$ ./flagmatic --n 6 --r 3 --induced-density 5.9  --dir output/max59
flagmatic version 1.5
============================================================================
Optimizing for density of 5.9.
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 12 flags of order 4.
Generated 5 types of order 4, with [64, 64, 64, 64, 64] flags of order 5.
Generated 2136 admissible graphs.
Approximate floating-point bound is 0.62500000

$ sage -python scripts/find_sharp_graphs.py --dir output/max59
Floating point bound is 0.625000000006370460.
4 members of H are sharp.
0.624999999987251531 : graph 1 (6:)
0.625000000004181211 : graph 893 (6:123124125126134135136145146156)
0.625000000006370460 : graph 2104 (6:123124125126134135136145146156234235236245246256)
0.625000000005618617 : graph 2134 (6:123124125126134135136145146235236245246256345346356456)
Written sharp graphs to flags.py

$ sage -python scripts/check_construction.py --n 6 --r 3 --induced-density 5.9 --vertex-transitive 2:112122
Density of 5.9 is 5/8.
4 graphs of order 6 occur as induced subgraphs of the blow-up:
6: has density 1/32 (0.031250)
6:123124125126134135136145146156 has density 3/16 (0.187500)
6:123124125126134135136145146156234235236245246256 has density 15/32 (0.468750)
6:123124125126134135136145146235236245246256345346356456 has density 5/16 (0.312500)

$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 2:112122 --dir output/max59
Constructed 1 out of 1 zero eigenvectors for type 1.
Constructed 2 out of 2 zero eigenvectors for type 2.
Constructed 1 out of 1 zero eigenvectors for type 3.
Constructed 0 out of 0 zero eigenvectors for type 4.
Constructed 0 out of 0 zero eigenvectors for type 5.
Constructed 1 out of 1 zero eigenvectors for type 6.
Constructed 3 out of 3 zero eigenvectors for type 7.
Written zev.py
Written field to flags.py

$ sage -python scripts/factor_approximate_q.py --dir output/max59
Floating point bound is 0.625000000006370460.
Type 1: smallest eigenvalue is 0.131219837362048564
Type 2: smallest eigenvalue is 0.016288538072509493
Type 3: smallest eigenvalue is 0.144840013734284789
Type 4: smallest eigenvalue is 0.126877809427999783
Type 5: smallest eigenvalue is 0.123613333741116119
Type 6: smallest eigenvalue is 0.049018046075125776
Type 7: smallest eigenvalue is 0.005163244188996869
Written r.py
Written qdashf.py

$ sage -python scripts/make_exact_qdash.py '5/8' --denominator 240 --dir output/max59 --diagonalize
Type 1: smallest eigenvalue is 0.134726840247339691
Type 2: smallest eigenvalue is 0.013409301550552553
Type 3: smallest eigenvalue is 0.137034063062108274
Type 4: smallest eigenvalue is 0.126160880500172601
Type 5: smallest eigenvalue is 0.121495946233677363
Type 6: smallest eigenvalue is 0.048052766793083290
Type 7: smallest eigenvalue is 0.002360011222993049
Diagonalizing matrices...
Written qdash.py
Written r.py
Added exact bound to flags.py

$ sage -python scripts/verify_bound.py --dir output/max59
Written q.py
Floating point bound (non-sharp graphs) is 0.623737450005478977
Exact bound (just sharp graphs) is 5/8
Bound (all graphs) is 5/8

$ sage -python scripts/make_certificate.py --dir output/max59
Written certificate to cert.js