=== Part 1: constructions ===
  degree sequences 3^(n-3)4^3, e(H)=(3n+3)/2 for R1,R2 (all odd n in [5,101]) and R3 (n=3 mod 4);
  closed forms of H_n (R1) and H'_n (R2) agree with RESULT.md; delta(G_n) = ceil(n/2); G_n[A] a forest, B independent.
  each reading gives one graph up to isomorphism (all 2n starts/directions, 7<=n<=25); R1, R2, R3 pairwise non-isomorphic.
  Heinig Def.28 graph X: 4-regular = True ; complement components (|V|,|E|) = [(3, 3), (4, 4)] ; X isomorphic to G_7: True
  adjacency spectrum of X = [4.0, 1.0, 0.0, 0.0, -1.0, -1.0, -3.0] (Heinig states (4,1,-1,-1,0,0,-3))
  part 1 time 0.9s
=== Part 2: exact structural test (B independent, A-B complete => reduce to independent s-sets) ===
  NOTE n=5, R2: independent s-set [(0, 2)] exists (RESULT.md R2 argument needs s>=3); leftover K3, still no embedding
  n=  5  R1: 1 indep. s-sets, H-J edges [[(2, 3), (2, 4), (3, 4)]] | R2: 1 indep. s-sets, H-J edges [[(1, 3), (1, 4), (3, 4)]] | R3: n/a
  n=  7  R1: 2 indep. s-sets, H-J edges [[(0, 5), (4, 5)], [(3, 5), (5, 6)]] | R2: 0 indep. s-sets, H-J edges [] | R3: 0 indep. s-sets, H-J edges []
  n=  9  R1: 1 indep. s-sets, H-J edges [[(6, 7), (6, 8), (7, 8)]] | R2: 0 indep. s-sets, H-J edges [] | R3: n/a
  n= 11  R1: 2 indep. s-sets, H-J edges [[(0, 9), (8, 9)], [(7, 9), (9, 10)]] | R2: 0 indep. s-sets, H-J edges [] | R3: 0 indep. s-sets, H-J edges []
  n= 13  R1: 1 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: n/a
  n= 15  R1: 2 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: 0 indep. s-sets, H-J edges [..]
  n= 17  R1: 1 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: n/a
  n= 19  R1: 2 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: 0 indep. s-sets, H-J edges [..]
  n= 21  R1: 1 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: n/a
  n= 31  R1: 2 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: 0 indep. s-sets, H-J edges [..]
  n= 41  R1: 1 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: n/a
  n= 51  R1: 2 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: 0 indep. s-sets, H-J edges [..]
  n= 61  R1: 1 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: n/a
  n= 71  R1: 2 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: 0 indep. s-sets, H-J edges [..]
  n= 81  R1: 1 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: n/a
  n= 91  R1: 2 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: 0 indep. s-sets, H-J edges [..]
  n=101  R1: 1 indep. s-sets, H-J edges [..] | R2: 0 indep. s-sets, H-J edges [..] | R3: n/a
  -> no embedding for any odd n in [5,101], all three readings; R1 sets/leftovers exactly as in RESULT.md.
  part 2 time 1.0s
=== Part 3: generic exact tests (no structural input) ===
  n= 7  R1 SAT(glucose)=False SAT(minisat)=False 0.0s; R1 BT=False (24 nodes, 0.0s); R1 VF2=False 0.0s; R2 SAT(glucose)=False SAT(minisat)=False 0.0s; R2 BT=False (16 nodes, 0.0s); R2 VF2=False 0.0s; R3 SAT(glucose)=False SAT(minisat)=False 0.0s; R3 BT=False (20 nodes, 0.0s); R3 VF2=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT+VF2)
  n= 9  R1 SAT(glucose)=False SAT(minisat)=False 0.0s; R1 BT=False (110 nodes, 0.0s); R1 VF2=False 0.1s; R2 SAT(glucose)=False SAT(minisat)=False 0.0s; R2 BT=False (39 nodes, 0.0s); R2 VF2=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT+VF2)
  n=11  R1 SAT(glucose)=False SAT(minisat)=False 0.0s; R1 BT=False (272 nodes, 0.0s); R1 VF2=False 3.6s; R2 SAT(glucose)=False SAT(minisat)=False 0.0s; R2 BT=False (74 nodes, 0.0s); R2 VF2=False 0.3s; R3 SAT(glucose)=False SAT(minisat)=False 0.0s; R3 BT=False (50 nodes, 0.0s); R3 VF2=False 0.5s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT+VF2)
  n=13  R1 SAT(glucose)=False SAT(minisat)=False 0.0s; R1 BT=False (1538 nodes, 0.0s); R1 VF2=False 169.2s; R2 SAT(glucose)=False SAT(minisat)=False 0.0s; R2 BT=False (154 nodes, 0.0s); R2 VF2=False 1.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT+VF2)
  n=15  R1 SAT(glucose)=False SAT(minisat)=False 0.0s; R1 BT=False (4854 nodes, 0.0s); R2 SAT(glucose)=False SAT(minisat)=False 0.0s; R2 BT=False (158 nodes, 0.0s); R3 SAT(glucose)=False SAT(minisat)=False 0.0s; R3 BT=False (98 nodes, 0.0s); controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT)
  n=17  R1 SAT(glucose)=False SAT(minisat)=False 0.0s; R1 BT=False (34960 nodes, 0.1s); R2 SAT(glucose)=False SAT(minisat)=False 0.0s; R2 BT=False (387 nodes, 0.0s); controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT)
  n=19  R1 SAT(glucose)=False SAT(minisat)=False 0.0s; R1 BT=False (139212 nodes, 0.2s); R2 SAT(glucose)=False SAT(minisat)=False 0.0s; R2 BT=False (312 nodes, 0.0s); R3 SAT(glucose)=False SAT(minisat)=False 0.0s; R3 BT=False (172 nodes, 0.0s); controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT)
  n=21  R1 SAT(glucose)=False SAT(minisat)=False 0.0s; R1 BT=False (1279994 nodes, 2.3s); R2 SAT(glucose)=False SAT(minisat)=False 0.0s; R2 BT=False (1028 nodes, 0.0s); controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT)
  n=23  R1 SAT(glucose)=False 0.0s; R1 BT=False (6550292 nodes, 12.1s); R2 SAT(glucose)=False 0.0s; R2 BT=False (548 nodes, 0.0s); R3 SAT(glucose)=False 0.0s; R3 BT=False (278 nodes, 0.0s); controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT)
  n=25  R1 SAT(glucose)=False 0.0s; R1 BT=False (74848034 nodes, 140.3s); R2 SAT(glucose)=False 0.0s; R2 BT=False (2379 nodes, 0.0s); controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural+BT)
  n=27  R1 SAT(glucose)=False 0.0s; R2 SAT(glucose)=False 0.0s; R3 SAT(glucose)=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=29  R1 SAT(glucose)=False 0.1s; R2 SAT(glucose)=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=31  R1 SAT(glucose)=False 0.0s; R2 SAT(glucose)=False 0.0s; R3 SAT(glucose)=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=33  R1 SAT(glucose)=False 0.2s; R2 SAT(glucose)=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=35  R1 SAT(glucose)=False 0.0s; R2 SAT(glucose)=False 0.0s; R3 SAT(glucose)=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=37  R1 SAT(glucose)=False 0.5s; R2 SAT(glucose)=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=39  R1 SAT(glucose)=False 0.0s; R2 SAT(glucose)=False 0.0s; R3 SAT(glucose)=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=41  R1 SAT(glucose)=False 0.7s; R2 SAT(glucose)=False 0.0s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=43  R1 SAT(glucose)=False 0.1s; R2 SAT(glucose)=False 0.1s; R3 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=45  R1 SAT(glucose)=False 0.9s; R2 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=47  R1 SAT(glucose)=False 0.1s; R2 SAT(glucose)=False 0.1s; R3 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=49  R1 SAT(glucose)=False 2.4s; R2 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=51  R1 SAT(glucose)=False 0.1s; R2 SAT(glucose)=False 0.1s; R3 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=53  R1 SAT(glucose)=False 3.1s; R2 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=55  R1 SAT(glucose)=False 0.1s; R2 SAT(glucose)=False 0.1s; R3 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=57  R1 SAT(glucose)=False 4.4s; R2 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=59  R1 SAT(glucose)=False 0.1s; R2 SAT(glucose)=False 0.1s; R3 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
  n=61  R1 SAT(glucose)=False 6.3s; R2 SAT(glucose)=False 0.1s; controls: H_R1 found in C_n^2 (SAT) and in G_n+1 edge (SAT+structural)
ALL AUDIT CORE CHECKS PASSED  (total 485.8s)
