$ ./flagmatic --n 6 --r 3 --induced-density 4.2 --forbid-k4- --forbid-c5 --forbid-f32 --dir output/k4-c5f32max42
flagmatic version 1.5
============================================================================
Optimizing for density of 4.2.
Forbidding 4.3
Forbidding 5:123124135245345
Forbidding 5:123124125345
Using admissible graphs of order 6.
Generated 1 type of order 0, with 2 flags of order 3.
Generated 1 type of order 2, with 8 flags of order 4.
Generated 3 types of order 4, with [41, 25, 15] flags of order 5.
Generated 79 admissible graphs.
Approximate floating-point bound is 0.44444444

$ sage -python scripts/find_sharp_graphs.py --dir output/k4-c5f32max42
Floating point bound is 0.444444444639476521.
4 members of H are sharp.
0.444444444613774414 : graph 1 (6:)
0.444444444554685902 : graph 12 (6:123124125126)
0.444444444639476521 : graph 46 (6:123124125136146156)
0.444444444554626283 : graph 77 (6:123124135145236246356456)
Written sharp graphs to flags.py

$ sage -python scripts/check_construction.py --n 6 --r 3 --induced-density 4.2 --vertex-transitive 3:123
Density of 4.2 is 4/9.
4 graphs of order 6 occur as induced subgraphs of the blow-up:
6: has density 7/27 (0.259259)
6:123124125126 has density 10/81 (0.123457)
6:123124125136146156 has density 40/81 (0.493827)
6:123124135145236246356456 has density 10/81 (0.123457)

$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 3:123 --dir output/k4-c5f32max42
Constructed 1 out of 1 zero eigenvectors for type 1.
Constructed 2 out of 2 zero eigenvectors for type 2.
Constructed 8 out of 8 zero eigenvectors for type 3.
Constructed 0 out of 0 zero eigenvectors for type 4.
Constructed 1 out of 1 zero eigenvectors for type 5.
Written zev.py
Written field to flags.py

$ sage -python scripts/factor_approximate_q.py --dir output/k4-c5f32max42
Floating point bound is 0.444444444639476521.
Type 1: smallest eigenvalue is 1.163976457877306636
Type 2: smallest eigenvalue is 0.013762074794995239
Type 3: smallest eigenvalue is 0.152351406540720685
Type 4: smallest eigenvalue is 0.120797376973252338
Type 5: smallest eigenvalue is 0.109927102715333291
Written r.py
Written qdashf.py

$ sage -python scripts/make_exact_qdash.py '4/9' --denominator 32 --dir output/k4-c5f32max42 --diagonalize
Type 1: smallest eigenvalue is 1.269703112637055709
Type 2: smallest eigenvalue is 0.002126543583520779
Type 3: smallest eigenvalue is 0.156250000000000083
Type 4: smallest eigenvalue is 0.086261278222114213
Type 5: smallest eigenvalue is 0.073138604397477519
Diagonalizing matrices...
Written qdash.py
Written r.py
Added exact bound to flags.py

$ sage -python scripts/verify_bound.py --dir output/k4-c5f32max42
Written q.py
Floating point bound (non-sharp graphs) is 0.441566666631444282
Exact bound (just sharp graphs) is 4/9
Bound (all graphs) is 4/9

$ sage -python scripts/make_certificate.py --dir output/k4-c5f32max42
Written certificate to cert.js