0: True
CHECK N=3: annihilator of U_N has dimension d_N - dim U_N = 0: True
CHECK N=4: annihilator of U_N has dimension d_N - dim U_N = 0: True
CHECK kernel certificate: for every annihilator vector x of U_N, sum_b x_b abar_b = 0 exactly (graph-invisible numerical direction): True
# wrote graph_contact_map.txt sha256=49b59c00dc788efcb48681f4bb711fa11350f251404977aba5d251df6018628e
# === COMPARISON: ambient prescription freedom vs graph-visible collision freedom (FORMAL) ===
#   raw labelled contact slots (XVI-L count)          : 14321
#   coherent assignments dim C_coh (M.2, (S-bv))       : 3321
#   graph-visible collision freedom dim im G (formal)  : 3321
#   graph-invisible coherent directions dim ker G      : 0
#   regression-preserving: dim C_reg 3150 -> dim im 3150, ker 0
# total runtime 0.3s
ALL CHECKS PASSED