Listing: Listing

# graph_general.py output   (python 3.13.5, sympy 1.14.0, exact QQ arithmetic via fractions.Fraction)
# M.1 GENERAL-h assembly of the XVI-L complete-source two-edge graph (independent h-jets)
CHECK frozen input present: XVI-L-artifacts/source_full_table.txt: True
# sha256(XVI-L-artifacts/source_full_table.txt) = e13ce0ae29c769ac3b154b338a7dba2eaa75c2f12fa3427c93bdbe1cfb08430f
CHECK frozen input present: XVI-K-artifacts/hessian_full_out.txt: True
# sha256(XVI-K-artifacts/hessian_full_out.txt) = ce840f99f6df6ba31f6d415d78ec050a5ba09bb0c3153192d94c829f585ce490
CHECK frozen input present: XVI-L-artifacts/two_edge_coeff_table.txt: True
# sha256(XVI-L-artifacts/two_edge_coeff_table.txt) = cf53538133e87da76fa126e884223bab2871ac3a177f740005f66df4d3e0b1c7
CHECK frozen input present: XVI-L-artifacts/xvi_common.py: True
# sha256(XVI-L-artifacts/xvi_common.py) = 5b7b0c483a31489548efc901e3388afae7a86efc376073ab25416b34367b6f3d
CHECK xvi_common.py is byte-identical to XVI-L-artifacts/xvi_common.py: True
CHECK P_A table has 5056 entries (XVI-L L.1): True
CHECK source placements 1/8/36 for C_2/M_2/J_3: True
CHECK P_C2 uses only sigma 2-jet symbols: True
CHECK P_M2 uses only sigma 1-jet symbols: True
CHECK P_J3 uses only sigma: True
CHECK L coefficient count 2988 (XVI-K): True
CHECK slot symmetry L_ij^{pq} = L_ji^{qp} (entrywise, symbolic): True
CHECK each L^{pq}_{ij} is linear in h-jets of order exactly 2-|p|-|q| (XVI-K prop:hess(1)): True
# distinct residual-metric jet symbols occurring in L: 122
CHECK 45 ordered vertex placements (symbolic L): True
# T_i^r = (-P B^i)^r ; nnz = 22/100
# === GENERAL-h ASSEMBLY (all sectors) ===
# sector C_2 assembled in 0.1s; ordered nonzero (placement,mn) contributions 450
# sector M_2 assembled in 0.5s; ordered nonzero (placement,mn) contributions 3600
# sector J_3 assembled in 0.5s; ordered nonzero (placement,mn) contributions 10644
# assembly wall time 1.1s
CHECK edge interchange: ordered contribution (A;a,b;p,q) equals (A;b,a;q,p) for EVERY ordered placement with distinct swap (exhaustive over all enumerated placements: 1000 unordered pairs): True
CHECK Lambda_adm has 255 labels (XVI-L L.3): True
CHECK admissible per sector 25/84/250 (XVI-L): True
CHECK every monomial is exactly (one sigma-jet symbol) x (one h-jet symbol): bilinear in prep jet and residual-metric jet: True
CHECK sector grading: prep-jet order = 2-s, h-jet order = 2-v, N = s+v (s=0,1,2 for C2,M2,J3): True
CHECK no unintended generators (only sector prep symbols and XVI-K h-jet symbols): True
CHECK all coefficients exact rationals: True
CHECK output tensor stored as symmetric (mu<=nu) components (P_A symmetric in (mu,nu), XVI-L L.1 (C3)): True
CHECK C_2 formal support lies in its admissible block: True
CHECK M_2 formal support lies in its admissible block: True
CHECK J_3 formal support lies in its admissible block: True
CHECK XVI-L two_edge_coeff_table.txt parsed: 1065 nonzero entries: True
CHECK general-h table specialized to h=(w^1)^2 eta has exactly 1065 nonzero (A,lambda,mn) entries: True
CHECK specialized nonzero key set equals XVI-L key set (sector, label, component): True
CHECK EXACT SPECIALIZATION: every grouped coefficient equals the XVI-L background coefficient (all 1065 entries, coefficientwise in prep jet and w^1): True
CHECK background support recomputed: C2 25, M2 84, J3 202, union 235 (XVI-L): True
# === SUPPORT DISTINCTIONS ===
# C_2: |Lambda_adm|=25 {0: 1, 1: 4, 2: 20} ; |Lambda_graph^formal|=25 {0: 1, 1: 4, 2: 20} ; |Lambda_graph^background|=25 {0: 1, 1: 4, 2: 20}
# M_2: |Lambda_adm|=84 {1: 4, 2: 20, 3: 60} ; |Lambda_graph^formal|=84 {1: 4, 2: 20, 3: 60} ; |Lambda_graph^background|=84 {1: 4, 2: 20, 3: 60}
# J_3: |Lambda_adm|=250 {2: 20, 3: 60, 4: 170} ; |Lambda_graph^formal|=250 {2: 20, 3: 60, 4: 170} ; |Lambda_graph^background|=202 {2: 20, 3: 32, 4: 150}
# complete: |Lambda_adm|=255 {0: 1, 1: 4, 2: 20, 3: 60, 4: 170} ; |Lambda_graph^formal|=255 {0: 1, 1: 4, 2: 20, 3: 60, 4: 170} ; |Lambda_graph^background|=235 {0: 1, 1: 4, 2: 20, 3: 60, 4: 150}
CHECK Lambda_graph^background subset Lambda_graph^formal subset Lambda_adm: True
# labels in Lambda_adm but NOT in Lambda_graph^formal (0): 
# labels in Lambda_graph^formal but vanishing on the XVI-L background (20): {(), 0123} {3, 012} {33, 12} {33, 02} {33, 01} {2, 013} {23, 11} {23, 01} {23, 00} {22, 13} {22, 03} {22, 01} {1, 023} {13, 02} {13, 00} {12, 03} {12, 00} {123, 0} {11, 03} {11, 02}
# nonzero (lambda,mn) entries by sector: {'C_2': 250, 'M_2': 840, 'J_3': 2192}  bilinear terms: {'C_2': 4008, 'M_2': 8092, 'J_3': 6546}
# sector-summed a_lambda: nonzero (lambda,mn) entries 2322 ; bilinear terms 18646
# sample: a^{C_2,(0,0)}_{{0,0}} has 78 bilinear terms (sigma_2jet x d^2h)
#   first terms: 5*sig_11*h_00_11 ; 1*sig_11*h_00_22 ; 1*sig_11*h_00_33 ; -10*sig_11*h_01_01 ; -2*sig_11*h_02_02 ; -2*sig_11*h_03_03
# === INDEPENDENT C_2 ROUTE, GENERAL h (xvi_common.polar_s, all 25 labels x 10 mn) ===
CHECK GENERAL-h C_2 regression: all 25 labels x 10 components equal the independent polar_s route, coefficientwise in (sigma 2-jet) x (h-jet) (250 comparisons, 23.2s): True
# wrote graph_general_table.txt : 3282 nonzero (A,lambda,mn) lines
# sha256(graph_general_table.txt) = 4cd29d3c9f691340b314aecbfe7d6aef3590b9cee21dcdb486fe9fbcdd679e49
# total runtime 27.1s
ALL CHECKS PASSED