(F0) pairs in 2 blocks of D' and of D: True
(F1) complement of every D' block lies in D: True
     so D' and D contain no two disjoint triples: True
H_3: n=7, |E|=25, codegree histogram {3: 15, 5: 6}, min 3, floor((n-k+3)/2)=3; cyclic orders 360, tight Hamiltonian cycles 0; window criterion agrees on every order: True
H_4: n=8, |E|=50, codegree histogram {3: 40, 5: 16}, min 3, floor((n-k+3)/2)=3; cyclic orders 2520, tight Hamiltonian cycles 0; window criterion agrees on every order: True
H_5: n=9, |E|=96, codegree histogram {3: 75, 5: 51}, min 3, floor((n-k+3)/2)=3; cyclic orders 20160, tight Hamiltonian cycles 0; window criterion agrees on every order: True
gap vectors: 83; formula = actual windows: True; a complementary pair is always forced: True; case split of the written proof holds: True
example_k3_n9.txt: valid 3-graph on 9 vertices: True; |E|=50; codegree histogram {4: 33, 6: 3}; min 4; floor((n-k+3)/2)=4, (n-k+3)/2=4.5; tight Hamiltonian cycle: False
example_k5_n10.txt: valid 5-graph on 10 vertices: True; |E|=191; codegree histogram {4: 130, 5: 45, 6: 35}; min 4; floor((n-k+3)/2)=4, (n-k+3)/2=4.0; tight Hamiltonian cycle: False
DFS sanity, complete 3-graph on 9 and 5-graph on 10 vertices: True True
DFS on H_3: False; H_3 plus one of its 10 missing triples is Hamiltonian in 10 cases
H_6: n=10, |E|=170, min codegree 3; tight Hamiltonian cycle exists: True
KK H0 at (k,n)=(5,8): n > k^2: False; min codegree 2 (floor((n-k+1)/2) = 2); tight Hamiltonian cycle exists: True
KK H0 at (k,n)=(5,9): n > k^2: False; min codegree 2 (floor((n-k+1)/2) = 2); tight Hamiltonian cycle exists: True
KK H0 at (k,n)=(3,10): n > k^2: True; min codegree 4 (floor((n-k+1)/2) = 4); tight Hamiltonian cycle exists: False
