Listing: Listing

# contact_collapse.py output   (exact QQ arithmetic; conditional on (S-bv) through M.2)
# M.4 contact-collapse map: rank, kernel; injectivity of G does NOT imply injectivity after collapse
CHECK graph_general_table loaded (3282 lines; field indices a<=b): True
CHECK d_N = 1,4,10,20,35 (M.2): True
CHECK dim C_coh = 3321 contact variables: True
# sha256(graph_general_table.txt) = 4cd29d3c9f691340b314aecbfe7d6aef3590b9cee21dcdb486fe9fbcdd679e49
# sha256(kernel_basis.json) = fcbe2876abd2a6b410813f732356f829c970c22c3a333f7e4ec34909c0e0793b
# number of (D, parity) blocks: 40 ; max block size: 292
CHECK formal: rank-nullity: rank 3321 + ker 0 = 3321: True
# formal           dim im Collapse = 3321 ; dim ker Collapse = 0 ; nnz entries = 666507  (5.5s)
CHECK chi_plateau: rank-nullity: rank 3321 + ker 0 = 3321: True
# chi_plateau      dim im Collapse = 3321 ; dim ker Collapse = 0 ; nnz entries = 157549  (3.2s)
CHECK double_plateau: rank-nullity: rank 3299 + ker 22 = 3321: True
# double_plateau   dim im Collapse = 3299 ; dim ker Collapse = 22 ; nnz entries = 73320  (91.0s)
CHECK FORMAL: Collapse injective on C_coh (dim ker = 0): True
CHECK chi_plateau: Collapse injective: True
CHECK double_plateau: dim ker Collapse = 22: True
# NOTE: injectivity of G_formal (M.3) does not by itself imply injectivity of Collapse;
#       the formal reading happens to make Collapse injective as well (verified above).
# dim C_reg = 3150 (expected 3150)
CHECK dim C_reg = 3150: True
# formal           dim (ker Collapse cap C_reg) = 0 ; dim Collapse(C_reg) = 3150
# chi_plateau      dim (ker Collapse cap C_reg) = 0 ; dim Collapse(C_reg) = 3150
# double_plateau   dim (ker Collapse cap C_reg) = 0 ; dim Collapse(C_reg) = 3150
# wrote collapse_kernel.json collapse_kernel_certificates.txt
# === SUMMARY ===
# formal           dim im = 3321 ; dim ker = 0 ; ker_cap_C_reg = 0 ; perD (size,ker) = {0: [35, 0], 1: [160, 0], 2: [440, 0], 3: [944, 0], 4: [1742, 0]}
# chi_plateau      dim im = 3321 ; dim ker = 0 ; ker_cap_C_reg = 0 ; perD (size,ker) = {0: [35, 0], 1: [160, 0], 2: [440, 0], 3: [944, 0], 4: [1742, 0]}
# double_plateau   dim im = 3299 ; dim ker = 22 ; ker_cap_C_reg = 0 ; perD (size,ker) = {0: [35, 0], 1: [160, 0], 2: [440, 0], 3: [944, 4], 4: [1742, 18]}
# total runtime 105.4s
ALL CHECKS PASSED