$ ./flagmatic --n 6 --r 3 --induced-density 4.3 --forbid-k4 --dir output/k4max43
flagmatic version 1.5
============================================================================
Optimizing for density of 4.3.
Forbidding 4.4
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 11 flags of order 4.
Generated 4 types of order 4, with [64, 56, 50, 45] flags of order 5.
Generated 964 admissible graphs.
Approximate floating-point bound is 0.59259259

$ sage -python scripts/find_sharp_graphs.py --dir output/k4max43
Floating point bound is 0.592592592748368285.
8 members of H are sharp.
0.592592592482279912 : graph 1 (6:)
0.592592592643053195 : graph 13 (6:123124125126)
0.592592592677961050 : graph 677 (6:123124125136146156236246256)
0.592592592725136313 : graph 681 (6:123124125126134135136145146156)
0.592592592748368285 : graph 925 (6:123124125126134135136145146256356456)
0.592592592643013893 : graph 944 (6:123124125134135145236246256346356456)
0.592592592748062419 : graph 958 (6:123124125126134135136245246256345346356)
0.592592592713214295 : graph 964 (6:123124125134135146156236245246256345346356)
Written sharp graphs to flags.py

$ sage -python scripts/check_construction.py --n 6 --r 3 --induced-density 4.3 --vertex-transitive 3:112223331123
Density of 4.3 is 16/27.
8 graphs of order 6 occur as induced subgraphs of the blow-up:
6: has density 7/243 (0.028807)
6:123124125126 has density 5/81 (0.061728)
6:123124125136146156236246256 has density 20/243 (0.082305)
6:123124125126134135136145146156 has density 4/27 (0.148148)
6:123124125134135145236246256346356456 has density 5/81 (0.061728)
6:123124125126134135136145146256356456 has density 20/81 (0.246914)
6:123124125126134135136245246256345346356 has density 20/81 (0.246914)
6:123124125134135146156236245246256345346356 has density 10/81 (0.123457)

$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 3:112223331123 --dir output/k4max43
Constructed 1 out of 1 zero eigenvectors for type 1.
Constructed 3 out of 3 zero eigenvectors for type 2.
Constructed 5 out of 5 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.
Constructed 4 out of 4 zero eigenvectors for type 6.
Written zev.py
Written field to flags.py

$ sage -python scripts/factor_approximate_q.py --dir output/k4max43
Floating point bound is 0.592592592748368285.
Type 1: smallest eigenvalue is 0.188462452037512385
Type 2: smallest eigenvalue is 0.047590115926319641
Type 3: smallest eigenvalue is 0.127354977745658432
Type 4: smallest eigenvalue is 0.119952354146454665
Type 5: smallest eigenvalue is 0.099066496171228979
Type 6: smallest eigenvalue is 0.134182269813466037
Written r.py
Written qdashf.py

$ sage -python scripts/make_exact_qdash.py '16/27' --denominator 120 --dir output/k4max43 --diagonalize
Type 1: smallest eigenvalue is 0.187683599189045730
Type 2: smallest eigenvalue is 0.040659093110981398
Type 3: smallest eigenvalue is 0.134400060634046581
Type 4: smallest eigenvalue is 0.114867726450753854
Type 5: smallest eigenvalue is 0.058596934908722281
Type 6: smallest eigenvalue is 0.136652875970569548
Diagonalizing matrices...
Written qdash.py
Written r.py
Added exact bound to flags.py

$ sage -python scripts/verify_bound.py --dir output/k4max43
Written q.py
Floating point bound (non-sharp graphs) is 0.591159152281030331
Exact bound (just sharp graphs) is 16/27
Bound (all graphs) is 16/27

$ sage -python scripts/make_certificate.py --dir output/k4max43
Written certificate to cert.js