$ ./flagmatic --r 3 --n 7 --forbid-k4- --forbid-induced 4.1 --dir output/ff84
flagmatic version 1.5
============================================================================
Forbidding 4.3
Forbidding 4.1 as an induced subgraph.
Using admissible graphs of order 7.
Generated 1 type of order 1, with 3 flags of order 4.
Generated 2 types of order 3, with [14, 9] flags of order 5.
Generated 4 types of order 5, with [16, 9, 7, 6] flags of order 6.
Generated 10 admissible graphs.
Approximate floating-point bound is 0.27777778

$ sage -python scripts/find_sharp_graphs.py --dir output/ff84
Floating point bound is 0.277777779939706149.
9 members of H are sharp.
0.277777779378811540 : graph 1 (7:)
0.277777779387497259 : graph 2 (7:123124125126127)
0.277777779939706149 : graph 3 (7:123124125126137147157167)
0.277777779656864898 : graph 4 (7:123124125136137146147156157)
0.277777779558789739 : graph 5 (7:123124125126137147157267367467567)
0.277777779787379886 : graph 6 (7:123124125126137147257267357367457467)
0.277777779787393098 : graph 7 (7:123124125136146156237247257367467567)
0.277777779787340862 : graph 8 (7:123124125136137146147256257356357456457)
0.277777779101805511 : graph 10 (7:123124125136146157167237247256267356357456457)
Written sharp graphs to flags.py

$ sage -python scripts/check_construction.py --n 7 --r 3 --vertex-transitive 6:123234345451512136246356256146
Density is 5/18.
9 graphs of order 7 occur as induced subgraphs of the blow-up:
7: has density 1663/23328 (0.071288)
7:123124125126127 has density 35/486 (0.072016)
7:123124125126137147157167 has density 175/864 (0.202546)
7:123124125136137146147156157 has density 1225/11664 (0.105024)
7:123124125126137147157267367467567 has density 175/1944 (0.090021)
7:123124125136146156237247257367467567 has density 175/1296 (0.135031)
7:123124125126137147257267357367457467 has density 175/1296 (0.135031)
7:123124125136137146147256257356357456457 has density 175/1296 (0.135031)
7:123124125136146157167237247256267356357456457 has density 35/648 (0.054012)

$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 6:123234345451512136246356256146 --dir output/ff84
Constructed 1 out of 1 zero eigenvectors for type 1.
Constructed 5 out of 5 zero eigenvectors for type 2.
Constructed 1 out of 1 zero eigenvectors for type 3.
Constructed 16 out of 16 zero eigenvectors for type 4.
Constructed 4 out of 4 zero eigenvectors for type 5.
Constructed 3 out of 3 zero eigenvectors for type 6.
Constructed 1 out of 1 zero eigenvectors for type 7.
Written zev.py
Written field to flags.py

$ sage -python scripts/factor_approximate_q.py --dir output/ff84
Floating point bound is 0.277777779939706149.
Type 1: smallest eigenvalue is 0.825935693251547587
Type 2: smallest eigenvalue is 0.229848238859588549
Type 3: smallest eigenvalue is 0.150619995805630402
Type 4: zero matrix
Type 5: smallest eigenvalue is 0.783519984727020891
Type 6: smallest eigenvalue is 1.073366485789859492
Type 7: smallest eigenvalue is 0.487614639805665051
Written r.py
Written qdashf.py

$ sage -python scripts/make_exact_qdash.py '5/18' --denominator 48 --dir output/ff84 --diagonalize
Type 1: smallest eigenvalue is 0.826182425137056753
Type 2: smallest eigenvalue is 0.236313156340247743
Type 3: smallest eigenvalue is 0.152802778607211087
Type 4: zero matrix
Type 5: smallest eigenvalue is 0.778791211059178923
Type 6: smallest eigenvalue is 1.024967451027120502
Type 7: smallest eigenvalue is 0.417055476220995869
Diagonalizing matrices...
Written qdash.py
Written r.py
Added exact bound to flags.py

$ sage -python scripts/verify_bound.py --dir output/ff84
Written q.py
Floating point bound (non-sharp graphs) is 0.273474365569272959
Exact bound (just sharp graphs) is 5/18
Bound (all graphs) is 5/18

$ sage -python scripts/make_certificate.py --dir output/ff84
Written certificate to cert.js